Bell Szekeres Solution and Related Solutions of the Einstein Maxwell Equations by Barrabes & Hogan.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.1' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    744080,      19758]
NotebookOptionsPosition[    707890,      19221]
NotebookOutlinePosition[    708352,      19238]
CellTagsIndexPosition[    708309,      19235]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\<\
Notebook for :  Bell\[Dash]Szekeres Solution and Related Solutions of the \
Einstein\[Dash]Maxwell Equations Barrabes & Hogan\
\>", "Title",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.8217294718661222`*^9, 3.821729502043838*^9}, 
   3.8217295683553457`*^9, 3.821732221863006*^9, {3.821811203295624*^9, 
   3.8218112036548367`*^9}, {3.822041768762134*^9, 3.822041781290854*^9}, {
   3.822048009752109*^9, 3.8220480569607773`*^9}, {3.822504877727007*^9, 
   3.8225048874039307`*^9}, {3.822565447028533*^9, 3.822565457908236*^9}, {
   3.822822107930128*^9, 3.822822113128089*^9}, {3.823176459993638*^9, 
   3.823176470345335*^9}, {3.823359338529508*^9, 3.823359361520629*^9}, {
   3.8235974638251762`*^9, 3.823597473367338*^9}, {3.823618458364909*^9, 
   3.8236184669077578`*^9}, {3.8236833044709806`*^9, 3.823683312509585*^9}, {
   3.8236885755476217`*^9, 3.823688587026948*^9}, {3.823689672516461*^9, 
   3.823689672910822*^9}, {3.8237044493810883`*^9, 3.8237044672759027`*^9}, {
   3.8239668765180197`*^9, 3.8239668768923607`*^9}, {3.823969962518847*^9, 
   3.823969963027501*^9}},
 TextAlignment->Center,ExpressionUUID->"ac7ede52-fd73-4390-914d-b6e3e0416669"],

Cell["\<\
Geoff Cope
University of Utah
March 5, 2021 \
\>", "Author",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.821729507652328*^9, 3.821729529657844*^9}, 
   3.8220480097522783`*^9, {3.822048070235491*^9, 3.822048084689715*^9}, {
   3.8225654346519403`*^9, 3.8225654361641483`*^9}, {3.8231764728567343`*^9, 
   3.823176482313031*^9}, {3.8233640113399878`*^9, 3.823364023347041*^9}, {
   3.823422996286858*^9, 3.823422999926001*^9}, {3.823602893791738*^9, 
   3.823602896188092*^9}, {3.8236833287515574`*^9, 3.823683328958127*^9}, {
   3.823966903508623*^9, 3.823966903859309*^9}, {3.823966992570949*^9, 
   3.823966994785722*^9}},
 TextAlignment->Center,ExpressionUUID->"a7cf401a-8230-4cc9-8efc-897839b4cd03"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Hyperlink To Documentation", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820944675605734*^9, 
  3.8209446931410646`*^9}},ExpressionUUID->"ce347cdc-9576-41cd-aaa3-\
96a0b0d7f7db"],

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<GeneralRelativityTensors Documentation and Download\>\"", ",", 
   "\[IndentingNewLine]", 
   "\"\<https://github.com/BlackHolePerturbationToolkit\>\""}], 
  "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820944619768764*^9, 3.820944681268063*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"eccb8452-cc61-4fc3-b1bc-c9b4ad5b0a7f"],

Cell[BoxData[
 TemplateBox[{
  "\"GeneralRelativityTensors Documentation and Download\"", 
   "https://github.com/BlackHolePerturbationToolkit"},
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820944653562152*^9, 3.820944681268403*^9}, 
   3.821729905862431*^9, 3.821732641380642*^9, 3.8218069931429567`*^9, 
   3.821811425912986*^9, 3.822042652654992*^9, {3.822048793766124*^9, 
   3.8220488009116488`*^9}, 3.82250502887521*^9, 3.822505578829629*^9, 
   3.822565490613895*^9, 3.8225662097813597`*^9, 3.822606717894772*^9, 
   3.822739433713368*^9, 3.822822210464344*^9, 3.8233594284652433`*^9, 
   3.8233607803938913`*^9, 3.823360880234103*^9, 3.823361224481102*^9, 
   3.82336209870968*^9, 3.823364030542309*^9, 3.823597528606563*^9, 
   3.823618495251218*^9, 3.82368341365138*^9, 3.82368384184562*^9, 
   3.823684775269041*^9, 3.823688794270237*^9, 3.82369077711421*^9, 
   3.823704572306265*^9, 3.8239670360944*^9, 3.8239675178827963`*^9, 
   3.823970038559888*^9, 3.824025681964837*^9},
 CellLabel->"Out[1]=",ExpressionUUID->"10096b81-8220-4e62-ac0e-a96fce26a8ca"]
}, Closed]],

Cell[CellGroupData[{

Cell["Hyperlink  To Article ", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.820937794883616*^9, {3.820938266275806*^9, 3.82093829464357*^9}, 
   3.820943883376583*^9, {3.8210324492405148`*^9, 3.821032453951701*^9}, {
   3.8217297279218817`*^9, 3.8217297313782063`*^9}, {3.822593613363134*^9, 
   3.822593616181035*^9}, {3.822736144359599*^9, 3.8227361450547543`*^9}, {
   3.823359417697976*^9, 3.823359420672374*^9}, 
   3.826210942938623*^9},ExpressionUUID->"68e4d51f-e3c5-4e02-a588-\
bd630dbac483"],

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<Bell\[Dash]Szekeres Solution and Related Solutions of the Einstein\
\[Dash]Maxwell Equations Barrabes & Hogan\>\"", ",", "\[IndentingNewLine]", 
   "\"\<https://iopscience.iop.org/article/10.1088/0264-9381/23/17/010/meta\>\
\""}], "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.8218867746254797`*^9, 3.821886810805148*^9}, 
   3.823176507207197*^9, {3.823472730005904*^9, 3.823472744739744*^9}, {
   3.823597507106205*^9, 3.823597507709626*^9}, {3.8248234531732893`*^9, 
   3.824823465899825*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"bafb7e88-cde0-4e77-b0c8-e6a6e44d8cf1"],

Cell[BoxData[
 TemplateBox[{
  "\"Bell\[Dash]Szekeres Solution and Related Solutions of the \
Einstein\[Dash]Maxwell Equations Barrabes & Hogan\"", 
   "https://iopscience.iop.org/article/10.1088/0264-9381/23/17/010/meta"},
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.821886813557355*^9, 3.8231765072073307`*^9, 3.823359428608782*^9, 
   3.8233607804338617`*^9, 3.823360880363216*^9, 3.823361224626254*^9, 
   3.823362098931829*^9, 3.823364030688095*^9, 3.823472745219315*^9, {
   3.8235975109202147`*^9, 3.823597528650549*^9}, 3.823618495400096*^9, 
   3.823683413880138*^9, 3.823683841884781*^9, 3.823684775280538*^9, 
   3.823688794413259*^9, 3.8236907771492443`*^9, 3.823704572455369*^9, 
   3.8239670361077127`*^9, 3.8239675178933*^9, 3.823970038708452*^9, 
   3.824025682120349*^9, 3.824823467820938*^9},
 CellLabel->"Out[3]=",ExpressionUUID->"9dbf62eb-9b41-4694-a068-41e4c4b96247"],

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<Bell\[Dash]Szekeres Solution and Related Solutions of the Einstein\
\[Dash]Maxwell Equations Barrabes & Hogan\>\"", ",", "\[IndentingNewLine]", 
   "\"\<https://arxiv.org/abs/gr-qc/0608087\>\""}], "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.824823489632637*^9, 3.8248235043563623`*^9}, 
   3.825287765518345*^9},
 CellLabel->"In[4]:=",ExpressionUUID->"4c2b0552-70ac-47e9-9cbb-55f938d42dc7"],

Cell[BoxData[
 TemplateBox[{
  "\"Bell\[Dash]Szekeres Solution and Related Solutions of the \
Einstein\[Dash]Maxwell Equations Barrabes & Hogan\"", 
   "https://arxiv.org/abs/gr-qc/0608087"},
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.8248235047505407`*^9, 3.825287765518515*^9},
 CellLabel->"Out[4]=",ExpressionUUID->"75fac26d-16d4-4d92-988b-6c62b1cf7f0e"],

Cell[BoxData[
 RowBox[{"Hyperlink", "[", 
  RowBox[{
  "\"\<Colliding Plane Waves by Griffiths - Book\>\"", ",", 
   "\"\<ftp://nozdr.ru/biblio/kolxoz/P/PGr/Griffiths%20J.B.%20Colliding%\
20plane%20waves%20in%20general%20relativity%20(OUP,%201991)(ISBN%200198532091)\
(254s)_PGr_.pdf\>\""}], "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.821971700891346*^9, 3.821971727288177*^9}, 
   3.8220418523671618`*^9, {3.8220419016581783`*^9, 3.822041910552957*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"8c998aae-b2d8-4507-bbcb-d7d1ea4f5a21"],

Cell[BoxData[
 TemplateBox[{
  "\"Colliding Plane Waves by Griffiths - Book\"", 
   "ftp://nozdr.ru/biblio/kolxoz/P/PGr/Griffiths%20J.B.%20Colliding%20plane%\
20waves%20in%20general%20relativity%20(OUP,%201991)(ISBN%200198532091)(254s)_\
PGr_.pdf"},
  "HyperlinkURL"]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.8219717866333103`*^9, 3.822041852367313*^9, 3.822041913511463*^9, 
   3.8220426527016563`*^9, {3.822048793815063*^9, 3.8220488009576597`*^9}, 
   3.822505029060484*^9, 3.822505578941113*^9, 3.82256549066683*^9, 
   3.822566209832062*^9, 3.822606717963243*^9, 3.822739433796803*^9, 
   3.822822210610302*^9, 3.8233594286355753`*^9, 3.8233607804460297`*^9, 
   3.8233608803853903`*^9, 3.823361224649728*^9, 3.823362098967597*^9, 
   3.823364030715418*^9, 3.823597528661324*^9, 3.823618495426402*^9, 
   3.8236834139074087`*^9, 3.82368384189923*^9, 3.8236847753002243`*^9, 
   3.823688794441139*^9, 3.823690777159783*^9, 3.823704572476899*^9, 
   3.8239670361242037`*^9, 3.82396751791289*^9, 3.823970038722382*^9, 
   3.8240256821512117`*^9},
 CellLabel->"Out[3]=",ExpressionUUID->"f47bb930-7881-44e5-ab99-a93ae4d7e610"]
}, Closed]],

Cell[CellGroupData[{

Cell["Utilities and Package Load", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.820937646765551*^9, 3.8209376725449123`*^9}, 
   3.825287778263229*^9},ExpressionUUID->"8754be25-0c4a-418f-ae64-\
d23288ea7656"],

Cell[BoxData[{
 RowBox[{"ClearAll", "[", "\"\<Global`*\>\"", "]"}], "\[IndentingNewLine]", 
 RowBox[{"<<", "Utilities`CleanSlate`"}], "\[IndentingNewLine]", 
 RowBox[{"CleanSlate", "[", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ClearInOut", "[", "]"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"pdConv", "[", "f_", "]"}], ":=", 
  RowBox[{"TraditionalForm", "[", 
   RowBox[{"f", "/.", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"Derivative", "[", "inds__", "]"}], "[", "g_", "]"}], "[", 
      "vars__", "]"}], "\[RuleDelayed]", 
     RowBox[{"Apply", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"Defer", "[", 
         RowBox[{"D", "[", 
          RowBox[{
           RowBox[{"g", "[", "vars", "]"}], ",", "##"}], "]"}], "]"}], "&"}], 
       ",", 
       RowBox[{
        RowBox[{"Transpose", "[", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", "vars", "}"}], ",", 
           RowBox[{"{", "inds", "}"}]}], "}"}], "]"}], "/.", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"{", 
            RowBox[{"var_", ",", "0"}], "}"}], "\[RuleDelayed]", 
           RowBox[{"Sequence", "[", "]"}]}], ",", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"var_", ",", "1"}], "}"}], "\[RuleDelayed]", 
           RowBox[{"{", "var", "}"}]}]}], "}"}]}]}], "]"}]}]}], 
   "]"}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.8209376549030037`*^9, {3.821032517164062*^9, 3.821032518258361*^9}, 
   3.8252877782634068`*^9},
 CellLabel->"In[4]:=",ExpressionUUID->"c0ae56bc-4016-4e90-9a4d-80b9c4624ec2"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"  (CleanSlate) Contexts purged: \"\>", "\[InvisibleSpace]", 
   RowBox[{"{", "\<\"Global`\"\>", "}"}]}],
  SequenceForm["  (CleanSlate) Contexts purged: ", {"Global`"}],
  Editable->False]], "Print",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820932754769992*^9, 3.820933427630714*^9, 3.820937654903143*^9, 
   3.821729906190301*^9, 3.821732641685704*^9, 3.8218069933778133`*^9, 
   3.82181142618342*^9, 3.8220426528487463`*^9, {3.822048793940605*^9, 
   3.822048801089246*^9}, 3.822505029191699*^9, 3.822505579049889*^9, 
   3.822565490838564*^9, 3.822566210008327*^9, 3.822606718180009*^9, 
   3.8226371008270607`*^9, 3.822739433887854*^9, 3.822761800089258*^9, 
   3.8228172997642097`*^9, 3.822822210725956*^9, 3.822988687208267*^9, 
   3.823359428732101*^9, 3.823360780582996*^9, 3.823360880477087*^9, 
   3.823361224742215*^9, 3.8233620990886593`*^9, 3.8233640308219624`*^9, 
   3.8235320061137466`*^9, 3.823597528753026*^9, 3.823618495521882*^9, 
   3.823683414021819*^9, 3.823683842015107*^9, 3.823684775412067*^9, 
   3.823688794547976*^9, 3.823690777270031*^9, 3.8237045725706463`*^9, 
   3.823967036254635*^9, 3.823967518049459*^9, 3.823970038788274*^9, 
   3.824025682258999*^9, 3.825287778263542*^9},
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"3c7eeaa2-4433-4e5c-8173-cf45ab9922c7"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"  (CleanSlate) Approximate kernel memory recovered: \"\>", 
   "\[InvisibleSpace]", "\<\"7 Kb\"\>"}],
  SequenceForm["  (CleanSlate) Approximate kernel memory recovered: ", "7 Kb"],
  Editable->False]], "Print",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820932754769992*^9, 3.820933427630714*^9, 3.820937654903143*^9, 
   3.821729906190301*^9, 3.821732641685704*^9, 3.8218069933778133`*^9, 
   3.82181142618342*^9, 3.8220426528487463`*^9, {3.822048793940605*^9, 
   3.822048801089246*^9}, 3.822505029191699*^9, 3.822505579049889*^9, 
   3.822565490838564*^9, 3.822566210008327*^9, 3.822606718180009*^9, 
   3.8226371008270607`*^9, 3.822739433887854*^9, 3.822761800089258*^9, 
   3.8228172997642097`*^9, 3.822822210725956*^9, 3.822988687208267*^9, 
   3.823359428732101*^9, 3.823360780582996*^9, 3.823360880477087*^9, 
   3.823361224742215*^9, 3.8233620990886593`*^9, 3.8233640308219624`*^9, 
   3.8235320061137466`*^9, 3.823597528753026*^9, 3.823618495521882*^9, 
   3.823683414021819*^9, 3.823683842015107*^9, 3.823684775412067*^9, 
   3.823688794547976*^9, 3.823690777270031*^9, 3.8237045725706463`*^9, 
   3.823967036254635*^9, 3.823967518049459*^9, 3.823970038788274*^9, 
   3.8240256822637253`*^9, 3.825287778263666*^9},
 CellLabel->
  "During evaluation of \
In[4]:=",ExpressionUUID->"0a191a8f-85c6-442e-b8a6-4017aed2ceb3"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"\<\"Utilities`CleanSlate`\"\>", ",", "\<\"System`\"\>", 
   ",", "\<\"Global`\"\>"}], "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820932754773623*^9, 3.820933427635436*^9, 3.8209376549033947`*^9, 
   3.821729906193787*^9, 3.821732641691049*^9, 3.821806993386058*^9, 
   3.821811426187071*^9, 3.822042652852829*^9, {3.822048793944077*^9, 
   3.822048801092909*^9}, 3.822505029195156*^9, 3.8225055790570173`*^9, 
   3.8225654908422747`*^9, 3.8225662100125237`*^9, 3.8226067181902227`*^9, 
   3.822637100839163*^9, 3.8227394339100733`*^9, 3.822761800103311*^9, 
   3.822817299776285*^9, 3.822822210739685*^9, 3.822988687217742*^9, 
   3.823359428736412*^9, 3.823360780587545*^9, 3.8233608804810534`*^9, 
   3.823361224746982*^9, 3.823362099093968*^9, 3.823364030838743*^9, 
   3.8235320061191893`*^9, 3.823597528756508*^9, 3.8236184955254183`*^9, 
   3.823683414029439*^9, 3.823683842020509*^9, 3.823684775416593*^9, 
   3.823688794552709*^9, 3.823690777273932*^9, 3.8237045725743713`*^9, 
   3.823967036258197*^9, 3.823967518053287*^9, 3.8239700387921047`*^9, 
   3.824025682265245*^9, 3.825287778263782*^9},
 CellLabel->"Out[0]=",ExpressionUUID->"20b2b227-3a6e-497d-b6f8-a5246e9bd545"],

Cell[BoxData[
 RowBox[{"<<", "GeneralRelativityTensors`"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8209376549035053`*^9, 3.825287778263854*^9},
 CellLabel->"In[2]:=",ExpressionUUID->"3f1f32ae-fcc0-4f0a-9647-0b6233dcb972"],

Cell[BoxData[
 RowBox[{"Needs", "[", "\"\<VariationalMethods`\>\"", "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.82282432548825*^9, 3.822824327819418*^9}, 
   3.825287778263926*^9},
 CellLabel->"In[3]:=",ExpressionUUID->"23d9a452-32cf-47b3-9452-11124d2fb318"]
}, Closed]],

Cell[CellGroupData[{

Cell["Custom Notation", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.8225114042235403`*^9, 3.822511435665856*^9}, 
   3.823176577809782*^9, 
   3.825287791153748*^9},ExpressionUUID->"edc11028-66e7-49bd-9138-\
a49f79fb0990"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "dtReplace", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dtReplace", " ", "=", " ", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{"Dt", "[", "r", "]"}], "\[Rule]", " ", "dr"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "t", "]"}], "\[Rule]", " ", "dt"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "u", "]"}], "\[Rule]", " ", "du"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "v", "]"}], "\[Rule]", " ", "dv"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "x", "]"}], "\[Rule]", " ", "dx"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "y", "]"}], " ", "\[Rule]", " ", "dy"}], " ", ",", 
     " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "z", "]"}], "\[Rule]", " ", "dz"}], " ", ",", " ", 
     "\[IndentingNewLine]", " ", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Theta]", "]"}], " ", "\[Rule]", " ", 
      "d\[Theta]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Phi]", "]"}], " ", "\[Rule]", " ", "d\[Phi]"}], 
     "  ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Eta]", "]"}], " ", "\[Rule]", " ", "d\[Eta]"}], 
     "  ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Chi]", "]"}], "\[Rule]", " ", "d\[Chi]"}], " ", 
     ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Rho]", "]"}], " ", "\[Rule]", " ", "d\[Rho]"}], 
     " ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[CurlyRho]", "]"}], "\[Rule]", " ", 
      "d\[CurlyRho]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[CurlyPhi]", "]"}], " ", "\[Rule]", " ", 
      "d\[CurlyPhi]"}], " ", ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[Xi]", "]"}], "\[Rule]", " ", "d\[Xi]"}], " ", ",",
      "  ", "\[IndentingNewLine]", " ", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptT]", "]"}], " ", "\[Rule]", " ", 
      "d\[ScriptT]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptZ]", "]"}], " ", "\[Rule]", " ", 
      "d\[ScriptZ]"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "T", "]"}], "\[Rule]", " ", "dT"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "X", "]"}], "\[Rule]", " ", "dX"}], ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "Y", "]"}], "\[Rule]", " ", "dY"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "Z", "]"}], "\[Rule]", " ", "dZ"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "U", "]"}], "\[Rule]", " ", "dU"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "V", "]"}], "\[Rule]", " ", "dV"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[ScriptR]", "]"}], "\[Rule]", " ", "d\[ScriptR]"}],
      "  ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Dt", "[", "\[CapitalPhi]", "]"}], "\[Rule]", " ", 
      "d\[CapitalPhi]"}]}], "\[IndentingNewLine]", "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"dtReplace", " ", "//", " ", "TableForm"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.82317656063256*^9, 3.823176577809904*^9}, {
   3.823598236175474*^9, 3.823598253654046*^9}, {3.823598849383689*^9, 
   3.82359891091936*^9}, {3.8236913141384983`*^9, 3.823691322585009*^9}, {
   3.8237047861092253`*^9, 3.823704790612156*^9}, 3.825287791153907*^9},
 CellLabel->"In[4]:=",ExpressionUUID->"5af2edf2-72c8-4e3e-a207-0a6f5da17e9b"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{"Dt", "[", "r", "]"}], "\[Rule]", "dr"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "t", "]"}], "\[Rule]", "dt"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "u", "]"}], "\[Rule]", "du"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "v", "]"}], "\[Rule]", "dv"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "x", "]"}], "\[Rule]", "dx"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "y", "]"}], "\[Rule]", "dy"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "z", "]"}], "\[Rule]", "dz"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Theta]", "]"}], "\[Rule]", "d\[Theta]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Phi]", "]"}], "\[Rule]", "d\[Phi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Eta]", "]"}], "\[Rule]", "d\[Eta]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Chi]", "]"}], "\[Rule]", "d\[Chi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Rho]", "]"}], "\[Rule]", "d\[Rho]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[CurlyRho]", "]"}], "\[Rule]", "d\[CurlyRho]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[CurlyPhi]", "]"}], "\[Rule]", "d\[CurlyPhi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[Xi]", "]"}], "\[Rule]", "d\[Xi]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptT]", "]"}], "\[Rule]", "d\[ScriptT]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptZ]", "]"}], "\[Rule]", "d\[ScriptZ]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "T", "]"}], "\[Rule]", "dT"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "X", "]"}], "\[Rule]", "dX"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "Y", "]"}], "\[Rule]", "dY"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "Z", "]"}], "\[Rule]", "dZ"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "U", "]"}], "\[Rule]", "dU"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "V", "]"}], "\[Rule]", "dV"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[ScriptR]", "]"}], "\[Rule]", "d\[ScriptR]"}]},
     {
      RowBox[{
       RowBox[{"Dt", "[", "\[CapitalPhi]", "]"}], "\[Rule]", 
       "d\[CapitalPhi]"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{3.823598254375844*^9, 3.823598877146447*^9, 
  3.823598911379983*^9, 3.823618495599228*^9, 3.823683414107848*^9, 
  3.823683842051852*^9, 3.823684775483016*^9, 3.82368879462633*^9, 
  3.823690777330206*^9, 3.823691323069952*^9, 3.823704572638439*^9, 
  3.823704791783836*^9, 3.823967036322558*^9, 3.8239675180766773`*^9, 
  3.823970038900818*^9, 3.824025682372151*^9, 3.8252877911540327`*^9},
 CellLabel->
  "Out[6]//TableForm=",ExpressionUUID->"9f2e1ae7-3065-4332-8ba1-ebc19636aef6"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"a", "/:", 
    RowBox[{"Dt", "[", "a", "]"}], "=", "0"}], "  ", ";"}], 
  "  "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"b", " ", "/:", " ", 
    RowBox[{"Dt", "[", "b", "]"}], " ", "=", " ", "0"}], " ", ";"}], 
  "  "}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.823598195430221*^9, 3.823598210501268*^9}, {
   3.823602495092556*^9, 3.823602530987715*^9}, {3.8236188964036007`*^9, 
   3.8236189207008657`*^9}, {3.8237047330364532`*^9, 3.823704739867001*^9}, 
   3.825287791154132*^9},
 CellLabel->"In[7]:=",ExpressionUUID->"9ac3639f-654e-4369-90f2-92931352eab3"]
}, Closed]],

Cell[CellGroupData[{

Cell["Line Element and Metric Functions", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.},
 CellChangeTimes->{{3.820937548919169*^9, 3.8209375728447866`*^9}, 
   3.8209383129401073`*^9, 3.8220481344968433`*^9, {3.8225115057038183`*^9, 
   3.822511507783984*^9}, 
   3.822763734568725*^9},ExpressionUUID->"27556425-79d3-4b68-b0a5-\
90f78a961d6b"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "lineToMetric", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"lineToMetric", "[", 
    RowBox[{"lineelement_", " ", ",", " ", "differentials_"}], "]"}], ":=", 
   " ", "\[IndentingNewLine]", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"If", "[", 
      RowBox[{
       RowBox[{"i", "\[Equal]", "j"}], " ", ",", 
       RowBox[{"Coefficient", "[", 
        RowBox[{"lineelement", ",", " ", 
         RowBox[{
          RowBox[{"differentials", "[", 
           RowBox[{"[", "i", "]"}], "]"}], " ", 
          RowBox[{"differentials", "[", 
           RowBox[{"[", "j", "]"}], "]"}]}]}], "]"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "/", "2"}], ")"}], "*", 
        RowBox[{"Coefficient", "[", 
         RowBox[{"lineelement", ",", " ", 
          RowBox[{
           RowBox[{"differentials", "[", 
            RowBox[{"[", "i", "]"}], "]"}], " ", 
           RowBox[{"differentials", "[", 
            RowBox[{"[", "j", "]"}], "]"}]}]}], "]"}]}]}], "]"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"i", ",", "1", ",", 
       RowBox[{"Length", "[", "differentials", "]"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "1", ",", 
       RowBox[{"Length", "[", "differentials", "]"}]}], "}"}]}], "]"}]}], 
  "  ", ";"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.},
 CellChangeTimes->{3.821567412203915*^9, 3.821641945174967*^9, 
  3.821641981470141*^9, 3.8220481344970007`*^9, 3.822763734569355*^9},
 CellLabel->"In[9]:=",ExpressionUUID->"a23012f5-6128-4c78-b605-c749f413943d"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "metricToLine", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"metricToLine", "[", 
   RowBox[{"metric_", ",", " ", "differentials_"}], "]"}], ":=", " ", 
  "\[IndentingNewLine]", 
  RowBox[{"Sum", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"metric", "[", 
      RowBox[{"[", 
       RowBox[{"i", ",", "j"}], "]"}], "]"}], " ", 
     RowBox[{"differentials", "[", 
      RowBox[{"[", "i", "]"}], "]"}], " ", 
     RowBox[{"differentials", "[", 
      RowBox[{"[", "j", "]"}], "]"}]}], " ", ",", " ", 
    RowBox[{"{", 
     RowBox[{"i", ",", "1", ",", 
      RowBox[{"Length", "[", "differentials", "]"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"j", ",", "1", ",", 
      RowBox[{"Length", "[", "differentials", "]"}]}], "}"}]}], 
   "]"}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.},
 CellChangeTimes->{{3.822762557092309*^9, 3.8227626322008677`*^9}, 
   3.8227637345698223`*^9, 3.822988709740047*^9},
 CellLabel->"In[11]:=",ExpressionUUID->"c358de30-53ce-4237-8266-c73aa7430639"]
}, Closed]],

Cell[CellGroupData[{

Cell["Line Element and Metric 2.1", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.825287799472928*^9, 
  3.825287827199594*^9}},ExpressionUUID->"2ec33168-5c55-4470-ae8c-\
7b76d3f10d2f"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt1", "]"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt1", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"-", " ", 
     RowBox[{"Exp", "[", 
      RowBox[{"-", "U"}], "]"}]}], " ", 
    RowBox[{"(", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Exp", "[", "V", "]"}], " ", 
       SuperscriptBox["dx", "2"]}], "+", " ", 
      RowBox[{
       RowBox[{"Exp", "[", 
        RowBox[{"-", "V"}], "]"}], " ", 
       SuperscriptBox["dy", "2"]}]}], ")"}]}], " ", "+", " ", 
   RowBox[{"2", " ", 
    RowBox[{"Exp", "[", 
     RowBox[{"-", "M"}], "]"}], " ", "du", " ", "dv", " "}]}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.823969995385275*^9, 3.823970026655311*^9}, 
   3.8252878150103073`*^9},
 CellLabel->"In[13]:=",ExpressionUUID->"7d789c67-b0a1-40a0-9059-d6ebdda7bd71"],

Cell[BoxData[
 RowBox[{
  RowBox[{"2", " ", "du", " ", "dv", " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"-", "M"}]]}], "-", 
  RowBox[{
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"-", "U"}]], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      SuperscriptBox["dy", "2"], " ", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"-", "V"}]]}], "+", 
     RowBox[{
      SuperscriptBox["dx", "2"], " ", 
      SuperscriptBox["\[ExponentialE]", "V"]}]}], ")"}]}]}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{3.823970038961813*^9, 3.82402568242238*^9, 
  3.825287815010417*^9},
 CellLabel->"Out[14]=",ExpressionUUID->"cdf3f7f2-75f1-4145-b4a7-50b2955f4f9f"],

Cell[BoxData[
 RowBox[{
  RowBox[{"lineToMetric", "[", " ", 
   RowBox[{"eq2pt1", " ", ",", " ", 
    RowBox[{"{", 
     RowBox[{"du", ",", "dv", ",", "dx", ",", "dy"}], "}"}]}], "]"}], " ", "//",
   " ", "MatrixForm"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.823970091325972*^9, 3.823970107292408*^9}, 
   3.825287815010496*^9},
 CellLabel->"In[15]:=",ExpressionUUID->"27b7d8af-ae26-4ada-a9f1-c9a562e987ea"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"-", "M"}]], "0", "0"},
     {
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"-", "M"}]], "0", "0", "0"},
     {"0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", "U"}], "+", "V"}]]}], "0"},
     {"0", "0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", "U"}], "-", "V"}]]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.82397010282158*^9, 3.823970107523377*^9}, 
   3.8240256824325542`*^9, 3.82528781501058*^9},
 CellLabel->
  "Out[15]//MatrixForm=",ExpressionUUID->"e1b00276-502a-46bf-a209-\
8ee8aa4f0089"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt1a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt1a", " ", "=", " ", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"U", "\[Rule]", " ", 
      RowBox[{"U", "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{"V", "\[Rule]", " ", 
      RowBox[{"V", "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{"M", "\[Rule]", " ", 
      RowBox[{"M", "[", 
       RowBox[{"u", ",", "v"}], "]"}]}]}], "\[IndentingNewLine]", "}"}]}], 
  " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt1a", "  ", "//", " ", "TableForm"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.8239700576371813`*^9, 3.823970087308576*^9}, 
   3.825287815010674*^9},
 CellLabel->"In[16]:=",ExpressionUUID->"881bb4d0-dea5-4d1b-826a-dec8bd78d590"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{"U", "\[Rule]", 
       RowBox[{"U", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}]},
     {
      RowBox[{"V", "\[Rule]", 
       RowBox[{"V", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}]},
     {
      RowBox[{"M", "\[Rule]", 
       RowBox[{"M", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{3.823970087915142*^9, 3.824025682457467*^9, 
  3.8252878150107603`*^9},
 CellLabel->
  "Out[18]//TableForm=",ExpressionUUID->"da2c37ca-a7a9-4685-b378-\
578fb5ad82ac"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "metric2pt1", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"metric2pt1", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"lineToMetric", "[", " ", 
     RowBox[{"eq2pt1", " ", ",", " ", 
      RowBox[{"{", 
       RowBox[{"du", ",", "dv", ",", "dx", ",", "dy"}], "}"}]}], "]"}], "  ", 
    "/.", " ", "eq2pt1a"}]}], "  ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"metric2pt1", " ", "//", " ", "MatrixForm"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.8239701143491373`*^9, 3.8239701346283007`*^9}, 
   3.825287815010845*^9},
 CellLabel->"In[19]:=",ExpressionUUID->"04aa96da-4acc-4ec1-b893-b40d492306ad"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"-", 
        RowBox[{"M", "[", 
         RowBox[{"u", ",", "v"}], "]"}]}]], "0", "0"},
     {
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"-", 
        RowBox[{"M", "[", 
         RowBox[{"u", ",", "v"}], "]"}]}]], "0", "0", "0"},
     {"0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"U", "[", 
           RowBox[{"u", ",", "v"}], "]"}]}], "+", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}], "0"},
     {"0", "0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"U", "[", 
           RowBox[{"u", ",", "v"}], "]"}]}], "-", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.82397011854991*^9, 3.8239701351772842`*^9}, 
   3.824025682466413*^9, 3.825287815010932*^9},
 CellLabel->
  "Out[21]//MatrixForm=",ExpressionUUID->"85c1ae31-3144-4c35-be37-\
394b40a4bed3"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "inverse2pt1", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"inverse2pt1", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"Inverse", "[", " ", "metric2pt1", " ", "]"}], " ", "//", " ", 
     "Expand"}], " ", "//", " ", "Simplify"}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"inverse2pt1", " ", "//", " ", "MatrixForm"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.823971320172967*^9, 3.823971354387724*^9}, 
   3.825287815011004*^9},
 CellLabel->"In[22]:=",ExpressionUUID->"58fdf474-9751-4042-99ea-c6b1200d0c94"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"M", "[", 
        RowBox[{"u", ",", "v"}], "]"}]], "0", "0"},
     {
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"M", "[", 
        RowBox[{"u", ",", "v"}], "]"}]], "0", "0", "0"},
     {"0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"U", "[", 
          RowBox[{"u", ",", "v"}], "]"}], "-", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}], "0"},
     {"0", "0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"U", "[", 
          RowBox[{"u", ",", "v"}], "]"}], "+", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.8239713348280573`*^9, 3.823971354774908*^9}, 
   3.824025682493371*^9, 3.8252878150110903`*^9},
 CellLabel->
  "Out[24]//MatrixForm=",ExpressionUUID->"ad497150-bb18-4347-8ac4-\
5690b5c273c2"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"metric2pt1", " ", ".", " ", "inverse2pt1"}], " ", "//", " ", 
    "Expand"}], " ", "//", " ", "Simplify"}], " ", "//", " ", 
  "MatrixForm"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.8239713579572773`*^9, 3.823971367067218*^9}, 
   3.8252878150111628`*^9},
 CellLabel->"In[25]:=",ExpressionUUID->"826cfed4-fd43-42dd-86b7-b113604f0778"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0"},
     {"0", "1", "0", "0"},
     {"0", "0", "1", "0"},
     {"0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{3.823971367330544*^9, 3.824025682504026*^9, 
  3.825287815011244*^9},
 CellLabel->
  "Out[25]//MatrixForm=",ExpressionUUID->"3582fbad-e80c-46c1-933a-\
4c8b862412ea"],

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"inverse2pt1", "  ", ".", " ", "metric2pt1"}], "  ", "//", " ", 
     "Expand"}], " ", "//", " ", "Simplify"}], " ", "//", " ", 
   "MatrixForm"}]}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{{3.823971378240632*^9, 3.823971382610981*^9}, 
   3.825287815011325*^9},
 CellLabel->"In[26]:=",ExpressionUUID->"157ea336-3258-466d-97f1-be4420ebb419"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"1", "0", "0", "0"},
     {"0", "1", "0", "0"},
     {"0", "0", "1", "0"},
     {"0", "0", "0", "1"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.},
 CellChangeTimes->{3.823971382890867*^9, 3.824025682531083*^9, 
  3.825287815011407*^9},
 CellLabel->
  "Out[26]//MatrixForm=",ExpressionUUID->"c8bbb129-e32b-4ef0-85d9-\
c0ca987cbac8"]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt2", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt2", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"D", "[", 
     RowBox[{
      RowBox[{"\[Phi]2", "[", 
       RowBox[{"u", ",", "v"}], "]"}], " ", ",", "v"}], "]"}], " ", 
    "\[Equal]", " ", 
    RowBox[{
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"U", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "v"}], "]"}], " ", 
      RowBox[{"\[Phi]2", "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], " ", "-", 
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"V", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "u"}], "]"}], " ", 
      RowBox[{"\[Phi]0", "[", 
       RowBox[{"u", ",", "v"}], "]"}]}]}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt2", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8240266748743763`*^9, 3.824026755993248*^9}},
 CellLabel->
  "In[216]:=",ExpressionUUID->"f2c9328d-ebf1-4eae-8716-6ef93469e28f"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "v"}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.824026756433908*^9},
 CellLabel->
  "Out[218]//TraditionalForm=",ExpressionUUID->"ec0f4d12-3b28-4872-b3d5-\
2f686ffbbf71"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt3", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt3", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"D", "[", 
     RowBox[{
      RowBox[{"\[Phi]0", "[", 
       RowBox[{"u", ",", "v"}], "]"}], " ", ",", "u"}], "]"}], " ", 
    "\[Equal]", " ", 
    RowBox[{
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"U", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "u"}], "]"}], " ", 
      RowBox[{"\[Phi]0", "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], " ", "-", 
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"V", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "v"}], "]"}], " ", 
      RowBox[{"\[Phi]2", "[", 
       RowBox[{"u", ",", "v"}], "]"}]}]}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt2", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824026778179373*^9, 3.824026803562704*^9}},
 CellLabel->
  "In[219]:=",ExpressionUUID->"532e7043-8d39-4c9c-b979-722e556910b4"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "v"}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.8240268059310637`*^9},
 CellLabel->
  "Out[221]//TraditionalForm=",ExpressionUUID->"0bbd60b5-f24a-49c8-b1c2-\
43278bd31809"]
}, Open  ]],

Cell[CellGroupData[{

Cell[" Calculation of tensors from metric 2.1 ", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.824026460864416*^9, 3.8240264983129387`*^9}, {
  3.825287863261981*^9, 
  3.825287869336536*^9}},ExpressionUUID->"b4342229-4b4c-4ae1-b07f-\
a7eb2e3408cc"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "input", "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"input", "[", 
    RowBox[{
    "equationNumber_", ",", "equation_", ",", "metricName_", ",", 
     "displayName_", ",", "variables_", ",", "indices_"}], "]"}], ":=", " ", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Clear", "[", "tensorList", "]"}], ";", "\[IndentingNewLine]", 
      RowBox[{"tensorList", " ", "=", " ", 
       RowBox[{"{", "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"\"\<g\>\"", "<>", "equationNumber"}], ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<christoffel\>\"", "<>", "equationNumber"}], " ", ",", 
         " ", "\[IndentingNewLine]", 
         RowBox[{"\"\<riemann\>\"", "<>", "equationNumber"}], "  ", ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<ricci\>\"", "<>", "equationNumber"}], " ", ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<ricciscalar\>\"", "<>", "equationNumber"}], ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<kretschmannscalar\>\"", "<>", "equationNumber"}], "  ", 
         ",", "\[IndentingNewLine]", 
         RowBox[{"\"\<einstein\>\"", "<>", "equationNumber"}], "  ", ",", " ",
          "\[IndentingNewLine]", 
         RowBox[{"\"\<weyl\>\"", "<>", "equationNumber"}], "  ", ",", 
         "\[IndentingNewLine]", 
         RowBox[{"\"\<cotton\>\"", "<>", "equationNumber"}]}], "  ", 
        "\[IndentingNewLine]", "}"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "1", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"ToMetric", "[", 
        RowBox[{
         RowBox[{"{", " ", 
          RowBox[{"metricName", ",", " ", "displayName"}], " ", "}"}], " ", 
         ",", " ", "variables", ",", " ", "equation", ",", " ", "indices"}], 
        " ", "]"}]}], " ", ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "2", "]"}], "]"}], "  ", "=", " ", "\[IndentingNewLine]", 
       RowBox[{"ChristoffelSymbol", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], "]"}]}], " ", ";",
       "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "3", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"RiemannTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWithNested", "\[Rule]", " ", "Simplify"}]}], " ", 
        "]"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "4", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"RicciTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "5", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"RicciScalar", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "6", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"KretschmannScalar", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], "]"}]}], " ", ";",
       "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "7", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"EinsteinTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], "]"}]}], " ", ";",
       "  ", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "8", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"WeylTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";", "\[IndentingNewLine]", " ", 
      RowBox[{
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "9", "]"}], "]"}], " ", "=", " ", "\[IndentingNewLine]", 
       
       RowBox[{"CottonTensor", "[", " ", 
        RowBox[{
         RowBox[{"tensorList", "[", 
          RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", 
         RowBox[{"ActWith", "\[Rule]", " ", "Simplify"}]}], " ", "]"}]}], " ",
       ";"}]}], "\[IndentingNewLine]", "]"}]}], ";"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{
  3.820937492203251*^9, 3.821110229350912*^9, {3.823967538291772*^9, 
   3.8239675471538973`*^9}, 3.82402647282372*^9},
 CellLabel->"In[27]:=",ExpressionUUID->"97f1e155-14b5-4505-89b5-eb7b265a565b"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
   "Last", " ", "timing", " ", "took", " ", "4.72", " ", "for", " ", "all", 
    " ", "tensors"}], " ", "*)"}], " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"input", "[", " ", 
    RowBox[{
    "\"\<metric2pt1\>\"", ",", " ", "metric2pt1", ",", " ", 
     "\"\<BellSzekers\>\"", ",", 
     "\"\<\!\(\*SuperscriptBox[\(g\), \(BellS\)]\)\>\"", ",", 
     RowBox[{"{", 
      RowBox[{"u", ",", "v", ",", "x", ",", "y"}], "}"}], ",", " ", 
     "\"\<Greek\>\""}], "]"}], " ", "//", " ", "Timing"}]}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{
  3.820937492203436*^9, 3.821110229350998*^9, {3.822307281934704*^9, 
   3.822307303605431*^9}, {3.823967447386095*^9, 3.82396750850193*^9}, {
   3.8239676337366667`*^9, 3.823967640928253*^9}, {3.8239701614373283`*^9, 
   3.8239702144679956`*^9}, {3.8240256938286457`*^9, 3.824025696464918*^9}, 
   3.8240264728238792`*^9},ExpressionUUID->"94343561-7323-446a-bc32-\
f238d558bf5a"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"4.723522`", ",", "Null"}], "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970201796486*^9, 3.824025687217991*^9, 
  3.824026472823977*^9},
 CellLabel->"Out[29]=",ExpressionUUID->"3744f583-bf2a-41e6-b4e0-261f0a68b4e9"],

Cell[BoxData["tensorList"], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.823967564400813*^9, 3.823967565024124*^9}, 
   3.824026472824177*^9},
 CellLabel->"In[30]:=",ExpressionUUID->"c929543c-251d-47bd-a96e-af65ea77dbc3"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   TagBox[
    SubsuperscriptBox[
     SuperscriptBox["g", "BellS"], "\[Alpha]\[Beta]", ""],
    DisplayForm], ",", 
   TagBox[
    SubsuperscriptBox["\[CapitalGamma]", 
     RowBox[{"  ", "\[Beta]\[Gamma]"}], 
     RowBox[{"\[Alpha]", "    "}]],
    DisplayForm], ",", 
   TagBox[
    SubsuperscriptBox["R", "\[Alpha]\[Beta]\[Gamma]\[Delta]", ""],
    DisplayForm], ",", 
   TagBox[
    SubsuperscriptBox["R", "\[Beta]\[Gamma]", ""],
    DisplayForm], ",", 
   TagBox["\<\"R\"\>",
    DisplayForm], ",", 
   TagBox["\<\"K\"\>",
    DisplayForm], ",", 
   TagBox[
    SubsuperscriptBox["G", "\[Alpha]\[Beta]", ""],
    DisplayForm], ",", 
   TagBox[
    SubsuperscriptBox["C", "\[Alpha]\[Beta]\[Gamma]\[Delta]", ""],
    DisplayForm], ",", 
   TagBox[
    SubsuperscriptBox["C", "\[Alpha]\[Beta]\[Gamma]", ""],
    DisplayForm]}], "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970224723918*^9, 3.824025687300172*^9, 
  3.824026472824286*^9},
 CellLabel->"Out[30]=",ExpressionUUID->"5195a509-2e97-4cbe-9e95-9a965dfd417d"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "1", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "1", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"TensorValues", "[", 
    RowBox[{"tensorList", "[", 
     RowBox[{"[", "1", "]"}], "]"}], "]"}], " ", "//", " ", "MatrixForm"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.82093459847665*^9, 3.820934601699522*^9}, 
   3.8209374922041063`*^9, 3.821110229351385*^9, 3.82402647282448*^9},
 CellLabel->"In[31]:=",ExpressionUUID->"ea42e993-fd04-4304-bdbb-dada5f7448f8"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox[
   SuperscriptBox["g", "BellS"], "\[Alpha]\[Beta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970232313205*^9, 3.8240256873107367`*^9, 
  3.8240264728245783`*^9},
 CellLabel->"Out[31]=",ExpressionUUID->"42afd90d-5496-4bff-9012-95fe3656911a"],

Cell[BoxData["\<\"BellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970232313205*^9, 3.824025687313176*^9, 
  3.824026472824662*^9},
 CellLabel->"Out[32]=",ExpressionUUID->"046f46c4-d6f3-4b4f-b59e-5e7f67c64fd2"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"0", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"-", 
         RowBox[{"M", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}]], "0", "0"},
      {
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"-", 
         RowBox[{"M", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}]], "0", "0", "0"},
      {"0", "0", 
       RowBox[{"-", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}], "-", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}]]}], "0"},
      {"0", "0", "0", 
       RowBox[{"-", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{
          RowBox[{"-", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], "-", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}]]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970232313205*^9, 3.82402568734437*^9, 
  3.824026472824725*^9},
 CellLabel->
  "Out[33]//TraditionalForm=",ExpressionUUID->"3ad707e8-e032-40e7-b89f-\
3847b124080e"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "2", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "2", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "2", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], 
    " ", "//", " ", "Simplify"}], "  ", "//", " ", "MatrixForm"}], "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820934553796588*^9, 3.820934587380786*^9}, 
   3.8209374922046547`*^9, 3.821110229351994*^9, {3.8239681558924627`*^9, 
   3.8239681604507723`*^9}, {3.8239702495480747`*^9, 3.8239702526039124`*^9}, 
   3.824026472824851*^9},
 CellLabel->"In[34]:=",ExpressionUUID->"0864c69c-7656-4ce6-8b86-b94f14127e8a"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["\[CapitalGamma]", 
   RowBox[{"  ", "\[Beta]\[Gamma]"}], 
   RowBox[{"\[Alpha]", "    "}]],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.823970240593905*^9, 3.823970252905715*^9}, 
   3.824025687355397*^9, 3.824026472824945*^9},
 CellLabel->"Out[34]=",ExpressionUUID->"5897bc5f-4abd-4961-93f1-e3c70631cd33"],

Cell[BoxData["\<\"ChristoffelSymbolBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.823970240593905*^9, 3.823970252905715*^9}, 
   3.824025687361109*^9, 3.8240264728250313`*^9},
 CellLabel->"Out[35]=",ExpressionUUID->"d0c4dbbd-3350-4790-a9b9-388f5a86f7c7"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None]}]},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "+", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], ")"}]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], "+", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], ")"}]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {
            RowBox[{"-", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "v"}],
              MultilineFunction->None]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "+", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], ")"}]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "2"]}], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], "+", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], ")"}]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], ")"}]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], ")"}]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], ")"}]}]},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], ")"}]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None]}], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], ")"}]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None]}], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], ")"}]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None]}], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], ")"}]}]},
           {
            RowBox[{
             FractionBox["1", "2"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None]}], "-", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], ")"}]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.823970240593905*^9, 3.823970252905715*^9}, 
   3.824025687445476*^9, 3.82402647282509*^9},
 CellLabel->
  "Out[36]//TraditionalForm=",ExpressionUUID->"7fbeda92-1ebe-47b4-85a5-\
5e3db62bbea1"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "3", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "3", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "3", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], 
    " ", "//", " ", "Simplify"}], "  ", "//", " ", "MatrixForm"}], "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.82093461950063*^9, 3.820934623299252*^9}, 
   3.820937492205227*^9, 3.821110229352274*^9, {3.8239681359406633`*^9, 
   3.823968143179031*^9}, {3.8239702651809263`*^9, 3.823970267459793*^9}, 
   3.824026472825218*^9},
 CellLabel->"In[37]:=",ExpressionUUID->"25dcaf58-6ed4-4938-83e3-e7381f29fbd9"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["R", "\[Alpha]\[Beta]\[Gamma]\[Delta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239702677296343`*^9, 3.824025687459783*^9, 
  3.824026472825302*^9},
 CellLabel->"Out[37]=",ExpressionUUID->"50b4f8a5-5c00-441a-b767-f0925d9dcd0d"],

Cell[BoxData["\<\"RiemannTensorBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239702677296343`*^9, 3.8240256874646397`*^9, 
  3.824026472825383*^9},
 CellLabel->"Out[38]=",ExpressionUUID->"877816cb-35cc-4473-8c9c-1ac2ec828fef"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", 
           RowBox[{
            RowBox[{"-", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{"-", 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]]}], " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], "0", "0"},
          {
           RowBox[{
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{"-", 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0"},
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{
                 RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                 RowBox[{"\[PartialD]", "v"}]}],
                MultilineFunction->None]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}]},
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None]}], ")"}]}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}]},
          {"0", "0", "0", "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", 
           RowBox[{
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{"-", 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], "0", "0"},
          {
           RowBox[{
            RowBox[{"-", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{"-", 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]]}], " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{
                 RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                 RowBox[{"\[PartialD]", "v"}]}],
                MultilineFunction->None]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0"},
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None]}], ")"}]}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}]},
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}]},
          {"0", "0", "0", "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0"},
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{
                 RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                 RowBox[{"\[PartialD]", "v"}]}],
                MultilineFunction->None]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0"},
          {"0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{
                 RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                 RowBox[{"\[PartialD]", "v"}]}],
                MultilineFunction->None]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "-", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "2"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"2", " ", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}]}], ")"}]}]},
          {"0", "0", 
           RowBox[{
            FractionBox["1", "2"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"2", " ", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}]}], ")"}]}], "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}]},
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}]},
          {"0", "0", "0", "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "u"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["u", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None]}], ")"}]}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "2"], 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}]},
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "-", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}]},
          {"0", "0", "0", "0"},
          {
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None]}], ")"}]}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}], "+", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               RowBox[{"(", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None], "+", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "u"}],
                  MultilineFunction->None]}], ")"}]}]}], ")"}]}], 
           RowBox[{
            FractionBox["1", "4"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], "-", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], "+", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None]}], ")"}]}]}], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"], "-", 
              RowBox[{"2", " ", 
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", 
                 SuperscriptBox["v", "2"]}],
                MultilineFunction->None]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}], "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", 
           RowBox[{
            FractionBox["1", "2"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"2", " ", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}]}], ")"}]}]},
          {"0", "0", 
           RowBox[{
            FractionBox["1", "2"], " ", 
            SuperscriptBox["\[ExponentialE]", 
             RowBox[{
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}], "-", 
              RowBox[{"2", " ", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"V", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}], "-", 
              RowBox[{
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "u"}],
                MultilineFunction->None], " ", 
               FractionBox[
                RowBox[{"\[PartialD]", 
                 RowBox[{"U", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{"\[PartialD]", "v"}],
                MultilineFunction->None]}]}], ")"}]}], "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"},
          {"0", "0", "0", "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}}], "\[NoBreak]", ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239702677296343`*^9, 3.8240256883062983`*^9, 
  3.82402647282545*^9},
 CellLabel->
  "Out[39]//TraditionalForm=",ExpressionUUID->"d7b742c7-77ab-4a31-ba04-\
4d94bcff31af"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "4", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "4", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "4", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], 
    " ", "//", " ", "Simplify"}], " ", "//", " ", "MatrixForm"}], "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820934641180434*^9, 3.820934644683545*^9}, 
   3.820937492205658*^9, 3.821110229352577*^9, {3.8239681207165203`*^9, 
   3.823968125514682*^9}, {3.8239702823410254`*^9, 3.8239702841077843`*^9}, 
   3.824026472825573*^9},
 CellLabel->"In[40]:=",ExpressionUUID->"27b31eb5-f7d1-450b-9d14-bd230ac96d58"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["R", "\[Beta]\[Gamma]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970284419114*^9, 3.824025688373596*^9, 
  3.824026472825655*^9},
 CellLabel->"Out[40]=",ExpressionUUID->"af24bf5d-1a7b-4620-845c-ee5fbc24dc6e"],

Cell[BoxData["\<\"RicciTensorBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970284419114*^9, 3.824025688379505*^9, 
  3.8240264728257427`*^9},
 CellLabel->"Out[41]=",ExpressionUUID->"fed6241b-de5a-48e4-85f1-7d9a8e51c017"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None]}], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["u", "2"]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}]}], 
       RowBox[{
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}], "0", "0"},
      {
       RowBox[{
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}], 
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["v", "2"]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"]}]}], "0", "0"},
      {"0", "0", 
       RowBox[{
        RowBox[{"-", 
         FractionBox["1", "2"]}], " ", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}], "-", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}], "+", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"2", " ", 
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{
             RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
             RowBox[{"\[PartialD]", "v"}]}],
            MultilineFunction->None]}], "-", 
          RowBox[{"2", " ", 
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{
             RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
             RowBox[{"\[PartialD]", "v"}]}],
            MultilineFunction->None]}], "+", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], "-", 
             RowBox[{"2", " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}], "+", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], " ", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None]}]}], ")"}]}], "0"},
      {"0", "0", "0", 
       RowBox[{
        FractionBox["1", "2"], " ", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}], "-", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}], "-", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", 
           RowBox[{"2", " ", 
            RowBox[{"(", 
             RowBox[{
              FractionBox[
               RowBox[{
                SuperscriptBox["\[PartialD]", "2"], 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{
                RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                RowBox[{"\[PartialD]", "v"}]}],
               MultilineFunction->None], "+", 
              FractionBox[
               RowBox[{
                SuperscriptBox["\[PartialD]", "2"], 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{
                RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                RowBox[{"\[PartialD]", "v"}]}],
               MultilineFunction->None]}], ")"}]}]}], "+", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{"2", " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None]}], ")"}]}], "+", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], " ", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None]}]}], ")"}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970284419114*^9, 3.824025688467122*^9, 
  3.8240264728258047`*^9},
 CellLabel->
  "Out[42]//TraditionalForm=",ExpressionUUID->"7c3cabe5-c97e-4fc5-ac33-\
1c151093983d"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "5", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "5", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "5", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], 
    " ", "//", " ", "Simplify"}], "  ", "//", " ", "MatrixForm"}], "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820934650372052*^9, 3.820934653739538*^9}, 
   3.820937492206099*^9, 3.821110229352878*^9, {3.8239681099639072`*^9, 
   3.823968115074683*^9}, {3.823970294611989*^9, 3.8239702964996147`*^9}, 
   3.8240264728259287`*^9},
 CellLabel->"In[43]:=",ExpressionUUID->"1c9819e0-3def-4514-9dd3-65e636b6f4da"],

Cell[BoxData[
 TagBox["\<\"R\"\>",
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239702967601757`*^9, 3.824025688480268*^9, 
  3.8240264728260317`*^9},
 CellLabel->"Out[43]=",ExpressionUUID->"06b86e6c-1a1a-4c25-9060-0e479cc92ab0"],

Cell[BoxData["\<\"RicciScalarBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239702967601757`*^9, 3.824025688485145*^9, 
  3.8240264728261223`*^9},
 CellLabel->"Out[44]=",ExpressionUUID->"36a06700-09b0-4523-8761-23372709d98a"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{
    RowBox[{"-", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]]}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        RowBox[{"(", 
         RowBox[{
          FractionBox[
           RowBox[{
            SuperscriptBox["\[PartialD]", "2"], 
            RowBox[{"M", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{
            RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
            RowBox[{"\[PartialD]", "v"}]}],
           MultilineFunction->None], "+", 
          RowBox[{"2", " ", 
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{
             RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
             RowBox[{"\[PartialD]", "v"}]}],
            MultilineFunction->None]}]}], ")"}]}]}], "+", 
      RowBox[{"3", " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239702967601757`*^9, 3.824025688516757*^9, 
  3.824026472826185*^9},
 CellLabel->
  "Out[45]//TraditionalForm=",ExpressionUUID->"7bf87406-d17f-4890-ac23-\
43e3510cd116"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "6", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "6", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"TensorValues", "[", 
     RowBox[{"tensorList", "[", 
      RowBox[{"[", "6", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], " ",
    "//", " ", "Simplify"}], " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820934650372052*^9, 3.820934653739538*^9}, 
   3.820937492206099*^9, 3.821110229352878*^9, {3.823967604672648*^9, 
   3.823967608071101*^9}, {3.8239680942842827`*^9, 3.823968100866708*^9}, 
   3.824026472826305*^9},
 CellLabel->"In[46]:=",ExpressionUUID->"1f18a948-5b0a-47d7-a08c-1980f1ad26ec"],

Cell[BoxData[
 TagBox["\<\"K\"\>",
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239703056638327`*^9, 3.82402568853157*^9, 
  3.824026472826395*^9},
 CellLabel->"Out[46]=",ExpressionUUID->"b21c9c8d-a76b-41af-b519-8ccb6732c70a"],

Cell[BoxData["\<\"KretschmannScalarBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239703056638327`*^9, 3.8240256885362663`*^9, 
  3.824026472826478*^9},
 CellLabel->"Out[47]=",ExpressionUUID->"7e7ba2d3-c6ec-4a74-b3af-56e49dba2ce3"],

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"2", " ", 
     RowBox[{"M", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", 
      RowBox[{"2", " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], " ", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None]}], "+", 
            RowBox[{
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], " ", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None]}]}], ")"}]}], "+", 
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"2", " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None]}], "+", 
            RowBox[{"2", " ", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None]}], "-", 
            RowBox[{"3", " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None]}]}], ")"}]}]}], ")"}]}]}], "+", 
     RowBox[{"4", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], ")"}], "2"]}], "-", 
     RowBox[{"4", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{
        RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
        RowBox[{"\[PartialD]", "v"}]}],
       MultilineFunction->None]}], "-", 
     RowBox[{"4", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{
        RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
        RowBox[{"\[PartialD]", "v"}]}],
       MultilineFunction->None]}], "+", 
     RowBox[{"4", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], ")"}], "2"]}], "+", 
     RowBox[{"4", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], ")"}], "2"]}], "+", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", 
         RowBox[{"2", " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"M", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None]}]}], "-", 
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", 
           SuperscriptBox["u", "2"]}],
          MultilineFunction->None]}], "+", 
        RowBox[{"3", " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}], "+", 
        RowBox[{"2", " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}]}], ")"}]}], "+", 
     RowBox[{
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"4", " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], "-", 
           RowBox[{"2", " ", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["u", "2"]}],
                 MultilineFunction->None]}]}], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"], "+", 
              SuperscriptBox[
               RowBox[{"(", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], ")"}], "2"]}], ")"}]}]}], ")"}]}], 
        "+", 
        RowBox[{"4", " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], "+", 
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", 
             SuperscriptBox["u", "2"]}],
            MultilineFunction->None], "-", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}]}], ")"}]}]}], ")"}]}], "+", 
     RowBox[{"4", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["v", "2"]}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None]}], "-", 
     RowBox[{"2", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"]}], "+", 
     RowBox[{"4", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["v", "2"]}],
       MultilineFunction->None]}], "+", 
     RowBox[{"4", " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["u", "2"]}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["v", "2"]}],
       MultilineFunction->None]}], "-", 
     RowBox[{"2", " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["u", "2"]}],
       MultilineFunction->None], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"]}], "+", 
     RowBox[{"4", " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["u", "2"]}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["v", "2"]}],
       MultilineFunction->None]}], "-", 
     RowBox[{"4", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["v", "2"]}],
       MultilineFunction->None]}], "-", 
     RowBox[{"2", " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["v", "2"]}],
       MultilineFunction->None], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"]}], "-", 
     RowBox[{"2", " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", 
        SuperscriptBox["v", "2"]}],
       MultilineFunction->None], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"]}], "+", 
     RowBox[{"2", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"]}], "+", 
     RowBox[{"3", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"], " ", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"]}]}], ")"}]}], 
  TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239703056638327`*^9, 3.824025688674088*^9, 
  3.82402647282655*^9},
 CellLabel->
  "Out[48]//TraditionalForm=",ExpressionUUID->"8225afd1-c0da-4c79-988c-\
0a6bde291cfe"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "7", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "7", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"TensorValues", "[", 
     RowBox[{"tensorList", "[", 
      RowBox[{"[", "7", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], " ",
    "//", " ", "Simplify"}], " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.820934650372052*^9, 3.820934653739538*^9}, 
   3.820937492206099*^9, 3.821110229352878*^9, {3.823967611433382*^9, 
   3.8239676150077477`*^9}, {3.823968173308403*^9, 3.823968180490913*^9}, 
   3.82402647282668*^9},
 CellLabel->"In[49]:=",ExpressionUUID->"469cb02a-95c7-4d00-b7c0-15962aefd582"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["G", "\[Alpha]\[Beta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970313941002*^9, 3.8240256886894827`*^9, 
  3.824026472826764*^9},
 CellLabel->"Out[49]=",ExpressionUUID->"9b2c4d0a-8ddf-49f0-8af6-b68e7b979566"],

Cell[BoxData["\<\"EinsteinTensorBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970313941002*^9, 3.824025688694252*^9, 
  3.824026472826848*^9},
 CellLabel->"Out[50]=",ExpressionUUID->"f7777bb3-1f2b-4c9f-bb33-435248a5b302"],

Cell[BoxData[
 FormBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None]}], "+", 
       FractionBox[
        RowBox[{
         SuperscriptBox["\[PartialD]", "2"], 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", 
         SuperscriptBox["u", "2"]}],
        MultilineFunction->None], "-", 
       RowBox[{
        FractionBox["1", "2"], " ", 
        SuperscriptBox[
         RowBox[{"(", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None], ")"}], "2"]}], "-", 
       RowBox[{
        FractionBox["1", "2"], " ", 
        SuperscriptBox[
         RowBox[{"(", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None], ")"}], "2"]}]}], 
      RowBox[{
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}], "-", 
       FractionBox[
        RowBox[{
         SuperscriptBox["\[PartialD]", "2"], 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{
         RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
         RowBox[{"\[PartialD]", "v"}]}],
        MultilineFunction->None]}], "0", "0"},
     {
      RowBox[{
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}], "-", 
       FractionBox[
        RowBox[{
         SuperscriptBox["\[PartialD]", "2"], 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{
         RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
         RowBox[{"\[PartialD]", "v"}]}],
        MultilineFunction->None]}], 
      RowBox[{
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}], "+", 
       FractionBox[
        RowBox[{
         SuperscriptBox["\[PartialD]", "2"], 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", 
         SuperscriptBox["v", "2"]}],
        MultilineFunction->None], "-", 
       RowBox[{
        FractionBox["1", "2"], " ", 
        SuperscriptBox[
         RowBox[{"(", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], ")"}], "2"]}], "-", 
       RowBox[{
        FractionBox["1", "2"], " ", 
        SuperscriptBox[
         RowBox[{"(", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], ")"}], "2"]}]}], "0", "0"},
     {"0", "0", 
      RowBox[{
       RowBox[{"-", 
        FractionBox["1", "2"]}], " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"M", "(", 
          RowBox[{"u", ",", "v"}], ")"}], "-", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}], "+", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None]}], ")"}]}]}], "+", 
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], " ", 
          RowBox[{"(", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], "+", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], ")"}]}], "+", 
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], " ", 
          RowBox[{"(", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], "+", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], ")"}]}]}], ")"}]}], "0"},
     {"0", "0", "0", 
      RowBox[{
       RowBox[{"-", 
        FractionBox["1", "2"]}], " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"M", "(", 
          RowBox[{"u", ",", "v"}], ")"}], "-", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}], "-", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"2", " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None]}], ")"}]}]}], "+", 
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], " ", 
          RowBox[{"(", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], "-", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], ")"}]}], "+", 
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], " ", 
          RowBox[{"(", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], "-", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], ")"}]}]}], ")"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970313941002*^9, 3.82402568878054*^9, 
  3.8240264728269157`*^9},
 CellLabel->
  "Out[51]//TraditionalForm=",ExpressionUUID->"371ccef3-7e73-41b3-814d-\
e785bbbd9682"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "8", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "8", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"TensorValues", "[", 
     RowBox[{"tensorList", "[", 
      RowBox[{"[", "8", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], " ",
    "//", " ", "Simplify"}], " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.82093465870828*^9, 3.820934665723707*^9}, 
   3.820937492206532*^9, 3.821110229353163*^9, {3.8239681863164577`*^9, 
   3.82396819236261*^9}, 3.824026472827045*^9},
 CellLabel->"In[52]:=",ExpressionUUID->"fe54afe2-6fee-4c36-b691-dc7e0e045387"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["C", "\[Alpha]\[Beta]\[Gamma]\[Delta]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970325977126*^9, 3.8240256887972517`*^9, 
  3.824026472827137*^9},
 CellLabel->"Out[52]=",ExpressionUUID->"41265c6c-3b25-4a88-b22a-0c1a00889f04"],

Cell[BoxData["\<\"WeylTensorBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970325977126*^9, 3.824025688802031*^9, 
  3.824026472827231*^9},
 CellLabel->"Out[53]=",ExpressionUUID->"3363190b-557a-4abe-a1ec-f2a7525608d1"],

Cell[BoxData[
 FormBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "3"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{"-", 
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0"},
         {
          RowBox[{
           FractionBox["1", "3"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{"-", 
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}], "0"},
         {"0", "0", 
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0"},
         {
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", "0", 
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", "0", "0"},
         {
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]},
     {
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", 
          RowBox[{
           FractionBox["1", "3"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{"-", 
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0"},
         {
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "3"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{"-", 
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", 
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0"},
         {"0", "0", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}], "0"},
         {
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}], "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", 
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}]},
         {"0", "0", "0", "0"},
         {
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}], "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]},
     {
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}], "0"},
         {"0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0"},
         {
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0"},
         {"0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}], "0"},
         {
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}], "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", 
          RowBox[{
           FractionBox["1", "3"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"2", " ", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "3"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"2", " ", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]},
     {
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", "0", "0"},
         {
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["u", "2"]}],
              MultilineFunction->None], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "6"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", "0", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}]},
         {"0", "0", "0", "0"},
         {
          RowBox[{
           FractionBox["1", "6"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "2"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"-", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], "-", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "-", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], "+", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", 
               SuperscriptBox["v", "2"]}],
              MultilineFunction->None]}], ")"}]}], "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", 
          RowBox[{
           RowBox[{"-", 
            FractionBox["1", "3"]}], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"2", " ", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}]},
         {"0", "0", 
          RowBox[{
           FractionBox["1", "3"], " ", 
           SuperscriptBox["\[ExponentialE]", 
            RowBox[{
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}], "-", 
             RowBox[{"2", " ", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}]}]], " ", 
           RowBox[{"(", 
            RowBox[{
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "-", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None], "+", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], " ", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"V", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}]}], ")"}]}], "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}], 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"},
         {"0", "0", "0", "0"}
        },
        GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}}], "\[NoBreak]", ")"}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.823970325977126*^9, 3.824025689276886*^9, 
  3.824026472827297*^9},
 CellLabel->
  "Out[54]//TraditionalForm=",ExpressionUUID->"db5d3699-b4cd-49b3-bf1e-\
19dbdbbd7824"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"tensorList", "[", 
   RowBox[{"[", "9", "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"TensorName", "[", 
   RowBox[{"tensorList", "[", 
    RowBox[{"[", "9", "]"}], "]"}], "]"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "9", "]"}], "]"}], "]"}], "  ", "//", " ", "Expand"}], 
    " ", "//", " ", "Simplify"}], "  ", "//", " ", "MatrixForm"}], "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.82093465870828*^9, 3.820934665723707*^9}, 
   3.820937492206532*^9, 3.821110229353163*^9, {3.8239676252814713`*^9, 
   3.8239676285918293`*^9}, {3.823968202196871*^9, 3.823968207554695*^9}, {
   3.823970440124268*^9, 3.823970442004127*^9}, 3.824026472827426*^9},
 CellLabel->"In[55]:=",ExpressionUUID->"3103a7c9-bbf7-4410-ae44-783a83df09ee"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["C", "\[Alpha]\[Beta]\[Gamma]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239703388188877`*^9, 3.8239704422605743`*^9, 
  3.824025689302249*^9, 3.824026472827511*^9},
 CellLabel->"Out[55]=",ExpressionUUID->"42cd9383-d9e2-4077-8a99-adec80e28c1b"],

Cell[BoxData["\<\"CottonTensorBellSzekers\"\>"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239703388188877`*^9, 3.8239704422605743`*^9, 
  3.824025689307178*^9, 3.82402647282761*^9},
 CellLabel->"Out[56]=",ExpressionUUID->"039c28f6-84a8-4479-b38e-34d4a07ff496"],

Cell[BoxData[
 FormBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {
            RowBox[{
             FractionBox["1", "3"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                RowBox[{"2", " ", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "3"], 
                   RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None]}], ")"}]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None]}], ")"}]}]}], ")"}]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{
             FractionBox["1", "3"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None]}], ")"}]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None]}], ")"}]}]}], ")"}]}]},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {
            RowBox[{
             FractionBox["1", "3"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                RowBox[{
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None], " ", 
                 RowBox[{"(", 
                  RowBox[{
                   RowBox[{"-", 
                    RowBox[{"2", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}]}], "+", 
                   RowBox[{"2", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                   RowBox[{
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None]}]}], ")"}]}]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}]}], ")"}]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{
             FractionBox["1", "3"], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{"-", 
                   RowBox[{"2", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}]}], "+", 
                  RowBox[{"2", " ", 
                   FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None]}]}], ")"}]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}]}], ")"}]}]},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "6"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "+", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                RowBox[{"2", " ", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "3"], 
                   RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "-", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}]}], ")"}]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "+", 
                  RowBox[{"3", " ", 
                   SuperscriptBox[
                    RowBox[{"(", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]}], 
              ")"}]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "6"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "+", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                RowBox[{"3", " ", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None], " ", 
                 RowBox[{"(", 
                  RowBox[{
                   RowBox[{"-", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                   FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "-", 
                   RowBox[{"2", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                   RowBox[{
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None]}]}], ")"}]}]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None], " ", 
                   RowBox[{"(", 
                    RowBox[{
                    RowBox[{"3", " ", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], ")"}]}], "-", 
                  RowBox[{"2", " ", 
                   RowBox[{"(", 
                    RowBox[{
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "-", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "+", 
                    RowBox[{"3", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}]}], ")"}]}]}], ")"}]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                SuperscriptBox[
                 RowBox[{"(", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "6"]}], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "+", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                RowBox[{"2", " ", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "3"], 
                   RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "-", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}]}], ")"}]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "+", 
                  RowBox[{"3", " ", 
                   SuperscriptBox[
                    RowBox[{"(", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]}], 
              ")"}]}]},
           {
            RowBox[{
             RowBox[{"-", 
              FractionBox["1", "6"]}], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "+", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                RowBox[{"3", " ", 
                 FractionBox[
                  RowBox[{"\[PartialD]", 
                   RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{"\[PartialD]", "v"}],
                  MultilineFunction->None], " ", 
                 RowBox[{"(", 
                  RowBox[{
                   RowBox[{"-", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                   FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "-", 
                   RowBox[{"2", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                   RowBox[{
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None]}]}], ")"}]}]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None], " ", 
                   RowBox[{"(", 
                    RowBox[{
                    RowBox[{"3", " ", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], ")"}]}], "-", 
                  RowBox[{"2", " ", 
                   RowBox[{"(", 
                    RowBox[{
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "-", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "+", 
                    RowBox[{"3", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}]}], ")"}]}]}], ")"}]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                SuperscriptBox[
                 RowBox[{"(", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]},
      {
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "6"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"-", 
                RowBox[{"2", " ", 
                 FractionBox[
                  RowBox[{
                   SuperscriptBox["\[PartialD]", "3"], 
                   RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                  RowBox[{
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                   RowBox[{"\[PartialD]", "v"}]}],
                  MultilineFunction->None]}]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "-", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}]}], ")"}]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "-", 
                  RowBox[{"3", " ", 
                   SuperscriptBox[
                    RowBox[{"(", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]}], 
              ")"}]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {
            RowBox[{
             FractionBox["1", "6"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "-", 
                  RowBox[{"2", " ", 
                   FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None]}]}], ")"}]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{"-", 
                   RowBox[{"2", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}]}], "+", 
                  RowBox[{"2", " ", 
                   FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                  RowBox[{"6", " ", 
                   FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None], " ", 
                   RowBox[{"(", 
                    RowBox[{
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], "-", 
                    RowBox[{"3", " ", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}]}], ")"}]}]}], ")"}]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                SuperscriptBox[
                 RowBox[{"(", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {"0"},
           {"0"},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}], 
       RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
           {
            RowBox[{
             FractionBox["1", "6"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["u", "2"]}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "-", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}]}], ")"}]}], "-", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "+", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", 
                    SuperscriptBox["u", "2"]}],
                   MultilineFunction->None], "-", 
                  RowBox[{"3", " ", 
                   SuperscriptBox[
                    RowBox[{"(", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]}], 
              ")"}]}]},
           {
            RowBox[{
             FractionBox["1", "6"], " ", 
             SuperscriptBox["\[ExponentialE]", 
              RowBox[{
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}], "-", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
             RowBox[{"(", 
              RowBox[{
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  RowBox[{"2", " ", 
                   RowBox[{"(", 
                    RowBox[{
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "-", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None], "-", 
                    RowBox[{"3", " ", 
                    FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}]}], ")"}]}], "+", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None], " ", 
                   RowBox[{"(", 
                    RowBox[{
                    RowBox[{"3", " ", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], "-", 
                    FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None]}], ")"}]}]}], ")"}]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                RowBox[{"(", 
                 RowBox[{
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"M", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "-", 
                  FractionBox[
                   RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                   MultilineFunction->None], "-", 
                  RowBox[{"2", " ", 
                   FractionBox[
                    RowBox[{
                    SuperscriptBox["\[PartialD]", "2"], 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{
                    RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                    RowBox[{"\[PartialD]", "v"}]}],
                    MultilineFunction->None]}], "+", 
                  RowBox[{
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"U", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "u"}],
                    MultilineFunction->None], " ", 
                   FractionBox[
                    RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                    RowBox[{"\[PartialD]", "v"}],
                    MultilineFunction->None]}]}], ")"}]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"M", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{"6", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "3"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", 
                   SuperscriptBox["v", "2"]}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "v"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "-", 
               RowBox[{
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", 
                  SuperscriptBox["v", "2"]}],
                 MultilineFunction->None]}], "+", 
               RowBox[{"3", " ", 
                FractionBox[
                 RowBox[{"\[PartialD]", 
                  RowBox[{"V", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{"\[PartialD]", "u"}],
                 MultilineFunction->None], " ", 
                SuperscriptBox[
                 RowBox[{"(", 
                  FractionBox[
                   RowBox[{"\[PartialD]", 
                    RowBox[{"V", "(", 
                    RowBox[{"u", ",", "v"}], ")"}]}], 
                   RowBox[{"\[PartialD]", "v"}],
                   MultilineFunction->None], ")"}], "2"]}]}], ")"}]}]},
           {"0"},
           {"0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.5599999999999999]}, 
              Offset[0.27999999999999997`]}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}}],
         Column], "\[NoBreak]", ")"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.7]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}], "\[NoBreak]", ")"}],
   Function[BoxForm`e$, 
    MatrixForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8239703388188877`*^9, 3.8239704422605743`*^9, 
  3.8240256901223087`*^9, 3.82402647282768*^9},
 CellLabel->
  "Out[57]//TraditionalForm=",ExpressionUUID->"4885febb-a2b1-417c-9fa4-\
9a58c2b2392e"]
}, Closed]],

Cell[CellGroupData[{

Cell["Derivation of Field Equations ", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.82402643828969*^9, 3.824026453960885*^9}, {
  3.825287878398224*^9, 
  3.825287886062241*^9}},ExpressionUUID->"0497c6ca-0986-4949-80f3-\
3020af7b17c4"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "nonzeroRicci", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"nonzeroRicci", " ", "=", " ", 
   RowBox[{"{", " ", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{"TensorValues", "[", 
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "4", "]"}], "]"}], "]"}], "[", 
      RowBox[{"[", 
       RowBox[{"1", ",", "1"}], "]"}], "]"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"TensorValues", "[", 
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "4", "]"}], "]"}], "]"}], "[", 
      RowBox[{"[", 
       RowBox[{"1", ",", "2"}], "]"}], "]"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"TensorValues", "[", 
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "4", "]"}], "]"}], "]"}], "[", 
      RowBox[{"[", 
       RowBox[{"2", ",", "2"}], "]"}], "]"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{"TensorValues", "[", 
        RowBox[{"tensorList", "[", 
         RowBox[{"[", "4", "]"}], "]"}], "]"}], "[", 
       RowBox[{"[", 
        RowBox[{"3", ",", "3"}], "]"}], "]"}], "[", 
      RowBox[{"[", "3", "]"}], "]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{"TensorValues", "[", 
        RowBox[{"tensorList", "[", 
         RowBox[{"[", "4", "]"}], "]"}], "]"}], "[", 
       RowBox[{"[", 
        RowBox[{"4", ",", "4"}], "]"}], "]"}], "[", 
      RowBox[{"[", "3", "]"}], "]"}]}], "\[IndentingNewLine]", "}"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"nonzeroRicci", "  ", "//", " ", "TableForm"}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970356539381*^9, 3.8239704341106033`*^9}, 
   3.824026433416278*^9},
 CellLabel->"In[58]:=",ExpressionUUID->"01c3549b-df62-4083-9e27-a3517ae51a04"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None]}], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["u", "2"]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}]}]},
      {
       RowBox[{
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["v", "2"]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"]}]}]},
      {
       RowBox[{
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{
           RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
           RowBox[{"\[PartialD]", "v"}]}],
          MultilineFunction->None]}], "-", 
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{
           RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
           RowBox[{"\[PartialD]", "v"}]}],
          MultilineFunction->None]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], "-", 
           RowBox[{"2", " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}]}], ")"}]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{
        RowBox[{"-", 
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None], "+", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], ")"}]}]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"2", " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], "+", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None]}], ")"}]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970359321269*^9, 3.82397038449714*^9}, {
   3.823970420983902*^9, 3.823970434513886*^9}, 3.824025690239011*^9, 
   3.8240264334163933`*^9},
 CellLabel->
  "Out[60]//TraditionalForm=",ExpressionUUID->"39bd0798-e125-4f0d-88ba-\
a342e2d1b738"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "nonzeroEinstein", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"nonzeroEinstein", " ", "=", " ", 
   RowBox[{"{", " ", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{"TensorValues", "[", 
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "7", "]"}], "]"}], "]"}], "[", 
      RowBox[{"[", 
       RowBox[{"1", ",", "1"}], "]"}], "]"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"TensorValues", "[", 
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "7", "]"}], "]"}], "]"}], "[", 
      RowBox[{"[", 
       RowBox[{"1", ",", "2"}], "]"}], "]"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"TensorValues", "[", 
       RowBox[{"tensorList", "[", 
        RowBox[{"[", "7", "]"}], "]"}], "]"}], "[", 
      RowBox[{"[", 
       RowBox[{"2", ",", "2"}], "]"}], "]"}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{"TensorValues", "[", 
        RowBox[{"tensorList", "[", 
         RowBox[{"[", "7", "]"}], "]"}], "]"}], "[", 
       RowBox[{"[", 
        RowBox[{"3", ",", "3"}], "]"}], "]"}], "[", 
      RowBox[{"[", "3", "]"}], "]"}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{"TensorValues", "[", 
        RowBox[{"tensorList", "[", 
         RowBox[{"[", "7", "]"}], "]"}], "]"}], "[", 
       RowBox[{"[", 
        RowBox[{"4", ",", "4"}], "]"}], "]"}], "[", 
      RowBox[{"[", "3", "]"}], "]"}]}], "\[IndentingNewLine]", "}"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"nonzeroEinstein", "  ", "//", " ", "TableForm"}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.8239704526686907`*^9, 3.823970472891984*^9}, 
   3.824026433416596*^9},
 CellLabel->"In[61]:=",ExpressionUUID->"13d26424-f102-4a87-b777-e13eaaf052aa"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None]}], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["u", "2"]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}]}]},
      {
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "-", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None]}]},
      {
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "+", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["v", "2"]}],
         MultilineFunction->None], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"]}]}]},
      {
       RowBox[{
        RowBox[{"-", 
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None], "+", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None], "+", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], ")"}]}]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], "+", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None]}], ")"}]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], "+", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None]}], ")"}]}]}]},
      {
       RowBox[{
        RowBox[{"-", 
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None], "+", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None], "-", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], ")"}]}]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], "-", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None]}], ")"}]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"(", 
          RowBox[{
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], "-", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None]}], ")"}]}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.823970473781507*^9, 3.824025690312984*^9, 
  3.824026433416687*^9},
 CellLabel->
  "Out[63]//TraditionalForm=",ExpressionUUID->"c145c29e-8ba0-45f5-99c7-\
2c7edba55219"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt4", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt4", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"Flatten", "[", 
      RowBox[{"Solve", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"nonzeroEinstein", " ", "[", 
          RowBox[{"[", "2", "]"}], "]"}], " ", "\[Equal]", " ", "0"}], " ", 
        ",", 
        RowBox[{
         SuperscriptBox["U", 
          TagBox[
           RowBox[{"(", 
            RowBox[{"1", ",", "1"}], ")"}],
           Derivative],
          MultilineFunction->None], "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
     RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
    RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt4", " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970493738421*^9, 3.823970537162098*^9}, 
   3.824026433417267*^9},
 CellLabel->"In[64]:=",ExpressionUUID->"82d648df-d710-490c-8571-7d6f84238eab"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970496428384*^9, 3.823970537624201*^9}, 
   3.824025690342875*^9, 3.82402643341733*^9},
 CellLabel->
  "Out[66]//TraditionalForm=",ExpressionUUID->"c5823668-fba9-47a2-bb59-\
4a3ef9a4ce5b"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt5a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt5a", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"Flatten", "[", 
      RowBox[{"Solve", "[", " ", 
       RowBox[{
        RowBox[{
         RowBox[{"nonzeroEinstein", "  ", "[", 
          RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", " ", "0"}], " ", ",", 
        " ", 
        RowBox[{
         SuperscriptBox["U", 
          TagBox[
           RowBox[{"(", 
            RowBox[{"2", ",", "0"}], ")"}],
           Derivative],
          MultilineFunction->None], "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}], "[", 
     RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
    RowBox[{"Rule", " ", "\[Rule]", " ", "Equal"}]}]}], "   ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt5a", " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970569634561*^9, 3.82397063008985*^9}, 
   3.8240264334174747`*^9},
 CellLabel->"In[67]:=",ExpressionUUID->"7d3a4c0d-4bb6-4ca1-8157-0703bf8c7eab"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["u", "2"]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None]}]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.8239705703441277`*^9, 3.823970630515171*^9}, 
   3.8240256903716373`*^9, 3.824026433417542*^9},
 CellLabel->
  "Out[69]//TraditionalForm=",ExpressionUUID->"3a6b9889-dd2d-4e72-9d91-\
205b5635300f"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt5", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt5", " ", "=", "\[IndentingNewLine]", 
   RowBox[{"MultiplySides", "[", " ", 
    RowBox[{"eq2pt5a", ",", "2"}], "]"}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt5", " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970632803411*^9, 3.823970681025927*^9}, 
   3.824026433417667*^9},
 CellLabel->"In[70]:=",ExpressionUUID->"cd75163d-b7f2-4081-a250-c841c273c662"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    FractionBox[
     RowBox[{
      SuperscriptBox["\[PartialD]", "2"], 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", 
      SuperscriptBox["u", "2"]}],
     MultilineFunction->None]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{"2", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None]}]}], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], ")"}], "2"], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], ")"}], "2"]}]}], TraditionalForm]], "Output",\

 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970645277911*^9, 3.823970650319294*^9}, 
   3.8239706816228237`*^9, 3.824025690399807*^9, 3.8240264334177437`*^9},
 CellLabel->
  "Out[72]//TraditionalForm=",ExpressionUUID->"7e1d0358-4631-43ed-8329-\
504e7a660a62"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt6a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt6a", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"Flatten", "[", 
      RowBox[{"Solve", "[", "  ", 
       RowBox[{
        RowBox[{
         RowBox[{"nonzeroEinstein", " ", "[", 
          RowBox[{"[", "3", "]"}], "]"}], " ", "\[Equal]", " ", "0"}], "  ", 
        ",", " ", 
        RowBox[{
         SuperscriptBox["U", 
          TagBox[
           RowBox[{"(", 
            RowBox[{"0", ",", "2"}], ")"}],
           Derivative],
          MultilineFunction->None], "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}], "[", 
     RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
    RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt6a", "  ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970700938325*^9, 3.823970755394554*^9}, 
   3.824026433417894*^9},
 CellLabel->"In[73]:=",ExpressionUUID->"b9717b03-36f7-45d9-8330-8a8eba05269d"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["v", "2"]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970703157488*^9, 3.823970755831532*^9}, 
   3.8240256904294443`*^9, 3.8240264334179564`*^9},
 CellLabel->
  "Out[75]//TraditionalForm=",ExpressionUUID->"8049029e-cfb7-4976-b8d4-\
1ff7052d8645"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt6", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt6", " ", "=", "\[IndentingNewLine]", 
   RowBox[{"MultiplySides", "[", " ", 
    RowBox[{"eq2pt6a", " ", ",", " ", "2"}], " ", "]"}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt6", " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970758011478*^9, 3.823970793577936*^9}, 
   3.824026433418065*^9},
 CellLabel->"In[76]:=",ExpressionUUID->"916b72a7-ff6d-407b-a396-b783a6760aa0"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    FractionBox[
     RowBox[{
      SuperscriptBox["\[PartialD]", "2"], 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", 
      SuperscriptBox["v", "2"]}],
     MultilineFunction->None]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{"2", " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None]}]}], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], ")"}], "2"], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], ")"}], "2"]}]}], TraditionalForm]], "Output",\

 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970769001815*^9, 3.823970794037657*^9}, 
   3.8240256904583597`*^9, 3.824026433418133*^9},
 CellLabel->
  "Out[78]//TraditionalForm=",ExpressionUUID->"1fcc1d5c-7ddb-4dff-8686-\
34d1916637b0"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt7a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt7a", " ", "=", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"Flatten", "[", 
      RowBox[{"Solve", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"Expand", "[", 
          RowBox[{
           RowBox[{"nonzeroEinstein", "[", 
            RowBox[{"[", "5", "]"}], "]"}], "-", 
           RowBox[{"nonzeroEinstein", "[", 
            RowBox[{"[", "4", "]"}], "]"}]}], "]"}], " ", "\[Equal]", " ", 
         "0"}], " ", ",", " ", 
        RowBox[{
         SuperscriptBox["V", 
          TagBox[
           RowBox[{"(", 
            RowBox[{"1", ",", "1"}], ")"}],
           Derivative],
          MultilineFunction->None], "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
     RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
    RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt7a", " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970819314603*^9, 3.8239708894902678`*^9}, 
   3.824026433418284*^9},
 CellLabel->"In[79]:=",ExpressionUUID->"7608b58b-c2c0-4c2f-a6b7-27252ca6ebef"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970824875135*^9, 3.823970890637349*^9}, 
   3.82402569048726*^9, 3.8240264334183483`*^9},
 CellLabel->
  "Out[81]//TraditionalForm=",ExpressionUUID->"bfd980e2-0cb2-407a-bbb0-\
42c4521f482d"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt7", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt7", " ", "=", "\[IndentingNewLine]", 
   RowBox[{"MultiplySides", "[", " ", 
    RowBox[{"eq2pt7a", ",", "2"}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt7", "  ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970897345932*^9, 3.823970923170033*^9}, 
   3.824026433418462*^9},
 CellLabel->"In[82]:=",ExpressionUUID->"efa1dbc0-8cfe-49b1-a0ab-be8249e64392"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    FractionBox[
     RowBox[{
      SuperscriptBox["\[PartialD]", "2"], 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{
      RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
      RowBox[{"\[PartialD]", "v"}]}],
     MultilineFunction->None]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970913010975*^9, 3.823970923746912*^9}, 
   3.824025690517276*^9, 3.8240264334185333`*^9},
 CellLabel->
  "Out[84]//TraditionalForm=",ExpressionUUID->"ed0e3a2e-f2e3-4ff2-a4b7-\
1a1e9b1604e0"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"Flatten", "[", 
     RowBox[{"Solve", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"Expand", "[", 
         RowBox[{
          RowBox[{"nonzeroEinstein", "[", 
           RowBox[{"[", "5", "]"}], "]"}], "+", 
          RowBox[{"nonzeroEinstein", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}], "]"}], " ", "\[Equal]", " ", 
        "0"}], " ", ",", " ", 
       RowBox[{
        SuperscriptBox["M", 
         TagBox[
          RowBox[{"(", 
           RowBox[{"1", ",", "1"}], ")"}],
          Derivative],
         MultilineFunction->None], "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
   RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}], "  ", "//", " ", 
  "pdConv"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.8239709386346693`*^9, 3.823970975586102*^9}, 
   3.824026433418667*^9},
 CellLabel->"In[85]:=",ExpressionUUID->"666fdeca-44db-4de1-ab18-1d773135a3c1"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"M", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None]}]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970939548642*^9, 3.8239709759549007`*^9}, 
   3.8240256905467863`*^9, 3.824026433418737*^9},
 CellLabel->
  "Out[85]//TraditionalForm=",ExpressionUUID->"ccd03e5c-25d9-47a4-a132-\
44356f627047"],

Cell[BoxData[
 RowBox[{
  RowBox[{"eq2pt4", " ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", "//", " ", 
  "pdConv"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970981875642*^9, 3.823970994097889*^9}, 
   3.8240264334188337`*^9},
 CellLabel->"In[86]:=",ExpressionUUID->"8f16f23f-970d-4a5e-ba75-4fc94a5a198e"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823970984118395*^9, 3.8239709944970913`*^9}, 
   3.824025690555913*^9, 3.8240264334188957`*^9},
 CellLabel->
  "Out[86]//TraditionalForm=",ExpressionUUID->"1b94b374-1576-4ba4-8d1f-\
fb8021509deb"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt8a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt8a", " ", "=", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"Flatten", "[", 
        RowBox[{"Solve", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"Expand", "[", 
            RowBox[{
             RowBox[{"nonzeroEinstein", "[", 
              RowBox[{"[", "5", "]"}], "]"}], "+", 
             RowBox[{"nonzeroEinstein", "[", 
              RowBox[{"[", "4", "]"}], "]"}]}], "]"}], " ", "\[Equal]", " ", 
           "0"}], " ", ",", " ", 
          RowBox[{
           SuperscriptBox["M", 
            TagBox[
             RowBox[{"(", 
              RowBox[{"1", ",", "1"}], ")"}],
             Derivative],
            MultilineFunction->None], "[", 
           RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
      RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}], "  ", ")"}], " ", "/.", 
    " ", 
    RowBox[{"(", " ", 
     RowBox[{"eq2pt4", " ", "/.", " ", 
      RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], ")"}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt8a", "  ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971002235572*^9, 3.823971044529935*^9}, 
   3.824026433419085*^9},
 CellLabel->"In[87]:=",ExpressionUUID->"0a834094-8203-40b8-aa2a-4cdaa8071c41"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"M", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}], "-", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.823971011634865*^9, 3.823971045156125*^9, 
  3.824025690587617*^9, 3.824026433419209*^9},
 CellLabel->
  "Out[89]//TraditionalForm=",ExpressionUUID->"fb9ffb60-f9d8-4140-896d-\
bc592303a0b7"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt8", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt8", " ", "=", "\[IndentingNewLine]", 
   RowBox[{"MultiplySides", "[", 
    RowBox[{"eq2pt8a", " ", ",", "2"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt8", " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971051044434*^9, 3.823971083906088*^9}, 
   3.8240264334193897`*^9},
 CellLabel->"In[90]:=",ExpressionUUID->"99270483-fbf8-4384-8119-44bc52fd7946"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    FractionBox[
     RowBox[{
      SuperscriptBox["\[PartialD]", "2"], 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{
      RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
      RowBox[{"\[PartialD]", "v"}]}],
     MultilineFunction->None]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971054760035*^9, 3.823971084434679*^9}, 
   3.824025690617333*^9, 3.824026433419599*^9},
 CellLabel->
  "Out[92]//TraditionalForm=",ExpressionUUID->"e8363f05-76da-4539-8e63-\
c89ce19fb66f"]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Check", " ", "of", " ", "Equation", " ", "2.9"}], " ", "*)"}], 
  " "}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8240263843449163`*^9, 
  3.824026413136874*^9}},ExpressionUUID->"7eeb4c14-37bb-4bb6-8062-\
2aab8b2b4a06"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt9", "]"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt9", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Exp", "[", 
    RowBox[{"-", 
     RowBox[{"U", "[", 
      RowBox[{"u", ",", "v"}], "]"}]}], "]"}], " ", "\[Equal]", " ", 
   RowBox[{
    RowBox[{"f", "[", "u", "]"}], " ", "+", " ", 
    RowBox[{"g", "[", "v", "]"}], " "}]}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.824026016765567*^9, 3.824026040204052*^9}, 
   3.824026396859439*^9},
 CellLabel->
  "In[175]:=",ExpressionUUID->"6db4a4ad-ab78-4d2d-91a0-fecd7833a1cc"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{"-", 
    RowBox[{"U", "[", 
     RowBox[{"u", ",", "v"}], "]"}]}]], "\[Equal]", 
  RowBox[{
   RowBox[{"f", "[", "u", "]"}], "+", 
   RowBox[{"g", "[", "v", "]"}]}]}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.8240260417194567`*^9, 3.824026396859603*^9},
 CellLabel->
  "Out[176]=",ExpressionUUID->"d0da37b6-a599-475e-ae0a-20d665722304"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "uReplace", "]"}], "\[IndentingNewLine]", 
 RowBox[{"uReplace", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"Flatten", "[", 
     RowBox[{"Solve", "[", " ", 
      RowBox[{"eq2pt9", " ", ",", " ", 
       RowBox[{"U", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
   RowBox[{
    RowBox[{"C", "[", "1", "]"}], "\[Rule]", " ", "0", "  "}]}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.82402604422931*^9, 3.824026122870537*^9}, 
   3.824026396859743*^9},
 CellLabel->
  "In[188]:=",ExpressionUUID->"1d4a6267-5f4e-45aa-a850-2df5e57aa7d5"],

Cell[BoxData[
 RowBox[{
  RowBox[{"U", "[", 
   RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", 
  RowBox[{"Log", "[", 
   FractionBox["1", 
    RowBox[{
     RowBox[{"f", "[", "u", "]"}], "+", 
     RowBox[{"g", "[", "v", "]"}]}]], "]"}]}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8240260513465633`*^9, 3.8240260660352592`*^9}, {
   3.824026099998914*^9, 3.824026123086073*^9}, 3.82402639685988*^9},
 CellLabel->
  "Out[189]=",ExpressionUUID->"40369f05-d917-467f-9952-5ee18be4fe07"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"D", "[", " ", 
   RowBox[{"uReplace", " ", ",", " ", "u"}], " ", "]"}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"D", "[", " ", 
   RowBox[{"uReplace", " ", ",", " ", "v"}], " ", "]"}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"D", "[", 
   RowBox[{"D", "[", " ", 
    RowBox[{"uReplace", " ", ",", " ", "u", " ", ",", "v"}], "]"}], "]"}], 
  " ", "//", " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.824026107188768*^9, 3.824026140644038*^9}, 
   3.824026396860016*^9},
 CellLabel->
  "In[193]:=",ExpressionUUID->"140cec33-6804-403d-93f4-8fe86ce085d9"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "u"}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{"-", 
    FractionBox[
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"f", "(", "u", ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], 
     RowBox[{
      RowBox[{"f", "(", "u", ")"}], "+", 
      RowBox[{"g", "(", "v", ")"}]}]]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8240261129480467`*^9, 3.824026140985241*^9}, 
   3.824026396860087*^9},
 CellLabel->
  "Out[193]//TraditionalForm=",ExpressionUUID->"e52e42c3-a2ec-47c8-9b42-\
8751672d2a2d"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "v"}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{"-", 
    FractionBox[
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"g", "(", "v", ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], 
     RowBox[{
      RowBox[{"f", "(", "u", ")"}], "+", 
      RowBox[{"g", "(", "v", ")"}]}]]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8240261129480467`*^9, 3.8240261409883223`*^9}, 
   3.824026396860155*^9},
 CellLabel->
  "Out[194]//TraditionalForm=",ExpressionUUID->"c1543372-1802-40c4-b68c-\
7bc622020b4b"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   FractionBox[
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"f", "(", "u", ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"g", "(", "v", ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"f", "(", "u", ")"}], "+", 
       RowBox[{"g", "(", "v", ")"}]}], ")"}], "2"]]}], 
  TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8240261129480467`*^9, 3.824026140991247*^9}, 
   3.8240263968602467`*^9},
 CellLabel->
  "Out[195]//TraditionalForm=",ExpressionUUID->"37a53ba4-b6d9-4cbe-9727-\
ca46e0636eba"],

Cell[BoxData[
 RowBox[{"eq2pt4", " ", "//", " ", "pdConv"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.82402607242056*^9, 3.8240260836125793`*^9}, 
   3.824026396860362*^9},
 CellLabel->
  "In[181]:=",ExpressionUUID->"da4a99b1-1af5-4eda-a4e1-ecbfac4ba626"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8240260790266542`*^9, 3.824026083924749*^9}, 
   3.824026396860464*^9},
 CellLabel->
  "Out[181]//TraditionalForm=",ExpressionUUID->"95a830d0-8c22-4259-a7b4-\
26d5d7671f46"],

Cell[BoxData[{
 RowBox[{"eq2pt4", " ", "//", " ", "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt4", " ", "/.", " ", 
   RowBox[{"D", "[", " ", 
    RowBox[{"uReplace", " ", ",", " ", "u"}], " ", "]"}]}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"eq2pt4", " ", "/.", " ", 
    RowBox[{"D", "[", " ", 
     RowBox[{"uReplace", " ", ",", " ", "u"}], " ", "]"}]}], " ", "/.", "  ", 
   
   RowBox[{"D", "[", " ", 
    RowBox[{"uReplace", " ", ",", " ", "v"}], " ", "]"}]}], "  ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"eq2pt4", " ", "/.", " ", 
    RowBox[{"D", "[", " ", 
     RowBox[{"uReplace", " ", ",", " ", "u"}], " ", "]"}]}], " ", "/.", "  ", 
   
   RowBox[{"D", "[", " ", 
    RowBox[{"uReplace", " ", ",", " ", "v"}], " ", "]"}]}], "  ", "/.", " ", 
  RowBox[{"D", "[", 
   RowBox[{"D", "[", " ", 
    RowBox[{"uReplace", " ", ",", " ", "u", " ", ",", "v"}], "]"}], "]"}], 
  " "}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{{3.8240262890194263`*^9, 3.824026361722859*^9}, 
   3.8240263968606367`*^9},
 CellLabel->
  "In[212]:=",ExpressionUUID->"d880fbbf-f733-492a-811b-abe07524f5d8"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{
  3.824026290551064*^9, {3.824026326361156*^9, 3.824026396860701*^9}},
 CellLabel->
  "Out[212]//TraditionalForm=",ExpressionUUID->"775670b7-465f-4874-8040-\
f82dbec7a0fc"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{"-", 
    FractionBox[
     RowBox[{
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"f", "(", "u", ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None]}], 
     RowBox[{
      RowBox[{"f", "(", "u", ")"}], "+", 
      RowBox[{"g", "(", "v", ")"}]}]]}]}], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{
  3.824026290551064*^9, {3.824026326361156*^9, 3.824026396860767*^9}},
 CellLabel->
  "Out[213]//TraditionalForm=",ExpressionUUID->"536716b0-d7b4-446e-97a6-\
0a2c68ee71a7"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[LongEqual]", 
   FractionBox[
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"f", "(", "u", ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"g", "(", "v", ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"f", "(", "u", ")"}], "+", 
       RowBox[{"g", "(", "v", ")"}]}], ")"}], "2"]]}], 
  TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{
  3.824026290551064*^9, {3.824026326361156*^9, 3.824026396860833*^9}},
 CellLabel->
  "Out[214]//TraditionalForm=",ExpressionUUID->"4f4426e5-afe3-4b6c-aff8-\
fdd0b576b228"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{
  3.824026290551064*^9, {3.824026326361156*^9, 3.82402639686094*^9}},
 CellLabel->
  "Out[215]=",ExpressionUUID->"4e988d59-5564-4527-af17-061924b79f17"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Construction of null tetrad and check of orthognality and completeness \
relations  \
\>", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.824026535258623*^9, 3.824026560337151*^9}, {
  3.825287905995892*^9, 
  3.825287912744693*^9}},ExpressionUUID->"c6912e27-4aa1-44dd-bbf2-\
dcd9c65b2a68"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "\[ScriptL]", "]"}], "\[IndentingNewLine]", 
 RowBox[{"\[ScriptL]", "=", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"Exp", "[", 
      FractionBox[
       RowBox[{"-", "M"}], "2"], "]"}], ",", "0", ",", "0", ",", "0"}], "}"}],
    " ", "/.", " ", "eq2pt1a", " "}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.820933371686145*^9, 3.82093337715728*^9}, 
   3.8209374103413973`*^9, 3.820944472322248*^9, {3.823967911447504*^9, 
   3.823967916197978*^9}, {3.823968540109717*^9, 3.8239685564285727`*^9}, 
   3.823968587580859*^9, 3.82396866941901*^9, {3.8239711493371162`*^9, 
   3.82397121894984*^9}, {3.8239722022844763`*^9, 3.823972206738372*^9}, 
   3.824026530427024*^9},
 CellLabel->"In[93]:=",ExpressionUUID->"fe196da8-c141-432c-a79e-62d87c8b4bcd"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "2"]}], " ", 
     RowBox[{"M", "[", 
      RowBox[{"u", ",", "v"}], "]"}]}]], ",", "0", ",", "0", ",", "0"}], 
  "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.820933237654937*^9, 3.820933379685409*^9, 3.820933448095758*^9, 
   3.820937410341577*^9, 3.820944472322352*^9, {3.823968034002281*^9, 
   3.823968037684132*^9}, {3.82396855701134*^9, 3.823968592795348*^9}, 
   3.823971296238562*^9, 3.8239714273052597`*^9, 3.823971944995579*^9, 
   3.8239722192511263`*^9, 3.824025690628471*^9, 3.824026530427134*^9},
 CellLabel->"Out[94]=",ExpressionUUID->"1a289938-5842-4ffd-94d8-1b8bef3d9d87"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "\[ScriptN]", "]"}], "\[IndentingNewLine]", 
 RowBox[{"\[ScriptN]", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"Exp", "[", 
      FractionBox[
       RowBox[{"-", "M"}], "2"], "]"}], ",", "0", ",", "0"}], "}"}], " ", "/.",
    " ", "eq2pt1a", " "}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.820933298406392*^9, 3.820933313508857*^9}, 
   3.820937410341757*^9, 3.820944472322452*^9, {3.823967926390813*^9, 
   3.823967938078244*^9}, {3.82397118184247*^9, 3.823971221724759*^9}, {
   3.8239722094274054`*^9, 3.823972211596774*^9}, 3.8240265304272738`*^9},
 CellLabel->"In[95]:=",ExpressionUUID->"8c89aee3-65c1-49a8-9e2b-c5774c14564d"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0", ",", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "2"]}], " ", 
     RowBox[{"M", "[", 
      RowBox[{"u", ",", "v"}], "]"}]}]], ",", "0", ",", "0"}], 
  "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.820933313826449*^9, 3.820933381335147*^9, 3.820933448122315*^9, 
   3.820937410341963*^9, 3.820944472322535*^9, 3.823967938446355*^9, 
   3.82396803771756*^9, {3.82396856379178*^9, 3.823968592827444*^9}, 
   3.823971296297195*^9, 3.8239714273451967`*^9, 3.823971945038321*^9, 
   3.823972219287876*^9, 3.8240256906564217`*^9, 3.824026530427362*^9},
 CellLabel->"Out[96]=",ExpressionUUID->"e1821211-0047-44dc-9425-9c45f19e5e41"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "\[ScriptM]", "]"}], "\[IndentingNewLine]", 
 RowBox[{"\[ScriptM]", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     FractionBox["1", 
      SqrtBox["2"]], ")"}], 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", " ", 
      RowBox[{
       RowBox[{"Exp", "[", 
        FractionBox[
         RowBox[{"-", "U"}], "2"], "]"}], 
       RowBox[{"Exp", "[", 
        FractionBox["V", "2"], "]"}]}], ",", " ", 
      RowBox[{"\[ImaginaryI]", " ", 
       RowBox[{"Exp", "[", 
        FractionBox[
         RowBox[{"-", "U"}], "2"], "]"}], 
       RowBox[{"Exp", "[", 
        FractionBox[
         RowBox[{"-", "V"}], "2"], "]"}]}]}], "}"}]}], " ", "/.", " ", 
   "eq2pt1a", " "}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.820933317854281*^9, 3.8209333396620893`*^9}, 
   3.820937410342205*^9, 3.820944472322617*^9, {3.8239679452553387`*^9, 
   3.823967956845615*^9}, {3.8239712238335657`*^9, 3.8239712784335203`*^9}, 
   3.824026530427495*^9},
 CellLabel->"In[97]:=",ExpressionUUID->"b70c5d5e-37b0-4abd-a2cf-b33a307c83f2"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0", ",", "0", ",", 
   FractionBox[
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        FractionBox["1", "2"]}], " ", 
       RowBox[{"U", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], "+", 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"V", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}]}]], 
    SqrtBox["2"]], ",", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{
       RowBox[{
        RowBox[{"-", 
         FractionBox["1", "2"]}], " ", 
        RowBox[{"U", "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], "-", 
       RowBox[{
        FractionBox["1", "2"], " ", 
        RowBox[{"V", "[", 
         RowBox[{"u", ",", "v"}], "]"}]}]}]]}], 
    SqrtBox["2"]]}], "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.820933339966406*^9, 3.8209333835387917`*^9, 3.8209334481343927`*^9, 
   3.82093741034233*^9, 3.820944472322708*^9, 3.823967957571436*^9, 
   3.823968037726838*^9, {3.823968563805141*^9, 3.823968592838423*^9}, 
   3.8239712963071613`*^9, 3.823971427358354*^9, 3.8239719450513573`*^9, 
   3.823972219299691*^9, 3.824025690670985*^9, 3.824026530427579*^9},
 CellLabel->"Out[98]=",ExpressionUUID->"a96321b2-5d18-4b57-bff2-4f95d4f7950d"],

Cell[BoxData[{
 RowBox[{"Clear", "[", "\[ScriptM]bar", "]"}], "\[IndentingNewLine]", 
 RowBox[{"\[ScriptM]bar", " ", "=", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     FractionBox["1", 
      SqrtBox["2"]], ")"}], 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", " ", 
      RowBox[{
       RowBox[{"Exp", "[", 
        FractionBox[
         RowBox[{"-", "U"}], "2"], "]"}], 
       RowBox[{"Exp", "[", 
        FractionBox["V", "2"], "]"}]}], ",", " ", 
      RowBox[{
       RowBox[{"-", "\[ImaginaryI]"}], " ", 
       RowBox[{"Exp", "[", 
        FractionBox[
         RowBox[{"-", "U"}], "2"], "]"}], 
       RowBox[{"Exp", "[", 
        FractionBox[
         RowBox[{"-", "V"}], "2"], "]"}]}]}], "}"}]}], " ", "/.", " ", 
   "eq2pt1a", " "}]}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.820933342941945*^9, 3.8209333673030777`*^9}, 
   3.820937410342538*^9, 3.820944472322826*^9, {3.8239679651277733`*^9, 
   3.823967969398988*^9}, {3.823971226954356*^9, 3.823971228365078*^9}, {
   3.823971286537764*^9, 3.8239712869023438`*^9}, 3.823971416100823*^9, 
   3.82402653042771*^9},
 CellLabel->"In[99]:=",ExpressionUUID->"502b01ab-9d3a-43f4-97cf-d537edf6b81c"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0", ",", "0", ",", 
   FractionBox[
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        FractionBox["1", "2"]}], " ", 
       RowBox[{"U", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], "+", 
      RowBox[{
       FractionBox["1", "2"], " ", 
       RowBox[{"V", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}]}]], 
    SqrtBox["2"]], ",", 
   RowBox[{"-", 
    FractionBox[
     RowBox[{"\[ImaginaryI]", " ", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], " ", 
         RowBox[{"U", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}], "-", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]}]]}], 
     SqrtBox["2"]]}]}], "}"}]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.820933367920988*^9, 3.820933385725149*^9}, 
   3.82093344816428*^9, 3.820937410342681*^9, 3.820944472322927*^9, 
   3.823967969891004*^9, 3.823968037745193*^9, {3.823968563832972*^9, 
   3.82396859285539*^9}, 3.8239712963420553`*^9, 3.8239714273818274`*^9, 
   3.823971945073577*^9, 3.823972219319309*^9, 3.824025690703884*^9, 
   3.824026530427799*^9},
 CellLabel->
  "Out[100]=",ExpressionUUID->"6dc8c8e8-c9c4-4bae-baa5-ff309c16f3ca"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
   "Always", " ", "check", " ", "if", " ", "indices", " ", "needed", " ", 
    "are", " ", "up", " ", "or", " ", "down", " ", "and", " ", "they", " ", 
    "are", " ", "DOWN"}], " ", "*)"}], " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"l", " ", "=", " ", 
    RowBox[{"ToTensor", "[", " ", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"\"\<NewTensor\>\"", " ", ",", " ", "\"\<l\>\""}], "}"}], " ", 
      ",", " ", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", "\[ScriptL]", " ", ",", 
      " ", 
      RowBox[{"{", 
       RowBox[{"-", "\[Mu]"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", 
   RowBox[{"n", " ", "=", " ", 
    RowBox[{"ToTensor", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"\"\<NewTensor\>\"", " ", ",", " ", "\"\<n\>\""}], " ", "}"}], 
      " ", ",", " ", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", "\[ScriptN]", " ", ",", 
      " ", 
      RowBox[{"{", 
       RowBox[{"-", "\[Mu]"}], "}"}]}], " ", "]"}]}], " ", 
   "\[IndentingNewLine]", 
   RowBox[{"m", " ", "=", " ", 
    RowBox[{"ToTensor", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"\"\<NewTensor\>\"", " ", ",", " ", "\"\<m\>\""}], " ", "}"}], 
      " ", ",", " ", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", "\[ScriptM]", " ", ",", 
      " ", 
      RowBox[{"{", 
       RowBox[{"-", "\[Mu]"}], "}"}]}], " ", "]"}]}], " ", 
   "\[IndentingNewLine]", 
   RowBox[{"mbar", " ", "=", " ", 
    RowBox[{"ToTensor", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"\"\<NewTensor\>\"", " ", ",", " ", "\"\<mbar\>\""}], " ", 
       "}"}], " ", ",", " ", 
      RowBox[{"tensorList", "[", 
       RowBox[{"[", "1", "]"}], "]"}], " ", ",", " ", "\[ScriptM]bar", " ", 
      ",", " ", 
      RowBox[{"{", 
       RowBox[{"-", "\[Mu]"}], "}"}]}], " ", "]"}], " "}]}]}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.820937410342936*^9, 3.8209444723230133`*^9, {3.8239679754881287`*^9, 
   3.823967977734702*^9}, {3.823971899436349*^9, 3.823971905674711*^9}, 
   3.824026530428026*^9},
 CellLabel->
  "In[101]:=",ExpressionUUID->"b5e37d96-1d0f-4d4b-b55c-11f14530b6c7"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["l", "\[Mu]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.8239712963555813`*^9, 3.8239714273946657`*^9, 
  3.823971908956462*^9, 3.823971945087471*^9, 3.8239722193328543`*^9, 
  3.8240256907190027`*^9, 3.824026530428124*^9},
 CellLabel->
  "Out[101]=",ExpressionUUID->"f8b22cb3-9634-496f-b37a-daf767e11c75"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["n", "\[Mu]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.8239712963555813`*^9, 3.8239714273946657`*^9, 
  3.823971908956462*^9, 3.823971945087471*^9, 3.8239722193328543`*^9, 
  3.824025690724169*^9, 3.824026530428218*^9},
 CellLabel->
  "Out[102]=",ExpressionUUID->"64de66b5-a0d9-4467-822e-ee851ba5cdd4"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["m", "\[Mu]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.8239712963555813`*^9, 3.8239714273946657`*^9, 
  3.823971908956462*^9, 3.823971945087471*^9, 3.8239722193328543`*^9, 
  3.824025690729904*^9, 3.824026530428306*^9},
 CellLabel->
  "Out[103]=",ExpressionUUID->"1d3bc1ca-4f40-4faf-887f-00b1f481a77f"],

Cell[BoxData[
 TagBox[
  SubsuperscriptBox["mbar", "\[Mu]", ""],
  DisplayForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{3.8239712963555813`*^9, 3.8239714273946657`*^9, 
  3.823971908956462*^9, 3.823971945087471*^9, 3.8239722193328543`*^9, 
  3.824025690735392*^9, 3.824026530428389*^9},
 CellLabel->
  "Out[104]=",ExpressionUUID->"abc223f5-2925-4455-bf4f-e845261aefc3"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"l", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}], 
        RowBox[{"l", "[", "\[Mu]", "]"}]}], "]"}], "]"}], " ", "\[Equal]", 
     " ", "0"}], "  ", "//", " ", "Expand"}], " ", "//", " ", "Simplify"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"n", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}], 
        RowBox[{"n", "[", "\[Mu]", "]"}]}], "]"}], " ", "]"}], "\[Equal]", 
     " ", "0"}], "   ", "//", " ", "Expand"}], " ", "//", " ", "Simplify"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"m", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}], 
        RowBox[{"m", "[", "\[Mu]", "]"}]}], "]"}], "]"}], " ", "\[Equal]", 
     " ", "0"}], "   ", "//", " ", "Expand"}], " ", "//", " ", 
   "FullSimplify"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"mbar", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}], 
        RowBox[{"mbar", "[", "\[Mu]", "]"}]}], "]"}], "]"}], " ", "\[Equal]", 
     " ", "0"}], "  ", "//", " ", "Expand"}], " ", "//", " ", 
   "FullSimplify"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"l", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}], 
        RowBox[{"n", "[", "\[Mu]", "]"}]}], "]"}], "]"}], " ", "\[Equal]", 
     " ", "1"}], "//", " ", "Expand"}], " ", "//", " ", "FullSimplify"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"l", "[", "\[Mu]", "]"}], 
        RowBox[{"n", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}]}], "]"}], "]"}], " ", "\[Equal]", " ", 
     "1"}], "  ", "//", " ", "Expand"}], " ", "//", " ", "FullSimplify"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"m", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}], 
        RowBox[{"mbar", "[", "\[Mu]", "]"}]}], "]"}], "]"}], " ", "\[Equal]", 
     "  ", 
     RowBox[{"-", "1"}]}], " ", "//", " ", "Expand"}], " ", "//", " ", 
   "FullSimplify"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", 
      RowBox[{"ContractIndices", "[", 
       RowBox[{
        RowBox[{"m", "[", "\[Mu]", "]"}], 
        RowBox[{"mbar", "[", 
         RowBox[{"-", "\[Mu]"}], "]"}]}], "]"}], "]"}], " ", "\[Equal]", "  ", 
     RowBox[{"-", "1"}]}], " ", "//", " ", "Expand"}], " ", "//", " ", 
   "FullSimplify"}], " "}], "\[IndentingNewLine]", 
 RowBox[{"Clear", "[", "completenessDownIndices", 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"completenessDownIndices", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"MergeTensors", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"l", "[", 
       RowBox[{"-", "\[Mu]"}], "]"}], 
      RowBox[{"n", "[", 
       RowBox[{"-", "\[Nu]"}], "]"}]}], "+", 
     RowBox[{
      RowBox[{"n", "[", 
       RowBox[{"-", "\[Mu]"}], "]"}], 
      RowBox[{"l", "[", 
       RowBox[{"-", "\[Nu]"}], "]"}]}], " ", "-", " ", 
     RowBox[{
      RowBox[{"m", "[", 
       RowBox[{"-", "\[Mu]"}], "]"}], 
      RowBox[{"mbar", "[", 
       RowBox[{"-", "\[Nu]"}], "]"}]}], "+", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"m", "[", 
        RowBox[{"-", "\[Nu]"}], "]"}]}], 
      RowBox[{"mbar", "[", 
       RowBox[{"-", "\[Mu]"}], "]"}]}]}], "]"}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", " ", "completenessDownIndices", " ", "]"}], 
     "   ", "//", " ", "Expand"}], " ", "//", " ", "FullSimplify"}], " ", "//",
    " ", "MatrixForm"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"Thread", "[", 
      RowBox[{
       RowBox[{"Flatten", "[", "metric2pt1", "]"}], " ", "\[Equal]", " ", 
       "\[IndentingNewLine]", 
       RowBox[{"Flatten", "[", " ", 
        RowBox[{
        "TensorValues", "[", " ", "completenessDownIndices", " ", "]"}], 
        "]"}]}], " ", "]"}], " ", "//", " ", "Expand"}], " ", "//", " ", 
    "FullSimplify"}], "  ", "//", " ", "TableForm"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{"Clear", "[", "completenessUpIndices", 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"completenessUpIndices", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"MergeTensors", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"l", "[", "\[Mu]", "]"}], 
      RowBox[{"n", "[", "\[Nu]", "]"}]}], "+", 
     RowBox[{
      RowBox[{"n", "[", "\[Mu]", "]"}], 
      RowBox[{"l", "[", "\[Nu]", "]"}]}], " ", "-", " ", 
     RowBox[{
      RowBox[{"m", "[", "\[Mu]", "]"}], 
      RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "-", " ", 
     RowBox[{
      RowBox[{"m", "[", "\[Nu]", "]"}], 
      RowBox[{"mbar", "[", "\[Mu]", "]"}]}]}], "]"}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"TensorValues", "[", " ", "completenessUpIndices", " ", "]"}], 
     "   ", "//", " ", "Expand"}], " ", "//", " ", "FullSimplify"}], " ", "//",
    " ", "MatrixForm"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"Thread", "[", 
     RowBox[{
      RowBox[{"Flatten", "[", "inverse2pt1", "]"}], " ", "\[Equal]", " ", 
      "\[IndentingNewLine]", 
      RowBox[{"Flatten", "[", " ", 
       RowBox[{"TensorValues", "[", " ", "completenessUpIndices", " ", "]"}], 
       "]"}]}], " ", "]"}], "  ", "//", " ", "Expand"}], " ", "//", " ", 
   "FullSimplify"}], "  ", "//", " ", "TableForm"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{
  3.820937410343767*^9, 3.820944472323543*^9, {3.8237794627048893`*^9, 
   3.823779471575405*^9}, 3.823780788700976*^9, {3.823968050180369*^9, 
   3.823968056298918*^9}, {3.8239688232408648`*^9, 3.823968847128337*^9}, {
   3.823971389045491*^9, 3.823971395475389*^9}, {3.823971915940023*^9, 
   3.823971939515136*^9}, 3.824026530428814*^9},
 CellLabel->
  "In[105]:=",ExpressionUUID->"aa44a920-de2c-49d8-87bb-a3181fc83f16"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690768845*^9, 3.824026530428905*^9},
 CellLabel->
  "Out[105]=",ExpressionUUID->"801810df-4233-497e-a54c-d80638a617c4"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690774122*^9, 3.8240265304289837`*^9},
 CellLabel->
  "Out[106]=",ExpressionUUID->"a7028458-e848-4628-8439-d93a2df87dfb"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690780382*^9, 3.824026530429069*^9},
 CellLabel->
  "Out[107]=",ExpressionUUID->"099dc78d-e355-460a-a620-8b92588f9e88"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.82402569078581*^9, 3.824026530429154*^9},
 CellLabel->
  "Out[108]=",ExpressionUUID->"63b7ba3e-3315-4f27-83d4-74d9a9a04f8c"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.8240256907981777`*^9, 3.824026530429233*^9},
 CellLabel->
  "Out[109]=",ExpressionUUID->"6e4d415d-2677-4b14-99d8-e370006049af"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690827585*^9, 3.824026530429318*^9},
 CellLabel->
  "Out[110]=",ExpressionUUID->"47af53b3-f2d4-44f4-8dc5-2589eee195ab"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690834538*^9, 3.8240265304294024`*^9},
 CellLabel->
  "Out[111]=",ExpressionUUID->"a6c70b29-055e-489e-a7db-0984baf718ae"],

Cell[BoxData["True"], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690839697*^9, 3.82402653042948*^9},
 CellLabel->
  "Out[112]=",ExpressionUUID->"12063317-9055-43c2-8077-db880d670588"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"-", 
        RowBox[{"M", "[", 
         RowBox[{"u", ",", "v"}], "]"}]}]], "0", "0"},
     {
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"-", 
        RowBox[{"M", "[", 
         RowBox[{"u", ",", "v"}], "]"}]}]], "0", "0", "0"},
     {"0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"U", "[", 
           RowBox[{"u", ",", "v"}], "]"}]}], "+", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}], "0"},
     {"0", "0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"U", "[", 
           RowBox[{"u", ",", "v"}], "]"}]}], "-", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690920397*^9, 3.8240265304295588`*^9},
 CellLabel->
  "Out[115]//MatrixForm=",ExpressionUUID->"62a1e1ae-9ae1-4445-88ea-\
1cfe4c62cf14"],

Cell[BoxData[
 TagBox["True",
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690926804*^9, 3.8240265304296494`*^9},
 CellLabel->
  "Out[116]//TableForm=",ExpressionUUID->"a2c97f3e-d13b-4300-9f04-\
0a5f12b4f5b4"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"M", "[", 
        RowBox[{"u", ",", "v"}], "]"}]], "0", "0"},
     {
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"M", "[", 
        RowBox[{"u", ",", "v"}], "]"}]], "0", "0", "0"},
     {"0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"U", "[", 
          RowBox[{"u", ",", "v"}], "]"}], "-", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}], "0"},
     {"0", "0", "0", 
      RowBox[{"-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"U", "[", 
          RowBox[{"u", ",", "v"}], "]"}], "+", 
         RowBox[{"V", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.82402569098173*^9, 3.824026530429741*^9},
 CellLabel->
  "Out[119]//MatrixForm=",ExpressionUUID->"933e8540-72cf-4208-af33-\
be9fd733068f"],

Cell[BoxData[
 TagBox["True",
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.},
 CellChangeTimes->{{3.823971398516067*^9, 3.8239714274305*^9}, 
   3.8239719090543823`*^9, 3.82397194511889*^9, 3.82397221936222*^9, 
   3.824025690987679*^9, 3.824026530429821*^9},
 CellLabel->
  "Out[120]//TableForm=",ExpressionUUID->"6ea95e4a-98c0-41be-ad70-\
f159f80e4301"]
}, Closed]],

Cell[CellGroupData[{

Cell["Newman Penrose Quantities Calculated ", "Section",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.82528791785428*^9, 
  3.825287959542865*^9}},ExpressionUUID->"5bac3f92-a7f3-4499-938c-\
fd5ef8f4f96e"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "spinCoefficientReplace", "]"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"spinCoefficientReplace", "=", " ", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"\[Alpha]", "\[Rule]", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "/", "2"}], ")"}], 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{
            RowBox[{"MergeTensors", "[", 
             RowBox[{
              RowBox[{"CovariantD", "[", " ", 
               RowBox[{
                RowBox[{"l", "[", 
                 RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
              RowBox[{"n", "[", "\[Mu]", "]"}], " ", 
              RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
            "TensorValues"}], " ", ")"}], "-", "\[IndentingNewLine]", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"MergeTensors", "[", 
             RowBox[{
              RowBox[{"CovariantD", "[", " ", 
               RowBox[{
                RowBox[{"m", "[", 
                 RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
              RowBox[{"mbar", "[", "\[Mu]", "]"}], " ", 
              RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
            "TensorValues"}], ")"}]}], ")"}]}], " ", ")"}]}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{"\[Beta]", " ", "\[Rule]", " ", "\[IndentingNewLine]", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "/", "2"}], ")"}], 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{
            RowBox[{"MergeTensors", "[", " ", 
             RowBox[{
              RowBox[{"CovariantD", "[", " ", 
               RowBox[{
                RowBox[{"l", "[", 
                 RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
              RowBox[{"n", "[", "\[Mu]", "]"}], 
              RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
            "TensorValues"}], ")"}], "-", " ", "\[IndentingNewLine]", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"MergeTensors", "[", 
             RowBox[{
              RowBox[{"CovariantD", "[", " ", 
               RowBox[{
                RowBox[{"m", "[", 
                 RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
              RowBox[{"mbar", "[", "\[Mu]", "]"}], " ", 
              RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
            "TensorValues"}], " ", ")"}]}], ")"}]}], ")"}]}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"\[Gamma]", " ", "\[Rule]", " ", 
      RowBox[{"(*", " ", 
       RowBox[{
       "something", " ", "weird", " ", "here", " ", "correct", " ", 
        "definition", " ", "off", " ", "by", " ", "minus", " ", "sign"}], " ",
        "*)"}], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"(", 
          FractionBox["1", "2"], ")"}], 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"MergeTensors", "[", 
               RowBox[{
                RowBox[{"CovariantD", "[", " ", 
                 RowBox[{
                  RowBox[{"l", "[", 
                   RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                  RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
                RowBox[{"n", "[", "\[Mu]", "]"}], 
                RowBox[{"n", "[", "\[Nu]", "]"}]}], " ", "]"}], " ", "//", 
              " ", "TensorValues"}], "  ", "//", " ", "Expand"}], "  ", ")"}],
            "-", "\[IndentingNewLine]", 
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{
               RowBox[{"MergeTensors", "[", 
                RowBox[{
                 RowBox[{"CovariantD", "[", " ", 
                  RowBox[{
                   RowBox[{"m", "[", 
                    RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                   RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
                 RowBox[{"mbar", "[", "\[Mu]", "]"}], " ", 
                 RowBox[{"n", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
               "TensorValues"}], " ", "//", " ", "Expand"}], "  ", "//", " ", 
             "FullSimplify"}], " ", ")"}]}], ")"}]}], " ", "//", " ", 
        "Expand"}], " ", ")"}]}], " ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{"\[CurlyEpsilon]", " ", "\[Rule]", " ", 
      RowBox[{"(", " ", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"(", 
           RowBox[{"1", "/", "2"}], ")"}], 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"(", " ", 
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{"MergeTensors", "[", 
                 RowBox[{
                  RowBox[{"CovariantD", "[", 
                   RowBox[{
                    RowBox[{"l", "[", 
                    RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                    RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
                  RowBox[{"n", "[", "\[Mu]", "]"}], " ", 
                  RowBox[{"l", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
                "TensorValues"}], "  ", "//", " ", "Expand"}], "  ", "//", 
              " ", "FullSimplify"}], "  ", ")"}], "  ", "-", " ", 
            "\[IndentingNewLine]", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{"MergeTensors", "[", " ", 
                 RowBox[{
                  RowBox[{"CovariantD", "[", " ", 
                   RowBox[{
                    RowBox[{"m", "[", 
                    RowBox[{"-", "\[Mu]"}], "]"}], ",", 
                    RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
                  RowBox[{"mbar", "[", "\[Mu]", "]"}], " ", 
                  RowBox[{"l", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
                "TensorValues"}], " ", "//", " ", "Expand"}], " ", "//", " ", 
              "FullSimplify"}], ")"}]}], " ", ")"}]}], " ", "//", " ", 
         "Expand"}], "  ", "//", " ", "FullSimplify"}], " ", ")"}]}], " ", 
     ",", " ", "\[IndentingNewLine]", 
     RowBox[{"\[Kappa]", "\[Rule]", 
      RowBox[{"(", "  ", 
       RowBox[{
        RowBox[{"MergeTensors", "[", " ", 
         RowBox[{
          RowBox[{"CovariantD", "[", " ", 
           RowBox[{
            RowBox[{"l", "[", 
             RowBox[{"-", "\[Mu]"}], "]"}], " ", ",", 
            RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
          RowBox[{"m", "[", "\[Mu]", "]"}], " ", 
          RowBox[{"l", "[", "\[Nu]", "]"}]}], "  ", "]"}], "  ", "//", " ", 
        "TensorValues"}], " ", ")"}]}], " ", ",", " ", "\[IndentingNewLine]", 
     
     RowBox[{"\[Lambda]", "\[Rule]", " ", 
      RowBox[{"(*", " ", 
       RowBox[{"note", " ", "minus", " ", "sign"}], " ", "*)"}], 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], "*", 
       RowBox[{"(", " ", 
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{"MergeTensors", "[", " ", 
            RowBox[{
             RowBox[{"CovariantD", "[", " ", 
              RowBox[{
               RowBox[{"n", "[", 
                RowBox[{"-", "\[Mu]"}], "]"}], ",", 
               RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
             RowBox[{"mbar", "[", "\[Mu]", "]"}], " ", 
             RowBox[{"mbar", "[", "\[Nu]", "]"}]}], " ", "]"}], "  ", "//", 
           " ", "TensorValues"}], " ", "//", " ", "Expand"}], " ", "//", " ", 
         "FullSimplify"}], ")"}]}]}], "  ", ",", "\[IndentingNewLine]", 
     RowBox[{"\[Mu]", "\[Rule]", " ", 
      RowBox[{"(*", 
       RowBox[{"note", " ", "minus", " ", "sign"}], " ", "*)"}], 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], "*", 
       RowBox[{"(", " ", 
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{"MergeTensors", " ", "[", " ", 
            RowBox[{
             RowBox[{"CovariantD", "[", " ", 
              RowBox[{
               RowBox[{"n", "[", 
                RowBox[{"-", "\[Mu]"}], "]"}], " ", ",", " ", 
               RowBox[{"-", "\[Nu]"}]}], " ", "]"}], " ", 
             RowBox[{"mbar", "[", "\[Mu]", "]"}], " ", 
             RowBox[{"m", "[", "\[Nu]", "]"}]}], " ", "]"}], " ", "//", " ", 
           "TensorValues"}], "  ", "//", " ", "Expand"}], "  ", "//", " ", 
         "FullSimplify"}], " ", ")"}]}]}], "  ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{"\[Nu]", "\[Rule]", " ", 
      RowBox[{"(", " ", 
       RowBox[{
        RowBox[{"MergeTensors", "[", " ", 
         RowBox[{
          RowBox[{"CovariantD", "[", " ", 
           RowBox[{
            RowBox[{"n", "[", 
             RowBox[{"-", "\[Mu]"}], "]"}], ",", 
            RowBox[{"-", "\[Nu]"}]}], "]"}], 
          RowBox[{"m", "[", "\[Mu]", "]"}], " ", 
          RowBox[{"n", "[", "\[Nu]", "]"}]}], " ", "]"}], " ", "//", " ", 
        "TensorValues"}], " ", ")"}]}], " ", ",", " ", "\[IndentingNewLine]", 
     
     RowBox[{"\[Pi]", "\[Rule]", " ", 
      RowBox[{"(*", " ", 
       RowBox[{"Note", " ", "minus", " ", "sign"}], " ", "*)"}], 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], "*", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{"CovariantD", "[", " ", 
             RowBox[{
              RowBox[{"n", "[", 
               RowBox[{"-", "\[Mu]"}], "]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
            RowBox[{"mbar", "[", "\[Mu]", "]"}], " ", 
            RowBox[{"l", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
          "TensorValues"}], "  ", "//", " ", "Expand"}], " ", ")"}]}]}], " ", 
     ",", " ", "\[IndentingNewLine]", 
     RowBox[{"\[Rho]", " ", "\[Rule]", 
      RowBox[{"(", "  ", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"MergeTensors", "[", " ", 
           RowBox[{
            RowBox[{"CovariantD", "[", " ", 
             RowBox[{
              RowBox[{"l", "[", 
               RowBox[{"-", "\[Mu]"}], "]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
            RowBox[{"m", "[", "\[Mu]", "]"}], " ", 
            RowBox[{"mbar", "[", "\[Nu]", "]"}]}], " ", "]"}], " ", "//", " ",
           "TensorValues"}], "  ", "//", " ", "Expand"}], " ", "//", " ", 
        "FullSimplify"}], " ", ")"}]}], "  ", ",", " ", 
     RowBox[{"\[Sigma]", "\[Rule]", 
      RowBox[{"(", " ", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"MergeTensors", "[", " ", 
           RowBox[{
            RowBox[{"CovariantD", "[", 
             RowBox[{
              RowBox[{"l", "[", 
               RowBox[{"-", "\[Mu]"}], "]"}], " ", ",", " ", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
            RowBox[{"m", "[", "\[Mu]", "]"}], " ", 
            RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], " ", "//", " ", 
          "TensorValues"}], "  ", "//", " ", "Expand"}], " ", "//", " ", 
        "FullSimplify"}], ")"}]}], "  ", ",", " ", "\[IndentingNewLine]", 
     RowBox[{"\[Tau]", "\[Rule]", 
      RowBox[{"(", " ", 
       RowBox[{
        RowBox[{"MergeTensors", "[", " ", 
         RowBox[{
          RowBox[{"CovariantD", "[", " ", 
           RowBox[{
            RowBox[{"l", "[", 
             RowBox[{"-", "\[Mu]"}], "]"}], ",", 
            RowBox[{"-", "\[Nu]"}]}], "]"}], " ", 
          RowBox[{"m", "[", "\[Mu]", "]"}], " ", 
          RowBox[{"n", "[", "\[Nu]", " ", "]"}]}], "]"}], "//", " ", 
        "TensorValues"}], " ", ")"}]}]}], "   ", "\[IndentingNewLine]", 
    "}"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"spinCoefficientReplace", "   ", "//", " ", "TableForm"}], " ", "//",
   " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820667112307205*^9, {3.820691856877*^9, 3.8206918635710173`*^9}, {
   3.820692627802567*^9, 3.820692798874284*^9}, {3.820793246159666*^9, 
   3.8207932735596313`*^9}, {3.820933088885683*^9, 3.820933089524383*^9}, 
   3.820934520109788*^9, 3.8209373342691517`*^9, {3.82100327861626*^9, 
   3.8210032838458157`*^9}, {3.821003386912135*^9, 3.821003405643714*^9}, {
   3.8210037363804407`*^9, 3.8210037487041388`*^9}, 3.825287941673217*^9},
 CellLabel->
  "In[121]:=",ExpressionUUID->"6506df50-5203-4732-af8e-2abc3c7ce3d6"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       RowBox[{"\[Alpha]", "\[Rule]", "0"}]},
      {
       RowBox[{"\[Beta]", "\[Rule]", "0"}]},
      {
       RowBox[{"\[Gamma]", "\[Rule]", 
        RowBox[{
         FractionBox["1", "4"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{"\[CurlyEpsilon]", "\[Rule]", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "4"]}], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{"\[Kappa]", "\[Rule]", "0"}]},
      {
       RowBox[{"\[Lambda]", "\[Rule]", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{"\[Mu]", "\[Rule]", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{"\[Nu]", "\[Rule]", "0"}]},
      {
       RowBox[{"\[Pi]", "\[Rule]", "0"}]},
      {
       RowBox[{"\[Rho]", "\[Rule]", 
        RowBox[{
         FractionBox["1", "2"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{"\[Sigma]", "\[Rule]", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{
           FractionBox["1", "2"], " ", 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}]], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{"\[Tau]", "\[Rule]", "0"}]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.823971971162615*^9, 3.823972221041922*^9, 
  3.8240256925856857`*^9, 3.825287941673321*^9},
 CellLabel->
  "Out[123]//TraditionalForm=",ExpressionUUID->"239303f9-ef50-4f26-8ffc-\
00881d8d2e10"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "ricciScalarsReplace", "]"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ricciScalarsReplace", " ", "=", " ", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "oo"], "\[Rule]", " ", 
        RowBox[{"(*", " ", 
         RowBox[{
         "subscripts", " ", "used", " ", "here", " ", "are", " ", "the", " ", 
          "letter", " ", "\"\<O\>\"", " ", "not", " ", "the", " ", "number", 
          " ", 
          RowBox[{"\"\<0\>\"", ".", "  ", "For"}], " ", "whatever", " ", 
          "reason", " ", "the", " ", "occurence", " ", "of", " ", "two", " ", 
          "zeros", " ", "as", " ", "subscripts", " ", "evaluated", " ", "as", 
          " ", "a", " ", "product", " ", "and", " ", "gives", " ", "zero"}], 
         "  ", "*)"}], " ", "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"l", "[", "\[Mu]", "]"}], 
            RowBox[{"l", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], " ", "//", 
       " ", "Expand"}], " ", "//", " ", "FullSimplify"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "O1"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"l", "[", "\[Mu]", "]"}], 
            RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], " ", "//", 
       " ", "Expand"}], " ", "//", " ", "FullSimplify"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "O2"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"m", "[", "\[Mu]", "]"}], 
            RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], " ", "//", 
       " ", "Expand"}], " ", "//", " ", "FullSimplify"}], ",", 
     "\[IndentingNewLine]", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "10"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"l", "[", "\[Mu]", "]"}], 
            RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "  ", "//",
        " ", "Expand"}], " ", "//", " ", "Simplify"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "11"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "4"], ")"}], "*", 
         RowBox[{"(", " ", 
          RowBox[{
           RowBox[{"(", " ", 
            RowBox[{"TensorValues", "[", 
             RowBox[{"MergeTensors", "[", 
              RowBox[{
               RowBox[{
                RowBox[{"tensorList", "[", 
                 RowBox[{"[", "4", "]"}], "]"}], "[", 
                RowBox[{
                 RowBox[{"-", "\[Mu]"}], ",", 
                 RowBox[{"-", "\[Nu]"}]}], "]"}], 
               RowBox[{"l", "[", "\[Mu]", "]"}], 
               RowBox[{"n", "[", "\[Nu]", "]"}]}], "]"}], "]"}], ")"}], "+", 
           " ", 
           RowBox[{"(", 
            RowBox[{"TensorValues", "[", 
             RowBox[{"MergeTensors", "[", 
              RowBox[{
               RowBox[{
                RowBox[{"tensorList", "[", 
                 RowBox[{"[", "4", "]"}], "]"}], "[", 
                RowBox[{
                 RowBox[{"-", "\[Mu]"}], ",", 
                 RowBox[{"-", "\[Nu]"}]}], "]"}], 
               RowBox[{"m", "[", "\[Mu]", "]"}], 
               RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], "]"}], ")"}]}], 
          ")"}]}]}], " ", "//", " ", "Expand"}], " ", "//", " ", 
      "FullSimplify"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "12"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"n", "[", "\[Mu]", "]"}], 
            RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], " ", "//", 
       " ", "Expand"}], " ", "//", " ", "FullSimplify"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "20"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"mbar", "[", "\[Mu]", "]"}], 
            RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "//", 
       " ", "Expand"}], " ", "//", " ", "Simplify"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "21"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"n", "[", "\[Mu]", "]"}], 
            RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "  ", "//",
        " ", "Expand"}], " ", "//", " ", "Simplify"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "22"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox[
           RowBox[{"-", "1"}], "2"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "4", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"n", "[", "\[Mu]", "]"}], 
            RowBox[{"n", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "//", " ", 
       "Expand"}], " ", "//", " ", "FullSimplify"}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{"\[CapitalLambda]", "\[Rule]", " ", "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          FractionBox["1", "24"], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"tensorList", "[", 
           RowBox[{"[", "5", "]"}], "]"}], "]"}]}]}], "//", " ", "Expand"}], 
      " ", "//", " ", "FullSimplify"}]}], "\[IndentingNewLine]", "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ricciScalarsReplace", "   ", "//", " ", "TableForm"}], " ", "//", 
  " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{{3.8207941683808823`*^9, 3.820794170188884*^9}, {
   3.820794210004217*^9, 3.820794295371916*^9}, {3.820794355374641*^9, 
   3.8207944173021507`*^9}, {3.8209358220143003`*^9, 3.820935854138783*^9}, 
   3.820937334270711*^9, {3.821003405651829*^9, 3.821003467622817*^9}, {
   3.821003736380765*^9, 3.821003748704556*^9}, 3.825287941673438*^9},
 CellLabel->
  "In[124]:=",ExpressionUUID->"5944b505-9b73-4322-93e8-6b0b06eac3d6"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "oo"], "\[Rule]", 
        RowBox[{
         FractionBox["1", "4"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"2", " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "v"}],
              MultilineFunction->None], " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "v"}],
              MultilineFunction->None]}]}], "-", 
           RowBox[{"2", " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", 
              SuperscriptBox["v", "2"]}],
             MultilineFunction->None]}], "+", 
           SuperscriptBox[
            RowBox[{"(", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "v"}],
              MultilineFunction->None], ")"}], "2"], "+", 
           SuperscriptBox[
            RowBox[{"(", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "v"}],
              MultilineFunction->None], ")"}], "2"]}], ")"}]}]}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "O1"], "\[Rule]", "0"}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "O2"], "\[Rule]", 
        RowBox[{
         FractionBox["1", "4"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"2", " ", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None]}]}], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}]}], ")"}]}]}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "10"], "\[Rule]", "0"}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "11"], "\[Rule]", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "8"]}], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"2", " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"M", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}], "-", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}]}], ")"}]}]}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "12"], "\[Rule]", "0"}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "20"], "\[Rule]", 
        RowBox[{
         FractionBox["1", "4"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"2", " ", 
             FractionBox[
              RowBox[{
               SuperscriptBox["\[PartialD]", "2"], 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{
               RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
               RowBox[{"\[PartialD]", "v"}]}],
              MultilineFunction->None]}]}], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None]}], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}]}], ")"}]}]}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "21"], "\[Rule]", "0"}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPhi]", "22"], "\[Rule]", 
        RowBox[{
         FractionBox["1", "4"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"2", " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"M", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], " ", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None]}]}], "-", 
           RowBox[{"2", " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", 
              SuperscriptBox["u", "2"]}],
             MultilineFunction->None]}], "+", 
           SuperscriptBox[
            RowBox[{"(", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"U", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], ")"}], "2"], "+", 
           SuperscriptBox[
            RowBox[{"(", 
             FractionBox[
              RowBox[{"\[PartialD]", 
               RowBox[{"V", "(", 
                RowBox[{"u", ",", "v"}], ")"}]}], 
              RowBox[{"\[PartialD]", "u"}],
              MultilineFunction->None], ")"}], "2"]}], ")"}]}]}]},
      {
       RowBox[{"\[CapitalLambda]", "\[Rule]", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "24"]}], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"2", " ", 
             RowBox[{"(", 
              RowBox[{
               FractionBox[
                RowBox[{
                 SuperscriptBox["\[PartialD]", "2"], 
                 RowBox[{"M", "(", 
                  RowBox[{"u", ",", "v"}], ")"}]}], 
                RowBox[{
                 RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                 RowBox[{"\[PartialD]", "v"}]}],
                MultilineFunction->None], "+", 
               RowBox[{"2", " ", 
                FractionBox[
                 RowBox[{
                  SuperscriptBox["\[PartialD]", "2"], 
                  RowBox[{"U", "(", 
                   RowBox[{"u", ",", "v"}], ")"}]}], 
                 RowBox[{
                  RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
                  RowBox[{"\[PartialD]", "v"}]}],
                 MultilineFunction->None]}]}], ")"}]}]}], "+", 
           RowBox[{"3", " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"U", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}]}], ")"}]}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8239719855577707`*^9, 3.823972221331985*^9, 
  3.8240256931126966`*^9, 3.8252879416735163`*^9},
 CellLabel->
  "Out[126]//TraditionalForm=",ExpressionUUID->"4ea7fdd0-3611-444f-849d-\
86fd7e68ab6f"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "weylScalarsReplace", "]"}], 
  RowBox[{"(*", " ", 
   RowBox[{"Definitions", " ", "from", " ", "Griffiths"}], " ", "*)"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"weylScalarsReplace", " ", "=", " ", 
   RowBox[{"{", "\[IndentingNewLine]", "\[IndentingNewLine]", "   ", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "0"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "1"}], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "8", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Kappa]"}], ",", 
              RowBox[{"-", "\[Lambda]"}], ",", 
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"l", "[", "\[Kappa]", "]"}], 
            RowBox[{"m", "[", "\[Lambda]", "]"}], 
            RowBox[{"l", "[", "\[Mu]", "]"}], 
            RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "//", " ", 
       "Expand"}], " ", "//", " ", "FullSimplify"}], " ", ",", " ", "\n", 
     "\t ", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "1"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "1"}], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "8", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Kappa]"}], ",", 
              RowBox[{"-", "\[Lambda]"}], ",", 
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"l", "[", "\[Kappa]", "]"}], 
            RowBox[{"n", "[", "\[Lambda]", "]"}], 
            RowBox[{"l", "[", "\[Mu]", "]"}], 
            RowBox[{"m", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "//", " ", 
       "Expand"}], " ", "//", " ", "FullSimplify"}], " ", ",", " ", "\n", 
     "\t ", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "2"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "1"}], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "8", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Kappa]"}], ",", 
              RowBox[{"-", "\[Lambda]"}], ",", 
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"l", "[", "\[Kappa]", "]"}], 
            RowBox[{"m", "[", "\[Lambda]", "]"}], 
            RowBox[{"mbar", "[", "\[Mu]", "]"}], 
            RowBox[{"n", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], " ", "//", 
       " ", "Expand"}], " ", "//", " ", "FullSimplify"}], ",", " ", "\n", 
     "\t ", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "3"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "1"}], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "8", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Kappa]"}], ",", 
              RowBox[{"-", "\[Lambda]"}], ",", 
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"n", "[", "\[Kappa]", "]"}], 
            RowBox[{"l", "[", "\[Lambda]", "]"}], 
            RowBox[{"n", "[", "\[Mu]", "]"}], 
            RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "//", 
       " ", "Expand"}], " ", "//", " ", "FullSimplify"}], " ", ",", " ", "\n",
      "\t ", 
     RowBox[{
      RowBox[{
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "4"], "\[Rule]", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"-", "1"}], ")"}], "*", 
         RowBox[{"TensorValues", "[", 
          RowBox[{"MergeTensors", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"tensorList", "[", 
              RowBox[{"[", "8", "]"}], "]"}], "[", 
             RowBox[{
              RowBox[{"-", "\[Kappa]"}], ",", 
              RowBox[{"-", "\[Lambda]"}], ",", 
              RowBox[{"-", "\[Mu]"}], ",", 
              RowBox[{"-", "\[Nu]"}]}], "]"}], 
            RowBox[{"n", "[", "\[Kappa]", "]"}], 
            RowBox[{"mbar", "[", "\[Lambda]", "]"}], 
            RowBox[{"n", "[", "\[Mu]", "]"}], 
            RowBox[{"mbar", "[", "\[Nu]", "]"}]}], "]"}], "]"}]}]}], "//", 
       " ", "Expand"}], " ", "//", " ", "FullSimplify"}]}], 
    "\[IndentingNewLine]", "}"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"weylScalarsReplace", "  ", "//", " ", "TableForm"}], " ", "//", 
  " ", "pdConv"}]}], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{
  3.820667112308317*^9, {3.8206919186046867`*^9, 3.820691920188485*^9}, {
   3.820794507895151*^9, 3.820794582921618*^9}, 3.820937334271385*^9, 
   3.821003405651976*^9, 3.825287941673605*^9},
 CellLabel->
  "In[127]:=",ExpressionUUID->"9bcdbfbc-ee38-43fe-b505-753f5f9c6438"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "0"], "\[Rule]", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None], " ", 
            RowBox[{"(", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None], "-", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "v"}],
               MultilineFunction->None]}], ")"}]}], "+", 
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", 
             SuperscriptBox["v", "2"]}],
            MultilineFunction->None]}], ")"}]}]}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "1"], "\[Rule]", "0"}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "2"], "\[Rule]", 
        RowBox[{
         FractionBox["1", "6"], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{
             RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
             RowBox[{"\[PartialD]", "v"}]}],
            MultilineFunction->None], "-", 
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{
             RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
             RowBox[{"\[PartialD]", "v"}]}],
            MultilineFunction->None], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}]}], ")"}]}]}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "3"], "\[Rule]", "0"}]},
      {
       RowBox[{
        SubscriptBox["\[CapitalPsi]", "4"], "\[Rule]", 
        RowBox[{
         RowBox[{"-", 
          FractionBox["1", "2"]}], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "u"}],
             MultilineFunction->None], " ", 
            RowBox[{"(", 
             RowBox[{
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"M", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None], "-", 
              FractionBox[
               RowBox[{"\[PartialD]", 
                RowBox[{"U", "(", 
                 RowBox[{"u", ",", "v"}], ")"}]}], 
               RowBox[{"\[PartialD]", "u"}],
               MultilineFunction->None]}], ")"}]}], "+", 
           FractionBox[
            RowBox[{
             SuperscriptBox["\[PartialD]", "2"], 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", 
             SuperscriptBox["u", "2"]}],
            MultilineFunction->None]}], ")"}]}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.},
 CellChangeTimes->{3.8239720002490063`*^9, 3.823972226324471*^9, 
  3.824025697620126*^9, 3.825287941673685*^9},
 CellLabel->
  "Out[129]//TraditionalForm=",ExpressionUUID->"2a423914-9e12-4985-bbca-\
7cfcc19e3c8b"]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt10", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt10", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"Expand", "[", 
    RowBox[{"Assuming", "[", 
     RowBox[{
      RowBox[{
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"-", 
         RowBox[{"M", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]], " ", "\[NotEqual]", " ", "0"}], 
      " ", ",", " ", 
      RowBox[{"MultiplySides", "[", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"weylScalarsReplace", "[", 
           RowBox[{"[", "1", "]"}], "]"}], "  ", "/.", " ", 
          RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}], ")"}], " ", ",", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"-", 
          RowBox[{"M", "[", 
           RowBox[{"u", ",", "v"}], "]"}]}]]}], "]"}]}], "]"}], "]"}]}], 
  "   ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt10", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.823972021676303*^9, 3.8239721283783607`*^9}, {
  3.8239722424757977`*^9, 3.823972256610145*^9}},
 CellLabel->
  "In[130]:=",ExpressionUUID->"8a315062-9d79-4e7f-9dfe-f54253e00f37"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SubscriptBox["\[CapitalPsi]", "0"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"-", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}]]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None]}]}], "+", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.823972019057913*^9, 3.823972128738505*^9}, 
   3.823972226389618*^9, 3.823972257252502*^9, 3.8240256976872473`*^9},
 CellLabel->
  "Out[132]//TraditionalForm=",ExpressionUUID->"5fec5823-7eb9-44b7-92e8-\
d11baaf7433e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt11", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt11", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"weylScalarsReplace", "[", 
     RowBox[{"[", "2", "]"}], "]"}], "  ", "/.", " ", 
    RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt11", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.823972268314204*^9, 3.823972290330249*^9}},
 CellLabel->
  "In[133]:=",ExpressionUUID->"8b3de61d-c738-48bb-a97d-92b6f6c9f992"],

Cell[BoxData[
 FormBox[
  RowBox[{
   SubscriptBox["\[CapitalPsi]", "1"], "\[LongEqual]", "0"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{3.8239722907745447`*^9, 3.824025697698461*^9},
 CellLabel->
  "Out[135]//TraditionalForm=",ExpressionUUID->"5cffd79c-1311-4c8b-9c85-\
5a170b792b62"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt12a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt12a", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"Expand", "[", 
    RowBox[{"Assuming", "[", 
     RowBox[{
      RowBox[{
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"-", 
         RowBox[{"M", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]], " ", "\[NotEqual]", " ", "0"}], 
      " ", ",", " ", 
      RowBox[{"MultiplySides", "[", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"weylScalarsReplace", "[", 
           RowBox[{"[", "3", "]"}], "]"}], "  ", "/.", " ", 
          RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}], ")"}], " ", ",", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"-", 
          RowBox[{"M", "[", 
           RowBox[{"u", ",", "v"}], "]"}]}]]}], "]"}]}], "]"}], "]"}]}], "  ",
   ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt12a", "  ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8239721585144577`*^9, 3.8239721588262444`*^9}, {
  3.8239723268107443`*^9, 3.823972344425889*^9}},
 CellLabel->
  "In[136]:=",ExpressionUUID->"39aba092-3224-41c2-802f-79abd1131fb1"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SubscriptBox["\[CapitalPsi]", "2"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"-", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}]]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "6"], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "6"], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox["1", "6"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.823972159435967*^9, 3.823972226420485*^9, 
  3.823972345110124*^9, 3.824025697728992*^9},
 CellLabel->
  "Out[138]//TraditionalForm=",ExpressionUUID->"819bd8c5-ff53-488f-adc6-\
97753d2e1ebf"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Flatten", "[", 
    RowBox[{"Solve", "[", " ", 
     RowBox[{"eq2pt8", " ", ",", " ", 
      RowBox[{
       SuperscriptBox["M", 
        TagBox[
         RowBox[{"(", 
          RowBox[{"1", ",", "1"}], ")"}],
         Derivative],
        MultilineFunction->None], "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "pdConv"}]], "Input",
 CellChangeTimes->{{3.823972301244392*^9, 3.823972350297964*^9}, {
  3.827917988749482*^9, 
  3.827917989277996*^9}},ExpressionUUID->"edfe1279-2aab-487c-920c-\
337528e98699"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    FractionBox[
     RowBox[{
      SuperscriptBox["\[PartialD]", "2"], 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{
      RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
      RowBox[{"\[PartialD]", "v"}]}],
     MultilineFunction->None], "\[Rule]", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}], "-", 
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}]}], ")"}]}]}], "}"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.823972303111909*^9, 3.823972350651587*^9}, 
   3.824025697761883*^9},
 CellLabel->
  "Out[139]//TraditionalForm=",ExpressionUUID->"72d6d448-72c2-47b5-a894-\
141c4d56e716"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt12b", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt12b", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"eq2pt12a", " ", "/.", " ", 
     RowBox[{"Flatten", "[", 
      RowBox[{"Solve", "[", " ", 
       RowBox[{"eq2pt8", " ", ",", " ", 
        RowBox[{
         SuperscriptBox["M", 
          TagBox[
           RowBox[{"(", 
            RowBox[{"1", ",", "1"}], ")"}],
           Derivative],
          MultilineFunction->None], "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}]}], " ", "//", 
    " ", "Expand"}]}], "   ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt12b", " ", "//", "  ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.823972353500339*^9, 3.823972389313416*^9}, {
  3.8239724670354033`*^9, 3.8239724882181664`*^9}},
 CellLabel->
  "In[140]:=",ExpressionUUID->"fda1f1a2-9988-43cf-ba5c-d8e2b083ba42"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SubscriptBox["\[CapitalPsi]", "2"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"-", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}]]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{
      FractionBox["1", "6"], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"U", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{
        RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
        RowBox[{"\[PartialD]", "v"}]}],
       MultilineFunction->None]}]}], "-", 
    RowBox[{
     FractionBox["1", "12"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox["1", "4"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.823972362452825*^9, 3.823972389661557*^9}, 
   3.8239724885718803`*^9, 3.824025697792432*^9},
 CellLabel->
  "Out[142]//TraditionalForm=",ExpressionUUID->"7fe9139b-c7fe-4f4c-b0be-\
97d2d5cc90af"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"eq2pt4", "  ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], "  ", "//", " ", 
  "pdConv"}]], "Input",
 CellChangeTimes->{{3.823972397587996*^9, 3.823972413082103*^9}},
 CellLabel->
  "In[143]:=",ExpressionUUID->"013d799b-2ad4-4a6b-b1af-d565870aa378"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.823972399430078*^9, 3.823972413474675*^9}, 
   3.824025697801832*^9},
 CellLabel->
  "Out[143]//TraditionalForm=",ExpressionUUID->"2c7a6c30-70b6-4080-9159-\
826b0ab6261b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt12", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt12", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"eq2pt12a", " ", "/.", " ", 
      RowBox[{"Flatten", "[", 
       RowBox[{"Solve", "[", " ", 
        RowBox[{"eq2pt8", " ", ",", " ", 
         RowBox[{
          SuperscriptBox["M", 
           TagBox[
            RowBox[{"(", 
             RowBox[{"1", ",", "1"}], ")"}],
            Derivative],
           MultilineFunction->None], "[", 
          RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}]}], "  ", "/.", 
     " ", 
     RowBox[{"(", 
      RowBox[{"eq2pt4", "  ", "/.", " ", 
       RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", ")"}]}], " ", "//", 
    " ", "Expand"}]}], "   ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt12", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.823972419882967*^9, 3.823972459017898*^9}},
 CellLabel->
  "In[144]:=",ExpressionUUID->"839d76c2-309b-42e1-a12f-796165da3501"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SubscriptBox["\[CapitalPsi]", "2"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"-", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}]]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "4"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "4"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.823972431309157*^9, 3.82397245943366*^9}, 
   3.824025697833007*^9},
 CellLabel->
  "Out[146]//TraditionalForm=",ExpressionUUID->"1bfff447-a672-4aa6-ab1c-\
76824fd1913a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt13", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt13", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"weylScalarsReplace", "[", 
     RowBox[{"[", "4", "]"}], "]"}], " ", "/.", " ", 
    RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt13", " "}]}], "Input",
 CellChangeTimes->{{3.823972506378725*^9, 3.823972532698182*^9}},
 CellLabel->
  "In[147]:=",ExpressionUUID->"b1a5070e-f89d-4589-8165-3ca2b46ede63"],

Cell[BoxData[
 RowBox[{
  SubscriptBox["\[CapitalPsi]", "3"], "\[Equal]", "0"}]], "Output",
 CellChangeTimes->{{3.82397252294643*^9, 3.823972533120645*^9}, 
   3.8240256978443003`*^9},
 CellLabel->
  "Out[149]=",ExpressionUUID->"cc207088-a09c-4c72-87cc-124b548300ff"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt14", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt14", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{"Expand", "[", 
    RowBox[{"Assuming", "[", 
     RowBox[{
      RowBox[{
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"-", 
         RowBox[{"M", "[", 
          RowBox[{"u", ",", "v"}], "]"}]}]], " ", "\[NotEqual]", " ", "0"}], 
      " ", ",", " ", 
      RowBox[{"MultiplySides", "[", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"weylScalarsReplace", "[", 
           RowBox[{"[", "5", "]"}], "]"}], "  ", "/.", " ", 
          RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}], ")"}], " ", ",", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"-", 
          RowBox[{"M", "[", 
           RowBox[{"u", ",", "v"}], "]"}]}]]}], "]"}]}], "]"}], "]"}]}], 
  "   ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt14", " ", "//", "  ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8239721704671307`*^9, 3.823972170634142*^9}, {
  3.823972536572048*^9, 3.823972561106386*^9}},
 CellLabel->
  "In[150]:=",ExpressionUUID->"bc2e4f4e-b4eb-4101-a70d-b6d9672b700c"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SubscriptBox["\[CapitalPsi]", "4"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"-", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}]]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None]}]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["u", "2"]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.823972171186241*^9, 3.8239722264521503`*^9, 
  3.8239725614969997`*^9, 3.824025697874942*^9},
 CellLabel->
  "Out[152]//TraditionalForm=",ExpressionUUID->"e22c200a-9af3-4832-b97c-\
e23a421fa4b6"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt15", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt15", " ", "=", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"D", "[", 
     RowBox[{
      RowBox[{"Log", "[", 
       RowBox[{"\[Phi]2", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "]"}], ",", "v"}], "]"}], " ", 
    "\[Equal]", " ", 
    RowBox[{
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"U", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "v"}], "]"}]}], "-", " ", 
     RowBox[{
      RowBox[{"(", 
       FractionBox["1", "2"], ")"}], 
      RowBox[{"D", "[", " ", 
       RowBox[{
        RowBox[{"V", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "u"}], "]"}], " ", 
      RowBox[{"(", 
       FractionBox[
        RowBox[{"\[Phi]0", "[", 
         RowBox[{"u", ",", "v"}], "]"}], 
        RowBox[{"\[Phi]2", "[", 
         RowBox[{"u", ",", "v"}], "]"}]], ")"}]}]}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt15", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824026888210389*^9, 3.824027039514585*^9}},
 CellLabel->
  "In[227]:=",ExpressionUUID->"fda8bf62-c860-4406-9eeb-e8d28d5de66d"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"\[Phi]2", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None], 
    RowBox[{"\[Phi]2", "(", 
     RowBox[{"u", ",", "v"}], ")"}]], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    FractionBox[
     RowBox[{
      RowBox[{"\[Phi]0", "(", 
       RowBox[{"u", ",", "v"}], ")"}], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "u"}],
       MultilineFunction->None]}], 
     RowBox[{"2", " ", 
      RowBox[{"\[Phi]2", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}]]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240270002374783`*^9, 3.824027006654187*^9}, 
   3.824027040155003*^9},
 CellLabel->
  "Out[229]//TraditionalForm=",ExpressionUUID->"f6e7d302-ad10-480a-9c3f-\
fc7f033cdb73"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Expand", "[", 
   RowBox[{"Assuming", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"\[Phi]2", "[", 
       RowBox[{"u", ",", "v"}], "]"}], "\[NotEqual]", " ", "0"}], " ", ",", 
     " ", 
     RowBox[{"MultiplySides", "[", " ", 
      RowBox[{"eq2pt15", "  ", ",", " ", 
       RowBox[{"\[Phi]2", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], "]"}]}], "]"}], "]"}], " ", "//", 
  " ", "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt2", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824027064400874*^9, 3.824027116521529*^9}},
 CellLabel->
  "In[235]:=",ExpressionUUID->"d7d76105-42fe-48a6-b96f-e75884a6c548"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "v"}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240270789569674`*^9, 3.824027117194578*^9}},
 CellLabel->
  "Out[235]//TraditionalForm=",ExpressionUUID->"65f4888b-d831-4c0d-8863-\
dffceac7917c"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "v"}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240270789569674`*^9, 3.824027117223864*^9}},
 CellLabel->
  "Out[236]//TraditionalForm=",ExpressionUUID->"3039efab-fdbd-4a35-9d04-\
ddec522f6c86"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt16", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt16", " ", "=", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"D", "[", 
     RowBox[{
      RowBox[{"Log", "[", 
       RowBox[{"\[Phi]0", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "]"}], ",", "u"}], "]"}], " ", 
    "\[Equal]", " ", 
    RowBox[{
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"D", "[", 
       RowBox[{
        RowBox[{"U", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "u"}], "]"}]}], "-", " ", 
     RowBox[{
      RowBox[{"(", 
       FractionBox["1", "2"], ")"}], 
      RowBox[{"D", "[", " ", 
       RowBox[{
        RowBox[{"V", "[", 
         RowBox[{"u", ",", "v"}], "]"}], ",", "v"}], "]"}], " ", 
      RowBox[{"(", 
       FractionBox[
        RowBox[{"\[Phi]2", "[", 
         RowBox[{"u", ",", "v"}], "]"}], 
        RowBox[{"\[Phi]0", "[", 
         RowBox[{"u", ",", "v"}], "]"}]], ")"}]}]}]}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt16", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824027131798039*^9, 3.824027155845791*^9}},
 CellLabel->
  "In[237]:=",ExpressionUUID->"3de007ba-000d-4e22-b108-2f15af85375b"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"\[Phi]0", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], 
    RowBox[{"\[Phi]0", "(", 
     RowBox[{"u", ",", "v"}], ")"}]], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "-", 
    FractionBox[
     RowBox[{
      RowBox[{"\[Phi]2", "(", 
       RowBox[{"u", ",", "v"}], ")"}], " ", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None]}], 
     RowBox[{"2", " ", 
      RowBox[{"\[Phi]0", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}]]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.824027156634309*^9},
 CellLabel->
  "Out[239]//TraditionalForm=",ExpressionUUID->"62a44277-90c6-462f-b25a-\
0b86ec0ac81c"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Expand", "[", 
   RowBox[{"Assuming", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"\[Phi]0", "[", 
       RowBox[{"u", ",", "v"}], "]"}], "\[NotEqual]", " ", "0"}], " ", ",", 
     " ", 
     RowBox[{"MultiplySides", "[", " ", 
      RowBox[{"eq2pt16", "  ", ",", " ", 
       RowBox[{"\[Phi]0", "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], "]"}]}], "]"}], "]"}], " ", "//", 
  " ", "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt3", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824027166310134*^9, 3.824027197360393*^9}},
 CellLabel->
  "In[241]:=",ExpressionUUID->"ba718536-1fd3-4ad9-a2d1-5e5a7f00dec1"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "u"}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824027173850436*^9, 3.824027197818618*^9}},
 CellLabel->
  "Out[241]//TraditionalForm=",ExpressionUUID->"e1242f80-1873-4089-98eb-\
efb17ec9dd09"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", "u"}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]0", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"\[Phi]2", "(", 
      RowBox[{"u", ",", "v"}], ")"}], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824027173850436*^9, 3.824027197821877*^9}},
 CellLabel->
  "Out[242]//TraditionalForm=",ExpressionUUID->"deacaef1-2331-4cb1-88f6-\
24a5190c5f56"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt17", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt17", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"2", " ", 
     RowBox[{"D", "[", 
      RowBox[{
       RowBox[{"D", "[", 
        RowBox[{
         RowBox[{"Log", "[", 
          FractionBox[
           RowBox[{"\[Phi]2", "[", 
            RowBox[{"u", ",", "v"}], "]"}], 
           RowBox[{"\[Phi]0", "[", 
            RowBox[{"u", ",", "v"}], "]"}]], "]"}], ",", "v"}], "]"}], " ", 
       ",", "u"}], "]"}]}], "  ", "\[Equal]", "  ", 
    RowBox[{
     RowBox[{"D", "[", " ", 
      RowBox[{
       RowBox[{
        RowBox[{"D", "[", 
         RowBox[{
          RowBox[{"V", "[", 
           RowBox[{"u", ",", "v"}], "]"}], ",", "v"}], "]"}], " ", 
        RowBox[{"(", 
         FractionBox[
          RowBox[{"\[Phi]2", "[", 
           RowBox[{"u", ",", "v"}], "]"}], 
          RowBox[{"\[Phi]0", "[", 
           RowBox[{"u", ",", "v"}], "]"}]], ")"}]}], ",", "v"}], "]"}], "-", 
     " ", 
     RowBox[{"D", "[", " ", 
      RowBox[{
       RowBox[{
        RowBox[{"D", "[", 
         RowBox[{
          RowBox[{"V", "[", 
           RowBox[{"u", ",", "v"}], "]"}], ",", "u"}], "]"}], " ", 
        RowBox[{"(", 
         FractionBox[
          RowBox[{"\[Phi]0", "[", 
           RowBox[{"u", ",", "v"}], "]"}], 
          RowBox[{"\[Phi]2", "[", 
           RowBox[{"u", ",", "v"}], "]"}]], ")"}]}], ",", "u"}], "]"}]}]}]}], 
  " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"eq2pt17", " ", "//", " ", "Expand"}], " ", "//", " ", 
   "FullSimplify"}], "  ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8240272314270277`*^9, 3.824027443157813*^9}, {
  3.824027501032462*^9, 3.8240275110939302`*^9}},
 CellLabel->
  "In[266]:=",ExpressionUUID->"4cb86ebc-3a6b-46d7-a309-c3dd3ea1bf37"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     RowBox[{
      SuperscriptBox[
       RowBox[{"\[Phi]0", "(", 
        RowBox[{"u", ",", "v"}], ")"}], "2"], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"\[Phi]2", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{
           RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
           RowBox[{"\[PartialD]", "v"}]}],
          MultilineFunction->None]}], "+", 
        RowBox[{
         RowBox[{"\[Phi]0", "(", 
          RowBox[{"u", ",", "v"}], ")"}], " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", 
           SuperscriptBox["u", "2"]}],
          MultilineFunction->None]}], "+", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[Phi]0", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None]}]}], ")"}]}], "-", 
     RowBox[{
      RowBox[{"\[Phi]2", "(", 
       RowBox[{"u", ",", "v"}], ")"}], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"\[Phi]0", "(", 
          RowBox[{"u", ",", "v"}], ")"}], " ", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"2", " ", 
            FractionBox[
             RowBox[{
              SuperscriptBox["\[PartialD]", "2"], 
              RowBox[{"\[Phi]0", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{
              RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
              RowBox[{"\[PartialD]", "v"}]}],
             MultilineFunction->None]}], "+", 
           RowBox[{
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"V", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None], " ", 
            FractionBox[
             RowBox[{"\[PartialD]", 
              RowBox[{"\[Phi]2", "(", 
               RowBox[{"u", ",", "v"}], ")"}]}], 
             RowBox[{"\[PartialD]", "v"}],
             MultilineFunction->None]}]}], ")"}]}], "-", 
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[Phi]0", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[Phi]0", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}], ")"}]}], "+", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"\[Phi]2", "(", 
        RowBox[{"u", ",", "v"}], ")"}], "2"], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[Phi]0", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}], "-", 
        RowBox[{
         RowBox[{"\[Phi]0", "(", 
          RowBox[{"u", ",", "v"}], ")"}], " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", 
           SuperscriptBox["v", "2"]}],
          MultilineFunction->None]}]}], ")"}]}], "-", 
     FractionBox[
      RowBox[{
       SuperscriptBox[
        RowBox[{"\[Phi]0", "(", 
         RowBox[{"u", ",", "v"}], ")"}], "2"], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"\[Phi]2", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{
          RowBox[{"\[Phi]0", "(", 
           RowBox[{"u", ",", "v"}], ")"}], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None]}], "+", 
         RowBox[{"2", " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"\[Phi]2", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None]}]}], ")"}]}], 
      RowBox[{"\[Phi]2", "(", 
       RowBox[{"u", ",", "v"}], ")"}]]}], 
    RowBox[{"\[Phi]0", "(", 
     RowBox[{"u", ",", "v"}], ")"}]], "\[LongEqual]", "0"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.824027282177771*^9, 3.824027329274536*^9}, {
  3.824027397245099*^9, 3.824027443777486*^9}, {3.824027506591084*^9, 
  3.8240275116005297`*^9}},
 CellLabel->
  "Out[268]//TraditionalForm=",ExpressionUUID->"97176a5f-a0d2-4733-af2c-\
25769d8e09c7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt18", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt18", " ", "=", " ", 
   RowBox[{"{", " ", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{"\[Phi]0", "[", 
       RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", " ", 
      RowBox[{"\[CurlyPhi]0", "[", 
       RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"\[Phi]2", "[", 
       RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", " ", 
      RowBox[{"\[CurlyPhi]2", "[", 
       RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}], " ", ",", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"M", "[", 
       RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", " ", 
      RowBox[{"\[ScriptCapitalM]", "[", 
       RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]}], 
    "\[IndentingNewLine]", "}"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt18", " ", "//", " ", "TableForm"}]}], "Input",
 CellChangeTimes->{{3.8240278789572363`*^9, 3.82402792973919*^9}},
 CellLabel->
  "In[279]:=",ExpressionUUID->"272bf704-1dc4-47f2-b404-c2ce6f030c1d"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{"\[Phi]0", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", 
       RowBox[{"\[CurlyPhi]0", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]},
     {
      RowBox[{
       RowBox[{"\[Phi]2", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", 
       RowBox[{"\[CurlyPhi]2", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]},
     {
      RowBox[{
       RowBox[{"M", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", 
       RowBox[{"\[ScriptCapitalM]", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.824027930058876*^9},
 CellLabel->
  "Out[281]//TableForm=",ExpressionUUID->"38226315-73c6-41e5-acf6-\
3d092f41821f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt19", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt19", " ", "=", " ", 
   RowBox[{"{", " ", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{"\[Phi]0", "[", 
       RowBox[{"u", ",", "v"}], "]"}], " ", "\[Equal]", " ", 
      RowBox[{
       RowBox[{
        RowBox[{"\[ScriptV]", "'"}], "[", "v", "]"}], " ", 
       RowBox[{"\[CurlyPhi]0", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"\[Phi]2", "[", 
       RowBox[{"u", ",", "v"}], "]"}], "\[Equal]", " ", 
      RowBox[{
       RowBox[{
        RowBox[{"\[ScriptU]", "'"}], "[", "u", "]"}], " ", 
       RowBox[{"\[CurlyPhi]2", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]}], " ", ",", " ", 
     "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"Exp", "[", 
       RowBox[{"\[ScriptCapitalM]", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}], "]"}], " ", 
      "\[Equal]", " ", 
      RowBox[{
       RowBox[{"Exp", "[", 
        RowBox[{"M", "[", 
         RowBox[{"u", ",", "v"}], "]"}], "]"}], " ", 
       RowBox[{
        RowBox[{"\[ScriptU]", "'"}], "[", "u", "]"}], " ", 
       RowBox[{
        RowBox[{"\[ScriptV]", "'"}], "[", "v", "]"}]}]}]}], 
    "\[IndentingNewLine]", "}"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt19", " ", "//", " ", "TableForm"}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824027614348555*^9, 3.824027724011821*^9}, {
  3.824027765294814*^9, 3.8240278311751204`*^9}},
 CellLabel->
  "In[274]:=",ExpressionUUID->"cb3849c6-1e5a-4c91-b99e-128e3080a317"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       RowBox[{
        RowBox[{"\[Phi]0", "(", 
         RowBox[{"u", ",", "v"}], ")"}], "\[LongEqual]", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[ScriptV]", "(", "v", ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         RowBox[{"\[CurlyPhi]0", "(", 
          RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], ")"}]}]}]},
      {
       RowBox[{
        RowBox[{"\[Phi]2", "(", 
         RowBox[{"u", ",", "v"}], ")"}], "\[LongEqual]", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[ScriptU]", "(", "u", ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         RowBox[{"\[CurlyPhi]2", "(", 
          RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], ")"}]}]}]},
      {
       RowBox[{
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"\[ScriptCapitalM]", "(", 
          RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], ")"}]], "\[LongEqual]", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[ScriptU]", "(", "u", ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"\[ScriptV]", "(", "v", ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None], " ", 
         SuperscriptBox["\[ExponentialE]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]]}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824027807041265*^9, 3.824027834365788*^9}},
 CellLabel->
  "Out[276]//TraditionalForm=",ExpressionUUID->"95490a46-7167-4883-9a79-\
71c9e8b3178b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq2pt20", "]"}], "\[IndentingNewLine]", 
 RowBox[{"eq2pt20", " ", "=", " ", "\[IndentingNewLine]", 
  RowBox[{
   FractionBox[
    RowBox[{"\[Phi]2", "[", 
     RowBox[{"u", ",", "v"}], "]"}], 
    RowBox[{"\[Phi]0", "[", 
     RowBox[{"u", ",", "v"}], "]"}]], " ", "\[Equal]", " ", 
   FractionBox[
    RowBox[{"A", "[", "u", "]"}], 
    RowBox[{"B", "[", "v", "]"}]]}]}]}], "Input",
 CellChangeTimes->{{3.824027533931932*^9, 3.824027557402285*^9}},
 CellLabel->
  "In[277]:=",ExpressionUUID->"f586fa4c-3b9f-4ec7-aee4-85368d14a6ac"],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"\[Phi]2", "[", 
    RowBox[{"u", ",", "v"}], "]"}], 
   RowBox[{"\[Phi]0", "[", 
    RowBox[{"u", ",", "v"}], "]"}]], "\[Equal]", 
  FractionBox[
   RowBox[{"A", "[", "u", "]"}], 
   RowBox[{"B", "[", "v", "]"}]]}]], "Output",
 CellChangeTimes->{3.82402755886557*^9, 3.824027855036895*^9},
 CellLabel->
  "Out[278]=",ExpressionUUID->"7f7a5e61-06ab-4dde-a0d0-a20431cd76b0"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"eq2pt18", " ", "//", " ", "TableForm"}]], "Input",
 CellChangeTimes->{{3.82402797748871*^9, 3.824027983797946*^9}},
 CellLabel->
  "In[283]:=",ExpressionUUID->"f4fc0465-6f62-41bc-a7b2-e12fa06c3de0"],

Cell[BoxData[
 TagBox[
  TagBox[GridBox[{
     {
      RowBox[{
       RowBox[{"\[Phi]0", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", 
       RowBox[{"\[CurlyPhi]0", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]},
     {
      RowBox[{
       RowBox[{"\[Phi]2", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", 
       RowBox[{"\[CurlyPhi]2", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]},
     {
      RowBox[{
       RowBox[{"M", "[", 
        RowBox[{"u", ",", "v"}], "]"}], "\[Rule]", 
       RowBox[{"\[ScriptCapitalM]", "[", 
        RowBox[{"\[ScriptU]", ",", "\[ScriptV]"}], "]"}]}]}
    },
    GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.5599999999999999]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}],
   Column],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.8240279790618258`*^9, 3.824027984073248*^9}},
 CellLabel->
  "Out[283]//TableForm=",ExpressionUUID->"ceda0ad7-9faf-490a-b956-\
8d5c769b8ac7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt1", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt1", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"Flatten", "[", 
      RowBox[{"Solve", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"eq2pt10", "[", 
          RowBox[{"[", "2", "]"}], "]"}], " ", "\[Equal]", " ", "0"}], " ", 
        ",", " ", 
        RowBox[{
         SuperscriptBox["V", 
          TagBox[
           RowBox[{"(", 
            RowBox[{"0", ",", "2"}], ")"}],
           Derivative],
          MultilineFunction->None], "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
     RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
    RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt1", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824028180767407*^9, 3.82402818377353*^9}, {
  3.8240282318954287`*^9, 3.8240285422609587`*^9}},
 CellLabel->
  "In[369]:=",ExpressionUUID->"96c0f043-c5c6-46fe-a7bd-6f07917cb6b9"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["v", "2"]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.82402854901719*^9},
 CellLabel->
  "Out[371]//TraditionalForm=",ExpressionUUID->"69aeb040-3010-4078-b659-\
7f414208b438"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt2", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt2", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Expand", "[", 
     RowBox[{
      RowBox[{"-", "4"}], "*", 
      RowBox[{"eq2pt12", "[", 
       RowBox[{"[", 
        RowBox[{"2", ",", "1"}], "]"}], "]"}]}], "]"}], " ", "\[Equal]", " ", 
    
    RowBox[{"Expand", "[", 
     RowBox[{"4", "*", 
      RowBox[{"eq2pt12", "[", 
       RowBox[{"[", 
        RowBox[{"2", ",", "2"}], "]"}], "]"}]}], "]"}]}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt2", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824028180767407*^9, 3.82402818377353*^9}, {
  3.8240282318954287`*^9, 3.824028569777116*^9}},
 CellLabel->
  "In[372]:=",ExpressionUUID->"200a393b-eceb-4346-a507-5290f1d937bd"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}], "\[LongEqual]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.8240285701872187`*^9},
 CellLabel->
  "Out[374]//TraditionalForm=",ExpressionUUID->"78f39757-5c3f-4e79-b2ac-\
3340083325f6"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt3", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt3", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"Expand", "[", 
      RowBox[{
       RowBox[{"-", "2"}], "*", 
       RowBox[{"eq2pt14", "[", 
        RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "[", 
     RowBox[{"[", "3", "]"}], "]"}], "\[Equal]", " ", 
    RowBox[{
     RowBox[{"Expand", "[", 
      RowBox[{"2", "*", 
       RowBox[{"eq2pt14", "[", 
        RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "[", 
     RowBox[{"[", 
      RowBox[{"1", ";;", "2"}], "]"}], "]"}]}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt3", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824028180767407*^9, 3.82402818377353*^9}, {
  3.8240282318954287`*^9, 3.824028547616167*^9}, {3.824028577953174*^9, 
  3.824028591789098*^9}},
 CellLabel->
  "In[375]:=",ExpressionUUID->"06457696-f40e-43a6-afa9-d6d982d906f3"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["u", "2"]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240284536856747`*^9, 3.824028520243763*^9}, 
   3.824028592992824*^9},
 CellLabel->
  "Out[377]//TraditionalForm=",ExpressionUUID->"e4e5fa17-40e6-41a1-8f91-\
c90ef13bd767"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"D", "[", 
   RowBox[{"eq5pt2", ",", "v"}], "]"}], " ", "//", " ", "pdConv"}]], "Input",
 CellChangeTimes->{{3.824028956541045*^9, 3.824028967314219*^9}},
 CellLabel->
  "In[380]:=",ExpressionUUID->"23a6a1de-888a-468e-a403-7e2ad9ceb627"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}],
      MultilineFunction->None]}]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240289579107857`*^9, 3.824028967802289*^9}},
 CellLabel->
  "Out[380]//TraditionalForm=",ExpressionUUID->"822f41c0-b891-4075-90df-\
35b966dc2ad0"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"eq2pt4", " ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", "//", " ", 
  "pdConv"}]], "Input",
 CellChangeTimes->{{3.824029082912857*^9, 3.8240290990327272`*^9}, {
  3.824029147809102*^9, 3.824029152593752*^9}},
 CellLabel->
  "In[397]:=",ExpressionUUID->"35305c84-937f-404f-a055-0650c0446fe0"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824029083722706*^9, 3.8240290993523273`*^9}, 
   3.824029152982422*^9},
 CellLabel->
  "Out[397]//TraditionalForm=",ExpressionUUID->"0d401eea-bcfd-4813-b27c-\
2bec07867418"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Flatten", "[", 
    RowBox[{"Solve", "[", " ", 
     RowBox[{"eq2pt7", ",", " ", 
      RowBox[{
       SuperscriptBox["V", 
        TagBox[
         RowBox[{"(", 
          RowBox[{"1", ",", "1"}], ")"}],
         Derivative],
        MultilineFunction->None], "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "pdConv"}]], "Input",
 CellChangeTimes->{{3.824029118313266*^9, 3.824029160418419*^9}},
 CellLabel->
  "In[399]:=",ExpressionUUID->"7c16df9c-ab97-48d6-b064-589fcd6048f4"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824029111101062*^9, 3.82402916087239*^9}},
 CellLabel->
  "Out[399]//TraditionalForm=",ExpressionUUID->"b3fe0dc4-4b91-41b6-8f88-\
946d90efdb91"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt6a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt6a", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"D", "[", 
      RowBox[{"eq5pt2", ",", "v"}], "]"}], "  ", "/.", " ", 
     RowBox[{"(", 
      RowBox[{"eq2pt4", " ", "/.", " ", 
       RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", ")"}]}], " ", "/.", 
    " ", 
    RowBox[{
     RowBox[{"Flatten", "[", 
      RowBox[{"Solve", "[", " ", 
       RowBox[{"eq2pt7", ",", " ", 
        RowBox[{
         SuperscriptBox["V", 
          TagBox[
           RowBox[{"(", 
            RowBox[{"1", ",", "1"}], ")"}],
           Derivative],
          MultilineFunction->None], "[", 
         RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
     RowBox[{"[", "1", "]"}], "]"}]}]}], "  ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt6a", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8240291794371862`*^9, 3.8240292444529*^9}},
 CellLabel->
  "In[404]:=",ExpressionUUID->"830126f3-8963-490b-b2a9-912a6e70cd81"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None], ")"}], "2"]}]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox["1", "2"], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None]}], "+", 
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}]}], ")"}]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824029197109655*^9, 3.824029244906501*^9}},
 CellLabel->
  "Out[406]//TraditionalForm=",ExpressionUUID->"8921fd0c-44c1-4760-8bf6-\
2bdf1d8b68ce"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"Flatten", "[", 
    RowBox[{"Solve", "[", " ", 
     RowBox[{"eq2pt5", " ", ",", " ", 
      RowBox[{
       SuperscriptBox["U", 
        TagBox[
         RowBox[{"(", 
          RowBox[{"2", ",", "0"}], ")"}],
         Derivative],
        MultilineFunction->None], "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Flatten", "[", 
    RowBox[{"Solve", "[", " ", 
     RowBox[{"eq2pt6", "  ", ",", " ", 
      RowBox[{
       SuperscriptBox["U", 
        TagBox[
         RowBox[{"(", 
          RowBox[{"0", ",", "2"}], ")"}],
         Derivative],
        MultilineFunction->None], "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt1", " ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824029343859104*^9, 3.8240294303487043`*^9}, {
  3.8240295621582937`*^9, 3.824029562625765*^9}},
 CellLabel->
  "In[430]:=",ExpressionUUID->"d47310b2-3a90-4089-8131-6ce2b7afb3e6"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["u", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None]}]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.82402934577017*^9, 3.824029430935075*^9}, 
   3.824029564413089*^9},
 CellLabel->
  "Out[430]//TraditionalForm=",ExpressionUUID->"909c735b-1a0c-43ff-9548-\
aa1522498bf0"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["v", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.82402934577017*^9, 3.824029430935075*^9}, 
   3.8240295644177923`*^9},
 CellLabel->
  "Out[431]//TraditionalForm=",ExpressionUUID->"533fa4b7-1688-4e26-b36d-\
6c3274386504"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["v", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.82402934577017*^9, 3.824029430935075*^9}, 
   3.824029564421514*^9},
 CellLabel->
  "Out[432]//TraditionalForm=",ExpressionUUID->"f2514173-4c57-4ab8-ac07-\
088dad3b2855"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt6b", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt6b", " ", "=", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"(", " ", 
      RowBox[{
       RowBox[{
        RowBox[{"eq5pt6a", " ", "/.", " ", 
         RowBox[{
          RowBox[{"Flatten", "[", 
           RowBox[{"Solve", "[", " ", 
            RowBox[{"eq2pt5", " ", ",", " ", 
             RowBox[{
              SuperscriptBox["U", 
               TagBox[
                RowBox[{"(", 
                 RowBox[{"2", ",", "0"}], ")"}],
                Derivative],
               MultilineFunction->None], "[", 
              RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}], "[", 
          RowBox[{"[", "1", "]"}], "]"}]}], " ", "/.", " ", 
        RowBox[{
         RowBox[{"Flatten", "[", 
          RowBox[{"Solve", "[", " ", 
           RowBox[{"eq2pt6", "  ", ",", " ", 
            RowBox[{
             SuperscriptBox["U", 
              TagBox[
               RowBox[{"(", 
                RowBox[{"0", ",", "2"}], ")"}],
               Derivative],
              MultilineFunction->None], "[", 
             RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
         RowBox[{"[", "1", "]"}], "]"}]}], " ", "/.", 
       RowBox[{"(", 
        RowBox[{"eq5pt1", " ", "/.", " ", 
         RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", ")"}]}], " ", 
      ")"}], " ", "//", " ", "Expand"}], " ", "//", " ", "Simplify"}]}], 
  "   ", ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt6b", "   ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.82402945023724*^9, 3.824029488796682*^9}, {
  3.82402957079779*^9, 3.824029598045384*^9}, {3.824029678394445*^9, 
  3.82402969471462*^9}},ExpressionUUID->"c4095b8f-f136-4f60-aee7-\
fa3facae4933"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"2", " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"M", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}], "-", 
      RowBox[{"3", " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}], "-", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}], "\[LongEqual]", "0"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.824029464839711*^9, 3.824029489267412*^9}, {
   3.8240295805862494`*^9, 3.824029598438716*^9}, 3.82402969167094*^9},
 CellLabel->
  "Out[442]//TraditionalForm=",ExpressionUUID->"b8174b3e-b25e-4629-9fd4-\
92d067a8292c"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"eq5pt6b", "[", 
   RowBox[{"[", 
    RowBox[{"1", ",", "1"}], "]"}], "]"}], "  ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt6b", "[", 
   RowBox[{"[", 
    RowBox[{"1", ",", "2"}], "]"}], "]"}], "  ", "//", " ", 
  "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824029700528679*^9, 3.82402972691189*^9}},
 CellLabel->
  "In[448]:=",ExpressionUUID->"2693132c-7441-4d29-862a-1d763be2475b"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}], "-", 
   RowBox[{"3", " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824029670119833*^9, 3.824029727387588*^9}},
 CellLabel->
  "Out[448]//TraditionalForm=",ExpressionUUID->"7e8a7a3c-3cdb-466e-8b45-\
31b151180b83"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}], "-", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824029670119833*^9, 3.8240297273913927`*^9}},
 CellLabel->
  "Out[449]//TraditionalForm=",ExpressionUUID->"85e275b6-094d-48f5-ab98-\
9464ea87698e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt6c", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt6c", " ", "=", "\[IndentingNewLine]", 
   RowBox[{"eq5pt6b", "[", 
    RowBox[{"[", 
     RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt6c", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8240297365775957`*^9, 3.824029752951899*^9}},
 CellLabel->
  "In[450]:=",ExpressionUUID->"47603c4f-e336-4622-8a93-0c5468b950d2"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}], "-", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.824029753844594*^9},
 CellLabel->
  "Out[452]//TraditionalForm=",ExpressionUUID->"b40c0884-45b2-49c5-8d94-\
0fbadaf3ba0e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"D", "[", " ", 
   RowBox[{"eq5pt2", " ", ",", " ", "u"}], " ", "]"}], "  ", "//", " ", 
  "pdConv"}]], "Input",
 CellChangeTimes->{{3.82402995756539*^9, 3.824029983988003*^9}},
 CellLabel->
  "In[454]:=",ExpressionUUID->"fbfd08a6-f080-4785-b224-3069ea676b89"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["u", "2"]}],
      MultilineFunction->None]}]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["u", "2"]}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824029966856339*^9, 3.8240299844422703`*^9}},
 CellLabel->
  "Out[454]//TraditionalForm=",ExpressionUUID->"3dbe6c1c-36e1-4451-8dff-\
2674e4903799"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"Flatten", "[", 
    RowBox[{"Solve", "[", " ", 
     RowBox[{"eq2pt7", " ", ",", "  ", 
      RowBox[{
       SuperscriptBox["V", 
        TagBox[
         RowBox[{"(", 
          RowBox[{"1", ",", "1"}], ")"}],
         Derivative],
        MultilineFunction->None], "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], "  ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt4", " ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"Flatten", "[", 
     RowBox[{"Solve", "[", " ", 
      RowBox[{"eq2pt5", " ", ",", " ", 
       RowBox[{
        SuperscriptBox["U", 
         TagBox[
          RowBox[{"(", 
           RowBox[{"2", ",", "0"}], ")"}],
          Derivative],
         MultilineFunction->None], "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
   RowBox[{"Equal", " ", "\[Rule]", " ", "Rule"}]}], "  ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt3", " ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8240300373491096`*^9, 3.824030086643618*^9}, {
  3.824030153020151*^9, 3.824030186867836*^9}},
 CellLabel->
  "In[471]:=",ExpressionUUID->"f178ba5a-1b5d-45cd-ad22-e54441d7c4c1"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030020827468*^9, 3.8240300870482817`*^9}, 
   3.824030154711307*^9, 3.824030187426424*^9},
 CellLabel->
  "Out[471]//TraditionalForm=",ExpressionUUID->"be7963ee-f0ea-4471-9859-\
b49595d0eceb"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030020827468*^9, 3.8240300870482817`*^9}, 
   3.824030154711307*^9, 3.824030187431815*^9},
 CellLabel->
  "Out[472]//TraditionalForm=",ExpressionUUID->"a8d51062-689a-4bdb-b8e2-\
83adb90a5dc8"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["u", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None]}]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], ")"}], "2"]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030020827468*^9, 3.8240300870482817`*^9}, 
   3.824030154711307*^9, 3.8240301874360857`*^9},
 CellLabel->
  "Out[473]//TraditionalForm=",ExpressionUUID->"3491cf6f-a241-4620-9ac4-\
72ee57b2a24c"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["u", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030020827468*^9, 3.8240300870482817`*^9}, 
   3.824030154711307*^9, 3.8240301874399137`*^9},
 CellLabel->
  "Out[474]//TraditionalForm=",ExpressionUUID->"d5b45fab-08a6-4141-9826-\
e2f61d222b46"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt6a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt6a", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"D", "[", " ", 
           RowBox[{"eq5pt2", " ", ",", " ", "u"}], " ", "]"}], "  ", "/.", 
          " ", 
          RowBox[{
           RowBox[{"Flatten", "[", 
            RowBox[{"Solve", "[", " ", 
             RowBox[{"eq2pt7", " ", ",", "  ", 
              RowBox[{
               SuperscriptBox["V", 
                TagBox[
                 RowBox[{"(", 
                  RowBox[{"1", ",", "1"}], ")"}],
                 Derivative],
                MultilineFunction->None], "[", 
               RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], "  ", "/.", " ", 
         RowBox[{"(", 
          RowBox[{"eq2pt4", " ", "/.", " ", 
           RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], ")"}]}], " ", "/.", 
        " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           RowBox[{"Flatten", "[", 
            RowBox[{"Solve", "[", " ", 
             RowBox[{"eq2pt5", " ", ",", " ", 
              RowBox[{
               SuperscriptBox["U", 
                TagBox[
                 RowBox[{"(", 
                  RowBox[{"2", ",", "0"}], ")"}],
                 Derivative],
                MultilineFunction->None], "[", 
               RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
           RowBox[{"[", "1", "]"}], "]"}], " ", "/.", " ", 
          RowBox[{"Equal", " ", "\[Rule]", " ", "Rule"}]}], "  ", ")"}]}], 
       " ", "/.", " ", 
       RowBox[{"(", 
        RowBox[{"eq5pt3", " ", "/.", " ", 
         RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", ")"}]}], " ", 
      ")"}], " ", "//", " ", "Expand"}], " ", "//", " ", "Simplify"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt6a", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824030220971711*^9, 3.8240302883397293`*^9}},
 CellLabel->
  "In[476]:=",ExpressionUUID->"1cfda121-6020-4d90-b093-95ec1bfe886f"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"2", " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"M", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None]}], "-", 
      RowBox[{"3", " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None]}]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}], "-", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}], "\[LongEqual]", "0"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{3.824030255586214*^9, 3.8240302887515717`*^9},
 CellLabel->
  "Out[478]//TraditionalForm=",ExpressionUUID->"0143aed6-8a20-4d6a-9a65-\
629bfc5130dd"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"eq5pt6a", "[", 
   RowBox[{"[", 
    RowBox[{"1", ",", "1"}], "]"}], "]"}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt6a", "[", 
   RowBox[{"[", 
    RowBox[{"1", ",", "2"}], "]"}], "]"}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824030298116077*^9, 3.8240303129555407`*^9}},
 CellLabel->
  "In[482]:=",ExpressionUUID->"bb06d70b-c7a4-4414-bc3c-4c65dac1e19a"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"M", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None]}], "-", 
   RowBox[{"3", " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030301281702*^9, 3.8240303133282757`*^9}},
 CellLabel->
  "Out[482]//TraditionalForm=",ExpressionUUID->"5d72d3d8-fe4a-4714-a916-\
fcdbcd9c6537"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}], "-", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030301281702*^9, 3.8240303133320847`*^9}},
 CellLabel->
  "Out[483]//TraditionalForm=",ExpressionUUID->"e0241d85-0b83-419e-802e-\
42be0e62cbc7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"D", "[", 
   RowBox[{"eq5pt1", ",", "u"}], "]"}], " ", "//", " ", "pdConv"}]], "Input",
 CellChangeTimes->{{3.824030348154866*^9, 3.824030367937158*^9}},
 CellLabel->
  "In[487]:=",ExpressionUUID->"3342a31b-39f0-46fd-80a4-8d886277a027"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "3"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", 
      SuperscriptBox["v", "2"]}]}],
    MultilineFunction->None], "\[LongEqual]", 
   RowBox[{
    RowBox[{"-", 
     RowBox[{
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], " ", 
      FractionBox[
       RowBox[{
        SuperscriptBox["\[PartialD]", "2"], 
        RowBox[{"M", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{
        RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
        RowBox[{"\[PartialD]", "v"}]}],
       MultilineFunction->None]}]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030350262903*^9, 3.824030368402857*^9}},
 CellLabel->
  "Out[487]//TraditionalForm=",ExpressionUUID->"2ede799b-fa1d-4c6d-8e8f-\
723d7133f911"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"eq2pt7", " ", "//", "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Flatten", "[", 
   RowBox[{"Solve", "[", " ", 
    RowBox[{
     RowBox[{"D", "[", 
      RowBox[{"eq2pt7", ",", "v"}], "]"}], ",", " ", 
     RowBox[{
      SuperscriptBox["V", 
       TagBox[
        RowBox[{"(", 
         RowBox[{"1", ",", "2"}], ")"}],
        Derivative],
       MultilineFunction->None], "[", 
      RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824030465087523*^9, 3.8240305079499187`*^9}},
 CellLabel->
  "In[492]:=",ExpressionUUID->"6d358fc1-8d81-4cbe-b969-9a98c84ea821"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    FractionBox[
     RowBox[{
      SuperscriptBox["\[PartialD]", "2"], 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{
      RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
      RowBox[{"\[PartialD]", "v"}]}],
     MultilineFunction->None]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030461675935*^9, 3.824030508419573*^9}},
 CellLabel->
  "Out[492]//TraditionalForm=",ExpressionUUID->"35401713-47c3-46c4-bce1-\
14217387bf57"],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    FractionBox[
     RowBox[{
      SuperscriptBox["\[PartialD]", "3"], 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{
      RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}]}],
     MultilineFunction->None], "\[Rule]", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None]}], "+", 
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None]}], "+", 
       RowBox[{
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["v", "2"]}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None]}], "+", 
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", 
          SuperscriptBox["v", "2"]}],
         MultilineFunction->None]}]}], ")"}]}]}], "}"}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030461675935*^9, 3.824030508425899*^9}},
 CellLabel->
  "Out[493]//TraditionalForm=",ExpressionUUID->"98eed14a-a93a-4528-8c08-\
e12b1d20453a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "eq5pt8a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt8a", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"D", "[", 
       RowBox[{"eq5pt1", ",", "u"}], "]"}], " ", "/.", " ", 
      RowBox[{"Flatten", "[", 
       RowBox[{"Solve", "[", " ", 
        RowBox[{
         RowBox[{"D", "[", 
          RowBox[{"eq2pt7", ",", "v"}], "]"}], ",", " ", 
         RowBox[{
          SuperscriptBox["V", 
           TagBox[
            RowBox[{"(", 
             RowBox[{"1", ",", "2"}], ")"}],
            Derivative],
           MultilineFunction->None], "[", 
          RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}]}], "   ", "//", " ", 
     "Expand"}], " ", "//", " ", "Simplify"}]}], "  ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt8a", " ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824030536023054*^9, 3.8240305803350763`*^9}},
 CellLabel->
  "In[497]:=",ExpressionUUID->"9cb875b7-879e-425c-96e8-e99bcc07a7ad"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"2", " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{"2", " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", 
       SuperscriptBox["v", "2"]}],
      MultilineFunction->None]}]}], "\[LongEqual]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}], "+", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{
       SuperscriptBox["\[PartialD]", "2"], 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{
       RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
       RowBox[{"\[PartialD]", "v"}]}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.824030547737521*^9, 3.824030580965876*^9}},
 CellLabel->
  "Out[499]//TraditionalForm=",ExpressionUUID->"e5c02a3e-6fde-49d9-913b-\
b7c17e926466"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"Flatten", "[", 
    RowBox[{"Solve", "[", 
     RowBox[{"eq2pt8", ",", 
      RowBox[{
       SuperscriptBox["M", 
        TagBox[
         RowBox[{"(", 
          RowBox[{"1", ",", "1"}], ")"}],
         Derivative],
        MultilineFunction->None], "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], "  ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt3", "  ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Flatten", "[", 
    RowBox[{"Solve", "[", 
     RowBox[{"eq2pt6", " ", ",", 
      RowBox[{
       SuperscriptBox["U", 
        TagBox[
         RowBox[{"(", 
          RowBox[{"0", ",", "2"}], ")"}],
         Derivative],
        MultilineFunction->None], "[", 
       RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"Flatten", "[", 
     RowBox[{"Solve", "[", " ", 
      RowBox[{"eq2pt7", ",", "  ", 
       RowBox[{
        SuperscriptBox["V", 
         TagBox[
          RowBox[{"(", 
           RowBox[{"1", ",", "1"}], ")"}],
          Derivative],
         MultilineFunction->None], "[", 
        RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}], " ", "//", " ", "pdConv"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq2pt4", " ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", "//", " ", 
  "pdConv"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt1", " ", "/.", " ", 
   RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", "//", " ", 
  "pdConv"}]}], "Input",
 CellChangeTimes->{{3.824030649502605*^9, 3.8240306852987223`*^9}, {
  3.824030734349427*^9, 3.8240307348334217`*^9}, {3.8240307846699467`*^9, 
  3.824030785061449*^9}, {3.824030815397674*^9, 3.824030829453053*^9}, {
  3.824030863466734*^9, 3.824030877281673*^9}},
 CellLabel->
  "In[525]:=",ExpressionUUID->"cf7aab64-97cb-4ac8-acbb-799e6b36b6c6"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"M", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}], "-", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240306445042763`*^9, 3.824030685843665*^9}, 
   3.824030735662554*^9, 3.82403078649621*^9, 3.824030829961266*^9, 
   3.8240308778012743`*^9},
 CellLabel->
  "Out[525]//TraditionalForm=",ExpressionUUID->"02cc51f4-fcf8-4704-8fcb-\
3ec3e6b166e1"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["u", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "u"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240306445042763`*^9, 3.824030685843665*^9}, 
   3.824030735662554*^9, 3.82403078649621*^9, 3.824030829961266*^9, 
   3.8240308778054047`*^9},
 CellLabel->
  "Out[526]//TraditionalForm=",ExpressionUUID->"c8b57273-f960-4adf-a54d-\
894f4cc90ea9"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["v", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"2", " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"M", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], " ", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None]}]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"V", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], ")"}], "2"]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240306445042763`*^9, 3.824030685843665*^9}, 
   3.824030735662554*^9, 3.82403078649621*^9, 3.824030829961266*^9, 
   3.824030877810199*^9},
 CellLabel->
  "Out[527]//TraditionalForm=",ExpressionUUID->"8d3cd9c2-149a-40d7-9942-\
bbe49f6c5ebf"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None]}], "+", 
      RowBox[{
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"U", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "u"}],
        MultilineFunction->None], " ", 
       FractionBox[
        RowBox[{"\[PartialD]", 
         RowBox[{"V", "(", 
          RowBox[{"u", ",", "v"}], ")"}]}], 
        RowBox[{"\[PartialD]", "v"}],
        MultilineFunction->None]}]}], ")"}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240306445042763`*^9, 3.824030685843665*^9}, 
   3.824030735662554*^9, 3.82403078649621*^9, 3.824030829961266*^9, 
   3.824030877814756*^9},
 CellLabel->
  "Out[528]//TraditionalForm=",ExpressionUUID->"5290135c-344a-403c-919b-\
2bda3ecfd934"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"U", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{
     RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
     RowBox[{"\[PartialD]", "v"}]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240306445042763`*^9, 3.824030685843665*^9}, 
   3.824030735662554*^9, 3.82403078649621*^9, 3.824030829961266*^9, 
   3.8240308778182173`*^9},
 CellLabel->
  "Out[529]//TraditionalForm=",ExpressionUUID->"cdd45f7f-e676-4c1a-955d-\
3b205676242a"],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[PartialD]", "2"], 
     RowBox[{"V", "(", 
      RowBox[{"u", ",", "v"}], ")"}]}], 
    RowBox[{"\[PartialD]", 
     SuperscriptBox["v", "2"]}],
    MultilineFunction->None], "\[Rule]", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"U", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}], "-", 
    RowBox[{
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"M", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None], " ", 
     FractionBox[
      RowBox[{"\[PartialD]", 
       RowBox[{"V", "(", 
        RowBox[{"u", ",", "v"}], ")"}]}], 
      RowBox[{"\[PartialD]", "v"}],
      MultilineFunction->None]}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.8240306445042763`*^9, 3.824030685843665*^9}, 
   3.824030735662554*^9, 3.82403078649621*^9, 3.824030829961266*^9, 
   3.8240308778220654`*^9},
 CellLabel->
  "Out[530]//TraditionalForm=",ExpressionUUID->"9dc87395-ac2b-454e-975f-\
149d7eeaef00"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "eq5pt8b", "]"}], " ", 
  RowBox[{"(*", " ", 
   RowBox[{"Not", " ", "even", " ", "close"}], " ", "*)"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eq5pt8b", " ", "=", " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{
     RowBox[{"(", " ", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{"eq5pt8a", "  ", "/.", " ", 
            RowBox[{"Flatten", "[", 
             RowBox[{"Solve", "[", 
              RowBox[{"eq2pt8", ",", 
               RowBox[{
                SuperscriptBox["M", 
                 TagBox[
                  RowBox[{"(", 
                   RowBox[{"1", ",", "1"}], ")"}],
                  Derivative],
                 MultilineFunction->None], "[", 
                RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}]}], " ", "/.", 
           " ", 
           RowBox[{"(", 
            RowBox[{"eq5pt3", "  ", "/.", " ", 
             RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], ")"}]}], " ", "/.", 
          " ", 
          RowBox[{"Flatten", "[", 
           RowBox[{"Solve", "[", 
            RowBox[{"eq2pt6", " ", ",", 
             RowBox[{
              SuperscriptBox["U", 
               TagBox[
                RowBox[{"(", 
                 RowBox[{"0", ",", "2"}], ")"}],
                Derivative],
               MultilineFunction->None], "[", 
              RowBox[{"u", ",", "v"}], "]"}]}], "]"}], "]"}]}], " ", "/.", 
         " ", 
         RowBox[{"Flatten", "[", 
          RowBox[{"Solve", "[", " ", 
           RowBox[{"eq2pt7", ",", "  ", 
            RowBox[{
             SuperscriptBox["V", 
              TagBox[
               RowBox[{"(", 
                RowBox[{"1", ",", "1"}], ")"}],
               Derivative],
              MultilineFunction->None], "[", 
             RowBox[{"u", ",", "v"}], "]"}]}], " ", "]"}], "]"}]}], " ", "/.",
         " ", 
        RowBox[{"(", 
         RowBox[{"eq2pt4", " ", "/.", " ", 
          RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], " ", ")"}]}], " ", "/.",
        " ", 
       RowBox[{"(", 
        RowBox[{"eq5pt1", " ", "/.", " ", 
         RowBox[{"Equal", "\[Rule]", " ", "Rule"}]}], ")"}]}], " ", ")"}], 
     " ", "//", " ", "Expand"}], " ", "//", " ", "Simplify"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"eq5pt8b", "  ", "//", " ", "pdConv"}]}], "Input",
 CellChangeTimes->{{3.8240308999613523`*^9, 3.8240310260743313`*^9}},
 CellLabel->
  "In[535]:=",ExpressionUUID->"7b277787-2cbe-4012-9d58-a0ad0cbb4a62"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    SuperscriptBox[
     RowBox[{"(", 
      FractionBox[
       RowBox[{"\[PartialD]", 
        RowBox[{"V", "(", 
         RowBox[{"u", ",", "v"}], ")"}]}], 
       RowBox[{"\[PartialD]", "v"}],
       MultilineFunction->None], ")"}], "2"]}], "\[LongEqual]", 
   RowBox[{
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "u"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"U", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None], " ", 
    FractionBox[
     RowBox[{"\[PartialD]", 
      RowBox[{"V", "(", 
       RowBox[{"u", ",", "v"}], ")"}]}], 
     RowBox[{"\[PartialD]", "v"}],
     MultilineFunction->None]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.824030958116062*^9, {3.8240309974389687`*^9, 3.824031026914671*^9}},
 CellLabel->
  "Out[537]//TraditionalForm=",ExpressionUUID->"33c46d35-4f87-4c86-9fb6-\
0fc3e7984917"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
    "eq2pt2", ",", "\[IndentingNewLine]", "eq2pt3", ",", 
     "\[IndentingNewLine]", "eq2pt4", ",", "\[IndentingNewLine]", "eq2pt5", 
     ",", "\[IndentingNewLine]", "eq2pt6", " ", ",", "\[IndentingNewLine]", 
     "eq2pt7", ",", "\[IndentingNewLine]", "eq2pt8"}], "\[IndentingNewLine]", 
    "}"}], " ", "//", " ", "TableForm"}], " ", "//", " ", "pdConv"}]], "Input",\

 CellChangeTimes->{{3.824028979740931*^9, 3.824029039532392*^9}},
 CellLabel->
  "In[390]:=",ExpressionUUID->"460dcf6e-11c0-4731-95ac-f3b1f9bb71ae"],

Cell[BoxData[
 FormBox[
  TagBox[
   TagBox[GridBox[{
      {
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"\[Phi]2", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "v"}],
         MultilineFunction->None], "\[LongEqual]", 
        RowBox[{
         RowBox[{
          FractionBox["1", "2"], " ", 
          RowBox[{"\[Phi]2", "(", 
           RowBox[{"u", ",", "v"}], ")"}], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None]}], "-", 
         RowBox[{
          FractionBox["1", "2"], " ", 
          RowBox[{"\[Phi]0", "(", 
           RowBox[{"u", ",", "v"}], ")"}], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None]}]}]}]},
      {
       RowBox[{
        FractionBox[
         RowBox[{"\[PartialD]", 
          RowBox[{"\[Phi]0", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{"\[PartialD]", "u"}],
         MultilineFunction->None], "\[LongEqual]", 
        RowBox[{
         RowBox[{
          FractionBox["1", "2"], " ", 
          RowBox[{"\[Phi]0", "(", 
           RowBox[{"u", ",", "v"}], ")"}], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None]}], "-", 
         RowBox[{
          FractionBox["1", "2"], " ", 
          RowBox[{"\[Phi]2", "(", 
           RowBox[{"u", ",", "v"}], ")"}], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None]}]}]}]},
      {
       RowBox[{
        FractionBox[
         RowBox[{
          SuperscriptBox["\[PartialD]", "2"], 
          RowBox[{"U", "(", 
           RowBox[{"u", ",", "v"}], ")"}]}], 
         RowBox[{
          RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
          RowBox[{"\[PartialD]", "v"}]}],
         MultilineFunction->None], "\[LongEqual]", 
        RowBox[{
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "u"}],
          MultilineFunction->None], " ", 
         FractionBox[
          RowBox[{"\[PartialD]", 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", "v"}],
          MultilineFunction->None]}]}]},
      {
       RowBox[{
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", 
           SuperscriptBox["u", "2"]}],
          MultilineFunction->None]}], "\[LongEqual]", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"2", " ", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], " ", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None]}]}], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "u"}],
            MultilineFunction->None], ")"}], "2"]}]}]},
      {
       RowBox[{
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"U", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{"\[PartialD]", 
           SuperscriptBox["v", "2"]}],
          MultilineFunction->None]}], "\[LongEqual]", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"2", " ", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"M", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], " ", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None]}]}], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"U", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"], "+", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox[
            RowBox[{"\[PartialD]", 
             RowBox[{"V", "(", 
              RowBox[{"u", ",", "v"}], ")"}]}], 
            RowBox[{"\[PartialD]", "v"}],
            MultilineFunction->None], ")"}], "2"]}]}]},
      {
       RowBox[{
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"V", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{
           RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
           RowBox[{"\[PartialD]", "v"}]}],
          MultilineFunction->None]}], "\[LongEqual]", 
        RowBox[{
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None]}], "+", 
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None]}]}]}]},
      {
       RowBox[{
        RowBox[{"2", " ", 
         FractionBox[
          RowBox[{
           SuperscriptBox["\[PartialD]", "2"], 
           RowBox[{"M", "(", 
            RowBox[{"u", ",", "v"}], ")"}]}], 
          RowBox[{
           RowBox[{"\[PartialD]", "u"}], "\[ThinSpace]", 
           RowBox[{"\[PartialD]", "v"}]}],
          MultilineFunction->None]}], "\[LongEqual]", 
        RowBox[{
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"V", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None]}], "-", 
         RowBox[{
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "u"}],
           MultilineFunction->None], " ", 
          FractionBox[
           RowBox[{"\[PartialD]", 
            RowBox[{"U", "(", 
             RowBox[{"u", ",", "v"}], ")"}]}], 
           RowBox[{"\[PartialD]", "v"}],
           MultilineFunction->None]}]}]}]}
     },
     GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}}],
    Column],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.824028981792804*^9, {3.824029013618376*^9, 3.824029041935747*^9}},
 CellLabel->
  "Out[390]//TraditionalForm=",ExpressionUUID->"23df47b7-bc50-4d52-9250-\
b0a5efe6afa9"]
}, Open  ]]
},
WindowSize->{1272, 675},
WindowMargins->{{Automatic, 0}, {Automatic, 0}},
FrontEndVersion->"12.3 for Mac OS X x86 (64-bit) (May 11, 2021)",
StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", 
  CharacterEncoding -> "UTF-8"],
ExpressionUUID->"de4e3cb3-a779-4089-a1b4-f206314cf74a"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 1204, 18, 159, "Title",ExpressionUUID->"ac7ede52-fd73-4390-914d-b6e3e0416669",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[1787, 42, 746, 14, 76, "Author",ExpressionUUID->"a7cf401a-8230-4cc9-8efc-897839b4cd03",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[2570, 61, 228, 4, 69, "Section",ExpressionUUID->"ce347cdc-9576-41cd-aaa3-96a0b0d7f7db",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[2801, 67, 433, 9, 63, "Input",ExpressionUUID->"eccb8452-cc61-4fc3-b1bc-c9b4ad5b0a7f",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[3237, 78, 1129, 18, 43, "Output",ExpressionUUID->"10096b81-8220-4e62-ac0e-a96fce26a8ca",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[4403, 101, 545, 9, 55, "Section",ExpressionUUID->"68e4d51f-e3c5-4e02-a588-bd630dbac483",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[4951, 112, 682, 12, 63, "Input",ExpressionUUID->"bafb7e88-cde0-4e77-b0c8-e6a6e44d8cf1",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[5636, 126, 953, 16, 43, "Output",ExpressionUUID->"9dbf62eb-9b41-4694-a068-41e4c4b96247",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[6592, 144, 500, 9, 63, "Input",ExpressionUUID->"4c2b0552-70ac-47e9-9cbb-55f938d42dc7",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[7095, 155, 420, 8, 43, "Output",ExpressionUUID->"75fac26d-16d4-4d92-988b-6c62b1cf7f0e",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[7518, 165, 583, 10, 84, "Input",ExpressionUUID->"8c998aae-b2d8-4507-bbcb-d7d1ea4f5a21",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[8104, 177, 1176, 20, 43, "Output",ExpressionUUID->"f47bb930-7881-44e5-ab99-a93ae4d7e610",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}]
}, Closed]],
Cell[CellGroupData[{
Cell[9317, 202, 251, 4, 55, "Section",ExpressionUUID->"8754be25-0c4a-418f-ae64-d23288ea7656",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[9571, 208, 1668, 45, 189, "Input",ExpressionUUID->"c0ae56bc-4016-4e90-9a4d-80b9c4624ec2",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[11242, 255, 1401, 24, 24, "Print",ExpressionUUID->"3c7eeaa2-4433-4e5c-8173-cf45ab9922c7",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[12646, 281, 1415, 24, 24, "Print",ExpressionUUID->"0a191a8f-85c6-442e-b8a6-4017aed2ceb3",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[14064, 307, 1277, 20, 41, "Output",ExpressionUUID->"20b2b227-3a6e-497d-b6f8-a5246e9bd545",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[15344, 329, 268, 4, 41, "Input",ExpressionUUID->"3f1f32ae-fcc0-4f0a-9647-0b6233dcb972",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[15615, 335, 308, 5, 41, "Input",ExpressionUUID->"23d9a452-32cf-47b3-9452-11124d2fb318",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Closed]],
Cell[CellGroupData[{
Cell[15960, 345, 266, 5, 55, "Section",ExpressionUUID->"edc11028-66e7-49bd-9138-a49f79fb0990",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[16229, 352, 3865, 88, 630, "Input",ExpressionUUID->"5af2edf2-72c8-4e3e-a207-0a6f5da17e9b",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[20097, 442, 3178, 99, 483, "Output",ExpressionUUID->"9f2e1ae7-3065-4332-8ba1-ebc19636aef6",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[23278, 543, 675, 16, 63, "Input",ExpressionUUID->"9ac3639f-654e-4369-90f2-92931352eab3",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}]
}, Closed]],
Cell[CellGroupData[{
Cell[23990, 564, 362, 6, 55, "Section",ExpressionUUID->"27556425-79d3-4b68-b0a5-90f78a961d6b",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.}],
Cell[24355, 572, 1659, 41, 126, "Input",ExpressionUUID->"a23012f5-6128-4c78-b605-c749f413943d",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.}],
Cell[26017, 615, 1056, 26, 84, "Input",ExpressionUUID->"c358de30-53ce-4237-8266-c73aa7430639",
 CellGroupingRules->{"GroupTogetherGrouping", 10003.}]
}, Closed]],
Cell[CellGroupData[{
Cell[27110, 646, 227, 4, 55, "Section",ExpressionUUID->"2ec33168-5c55-4470-ae8c-7b76d3f10d2f",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[27340, 652, 891, 23, 86, "Input",ExpressionUUID->"7d789c67-b0a1-40a0-9059-d6ebdda7bd71",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[28234, 677, 724, 20, 44, "Output",ExpressionUUID->"cdf3f7f2-75f1-4145-b4a7-50b2955f4f9f",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[28961, 699, 456, 10, 41, "Input",ExpressionUUID->"27b7d8af-ae26-4ada-a9f1-c9a562e987ea",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[29420, 711, 1189, 35, 113, "Output",ExpressionUUID->"e1b00276-502a-46bf-a209-8ee8aa4f0089",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[30612, 748, 924, 20, 168, "Input",ExpressionUUID->"881bb4d0-dea5-4d1b-826a-dec8bd78d590",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[31539, 770, 993, 32, 87, "Output",ExpressionUUID->"da2c37ca-a7a9-4685-b378-578fb5ad82ac",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[32535, 804, 707, 14, 105, "Input",ExpressionUUID->"04aa96da-4acc-4ec1-b893-b40d492306ad",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[33245, 820, 1586, 47, 113, "Output",ExpressionUUID->"85c1ae31-3144-4c35-be37-394b40a4bed3",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[34834, 869, 641, 13, 105, "Input",ExpressionUUID->"58fdf474-9751-4042-99ea-c6b1200d0c94",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[35478, 884, 1485, 43, 113, "Output",ExpressionUUID->"ad497150-bb18-4347-8ac4-5690b5c273c2",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[36966, 929, 442, 10, 41, "Input",ExpressionUUID->"826cfed4-fd43-42dd-86b7-b113604f0778",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[37411, 941, 796, 23, 101, "Output",ExpressionUUID->"3582fbad-e80c-46c1-933a-4c8b862412ea",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[38210, 966, 463, 11, 41, "Input",ExpressionUUID->"157ea336-3258-466d-97f1-be4420ebb419",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}],
Cell[38676, 979, 796, 23, 101, "Output",ExpressionUUID->"c8bbb129-e32b-4ef0-85d9-c0ca987cbac8",
 CellGroupingRules->{"GroupTogetherGrouping", 10004.}]
}, Closed]],
Cell[CellGroupData[{
Cell[39509, 1007, 1096, 31, 119, "Input",ExpressionUUID->"f2c9328d-ebf1-4eae-8716-6ef93469e28f"],
Cell[40608, 1040, 1041, 33, 69, "Output",ExpressionUUID->"ec0f4d12-3b28-4872-b3d5-2f686ffbbf71"]
}, Open  ]],
Cell[CellGroupData[{
Cell[41686, 1078, 1094, 31, 122, "Input",ExpressionUUID->"532e7043-8d39-4c9c-b979-722e556910b4"],
Cell[42783, 1111, 1043, 33, 69, "Output",ExpressionUUID->"0bbd60b5-f24a-49c8-b1c2-43278bd31809"]
}, Open  ]],
Cell[CellGroupData[{
Cell[43863, 1149, 291, 5, 69, "Section",ExpressionUUID->"b4342229-4b4c-4ae1-b07f-a7eb2e3408cc",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[44157, 1156, 5569, 128, 714, "Input",ExpressionUUID->"97f1e155-14b5-4505-89b5-eb7b265a565b",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[49729, 1286, 1026, 22, 65, "Input",ExpressionUUID->"94343561-7323-446a-bc32-f238d558bf5a",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[50758, 1310, 307, 6, 41, "Output",ExpressionUUID->"3744f583-bf2a-41e6-b4e0-261f0a68b4e9",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[51068, 1318, 262, 4, 41, "Input",ExpressionUUID->"c929543c-251d-47bd-a96e-af65ea77dbc3",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[51333, 1324, 1111, 34, 45, "Output",ExpressionUUID->"5195a509-2e97-4cbe-9e95-9a965dfd417d",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[52447, 1360, 739, 17, 84, "Input",ExpressionUUID->"ea42e993-fd04-4304-bdbb-dada5f7448f8",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[53189, 1379, 354, 8, 45, "Output",ExpressionUUID->"42afd90d-5496-4bff-9012-95fe3656911a",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[53546, 1389, 269, 4, 41, "Output",ExpressionUUID->"046f46c4-d6f3-4b4f-b59e-5e7f67c64fd2",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[53818, 1395, 1605, 47, 108, "Output",ExpressionUUID->"3ad707e8-e032-40e7-b89f-3847b124080e",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[55426, 1444, 940, 22, 84, "Input",ExpressionUUID->"0864c69c-7656-4ce6-8b86-b94f14127e8a",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[56369, 1468, 410, 9, 45, "Output",ExpressionUUID->"5897bc5f-4abd-4961-93f1-e3c70631cd33",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[56782, 1479, 313, 4, 41, "Output",ExpressionUUID->"d0c4dbbd-3350-4790-a9b9-388f5a86f7c7",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[57098, 1485, 19120, 540, 368, "Output",ExpressionUUID->"7fbeda92-1ebe-47b4-85a5-5e3db62bbea1",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[76221, 2027, 933, 22, 84, "Input",ExpressionUUID->"25dcaf58-6ed4-4938-83e3-e7381f29fbd9",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[77157, 2051, 339, 7, 45, "Output",ExpressionUUID->"50b4f8a5-5c00-441a-b767-f0925d9dcd0d",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[77499, 2060, 286, 4, 41, "Output",ExpressionUUID->"877816cb-35cc-4473-8c9c-1ac2ec828fef",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[77788, 2066, 116537, 2898, 488, "Output",ExpressionUUID->"d7b742c7-77ab-4a31-ba04-4d94bcff31af",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[194328, 4966, 935, 22, 84, "Input",ExpressionUUID->"27b31eb5-f7d1-450b-9d14-bd230ac96d58",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[195266, 4990, 321, 7, 45, "Output",ExpressionUUID->"af24bf5d-1a7b-4620-845c-ee5fbc24dc6e",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[195590, 4999, 282, 4, 41, "Output",ExpressionUUID->"fed6241b-de5a-48e4-85f1-7d9a8e51c017",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[195875, 5005, 11948, 339, 158, "Output",ExpressionUUID->"7c3cabe5-c97e-4fc5-ac33-1c151093983d",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[207826, 5346, 936, 22, 84, "Input",ExpressionUUID->"1c9819e0-3def-4514-9dd3-65e636b6f4da",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[208765, 5370, 288, 6, 41, "Output",ExpressionUUID->"06b86e6c-1a1a-4c25-9060-0e479cc92ab0",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[209056, 5378, 284, 4, 41, "Output",ExpressionUUID->"36a06700-09b0-4523-8761-23372709d98a",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[209343, 5384, 2213, 66, 74, "Output",ExpressionUUID->"7bf87406-d17f-4890-ac23-43e3510cd116",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[211559, 5452, 884, 20, 84, "Input",ExpressionUUID->"1f18a948-5b0a-47d7-a08c-1980f1ad26ec",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[212446, 5474, 285, 6, 41, "Output",ExpressionUUID->"b21c9c8d-a76b-41af-b519-8ccb6732c70a",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[212734, 5482, 290, 4, 41, "Output",ExpressionUUID->"7e7ba2d3-c6ec-4a74-b3af-56e49dba2ce3",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[213027, 5488, 18507, 543, 260, "Output",ExpressionUUID->"8225afd1-c0da-4c79-988c-0a6bde291cfe",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[231537, 6033, 883, 20, 84, "Input",ExpressionUUID->"469cb02a-95c7-4d00-b7c0-15962aefd582",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[232423, 6055, 323, 7, 45, "Output",ExpressionUUID->"9b2c4d0a-8ddf-49f0-8af6-b68e7b979566",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[232749, 6064, 283, 4, 41, "Output",ExpressionUUID->"f7777bb3-1f2b-4c9f-bb33-435248a5b302",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[233035, 6070, 11288, 323, 158, "Output",ExpressionUUID->"371ccef3-7e73-41b3-814d-e785bbbd9682",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[244326, 6395, 832, 19, 84, "Input",ExpressionUUID->"fe54afe2-6fee-4c36-b691-dc7e0e045387",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[245161, 6416, 339, 7, 45, "Output",ExpressionUUID->"41265c6c-3b25-4a88-b22a-0c1a00889f04",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[245503, 6425, 279, 4, 41, "Output",ExpressionUUID->"3363190b-557a-4abe-a1ec-f2a7525608d1",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[245785, 6431, 75027, 1965, 488, "Output",ExpressionUUID->"db5d3699-b4cd-49b3-bf1e-19dbdbbd7824",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[320815, 8398, 979, 22, 84, "Input",ExpressionUUID->"3103a7c9-bbf7-4410-ae44-783a83df09ee",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[321797, 8422, 355, 7, 45, "Output",ExpressionUUID->"42cd9383-d9e2-4077-8a99-adec80e28c1b",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[322155, 8431, 306, 4, 41, "Output",ExpressionUUID->"039c28f6-84a8-4479-b38e-34d4a07ff496",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[322464, 8437, 121329, 2921, 398, "Output",ExpressionUUID->"4885febb-a2b1-417c-9fa4-9a58c2b2392e",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[443830, 11363, 278, 5, 55, "Section",ExpressionUUID->"0497c6ca-0986-4949-80f3-3020af7b17c4",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[444111, 11370, 1927, 50, 210, "Input",ExpressionUUID->"01c3549b-df62-4083-9e27-a3517ae51a04",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[446041, 11422, 9322, 272, 186, "Output",ExpressionUUID->"39bd0798-e125-4f0d-88ba-a342e2d1b738",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[455366, 11696, 1936, 50, 210, "Input",ExpressionUUID->"13d26424-f102-4a87-b777-e13eaaf052aa",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[457305, 11748, 9719, 281, 188, "Output",ExpressionUUID->"c145c29e-8ba0-45f5-99c7-2c7edba55219",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[467027, 12031, 1094, 28, 107, "Input",ExpressionUUID->"82d648df-d710-490c-8571-7d6f84238eab",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[468124, 12061, 997, 30, 72, "Output",ExpressionUUID->"c5823668-fba9-47a2-bb59-4a3ef9a4ce5b",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[469124, 12093, 1115, 28, 107, "Input",ExpressionUUID->"7d3a4c0d-4bb6-4ca1-8157-0703bf8c7eab",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[470242, 12123, 1666, 51, 74, "Output",ExpressionUUID->"3a6b9889-dd2d-4e72-9d91-205b5635300f",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[471911, 12176, 549, 11, 105, "Input",ExpressionUUID->"cd75163d-b7f2-4081-a250-c841c273c662",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[472463, 12189, 1585, 49, 74, "Output",ExpressionUUID->"7e1d0358-4631-43ed-8329-504e7a660a62",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[474051, 12240, 1115, 28, 107, "Input",ExpressionUUID->"b9717b03-36f7-45d9-8330-8a8eba05269d",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[475169, 12270, 1666, 51, 74, "Output",ExpressionUUID->"8049029e-cfb7-4976-b8d4-1ff7052d8645",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[476838, 12323, 564, 11, 105, "Input",ExpressionUUID->"916b72a7-ff6d-407b-a396-b783a6760aa0",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[477405, 12336, 1561, 49, 74, "Output",ExpressionUUID->"1fcc1d5c-7ddb-4dff-8686-34d1916637b0",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[478969, 12387, 1254, 32, 107, "Input",ExpressionUUID->"7608b58b-c2c0-4c2f-a6b7-27252ca6ebef",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[480226, 12421, 1549, 47, 72, "Output",ExpressionUUID->"bfd980e2-0cb2-407a-bbb0-42c4521f482d",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[481778, 12470, 546, 10, 105, "Input",ExpressionUUID->"efa1dbc0-8cfe-49b1-a0ab-be8249e64392",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[482327, 12482, 1457, 45, 72, "Output",ExpressionUUID->"ed0e3a2e-f2e3-4ff2-a4b7-1a1e9b1604e0",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[483787, 12529, 1051, 29, 44, "Input",ExpressionUUID->"666fdeca-44db-4de1-ab18-1d773135a3c1",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[484841, 12560, 1921, 58, 74, "Output",ExpressionUUID->"ccd03e5c-25d9-47a4-a132-44356f627047",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[486765, 12620, 377, 8, 41, "Input",ExpressionUUID->"8f16f23f-970d-4a5e-ba75-4fc94a5a198e",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[487145, 12630, 997, 30, 72, "Output",ExpressionUUID->"1b94b374-1576-4ba4-8d1f-fb8021509deb",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[488145, 12662, 1486, 38, 107, "Input",ExpressionUUID->"0a834094-8203-40b8-aa2a-4cdaa8071c41",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[489634, 12702, 1545, 47, 72, "Output",ExpressionUUID->"fb9ffb60-f9d8-4140-896d-bc592303a0b7",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[491182, 12751, 550, 11, 105, "Input",ExpressionUUID->"99270483-fbf8-4384-8119-44bc52fd7946",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[491735, 12764, 1455, 45, 72, "Output",ExpressionUUID->"e8363f05-76da-4539-8e63-c89ce19fb66f",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}]
}, Closed]],
Cell[CellGroupData[{
Cell[493227, 12814, 323, 8, 38, "Input",ExpressionUUID->"7eeb4c14-37bb-4bb6-8062-2aab8b2b4a06",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[493553, 12824, 631, 15, 84, "Input",ExpressionUUID->"6db4a4ad-ab78-4d2d-91a0-fecd7833a1cc",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[494187, 12841, 455, 12, 41, "Output",ExpressionUUID->"d0da37b6-a599-475e-ae0a-20d665722304",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[494645, 12855, 725, 17, 84, "Input",ExpressionUUID->"1d4a6267-5f4e-45aa-a850-2df5e57aa7d5",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[495373, 12874, 526, 13, 60, "Output",ExpressionUUID->"40369f05-d917-467f-9952-5ee18be4fe07",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[495902, 12889, 715, 18, 84, "Input",ExpressionUUID->"140cec33-6804-403d-93f4-8fe86ce085d9",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[496620, 12909, 789, 24, 79, "Output",ExpressionUUID->"e52e42c3-a2ec-47c8-9b42-8751672d2a2d",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[497412, 12935, 791, 24, 78, "Output",ExpressionUUID->"c1543372-1802-40c4-b68c-7bc622020b4b",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[498206, 12961, 1101, 35, 81, "Output",ExpressionUUID->"37a53ba4-b6d9-4cbe-9727-ca46e0636eba",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[499310, 12998, 301, 6, 41, "Input",ExpressionUUID->"da4a99b1-1af5-4eda-a4e1-ecbfac4ba626",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[499614, 13006, 979, 30, 72, "Output",ExpressionUUID->"95a830d0-8c22-4259-a7b4-26d5d7671f46",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[500596, 13038, 1240, 32, 105, "Input",ExpressionUUID->"d880fbbf-f733-492a-811b-abe07524f5d8",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[501839, 13072, 976, 30, 72, "Output",ExpressionUUID->"775670b7-465f-4874-8040-f82dbec7a0fc",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[502818, 13104, 1104, 34, 79, "Output",ExpressionUUID->"536716b0-d7b4-446e-97a6-0a2c68ee71a7",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[503925, 13140, 1101, 35, 81, "Output",ExpressionUUID->"4f4426e5-afe3-4b6c-aff8-fdd0b576b228",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}],
Cell[505029, 13177, 259, 5, 41, "Output",ExpressionUUID->"4e988d59-5564-4527-af17-061924b79f17",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.}]
}, Open  ]],
Cell[CellGroupData[{
Cell[505325, 13187, 341, 8, 69, "Section",ExpressionUUID->"c6912e27-4aa1-44dd-bbf2-dcd9c65b2a68",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[505669, 13197, 869, 17, 100, "Input",ExpressionUUID->"fe196da8-c141-432c-a79e-62d87c8b4bcd",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[506541, 13216, 774, 17, 54, "Output",ExpressionUUID->"1a289938-5842-4ffd-94d8-1b8bef3d9d87",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[507318, 13235, 779, 15, 100, "Input",ExpressionUUID->"8c89aee3-65c1-49a8-9e2b-c5774c14564d",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[508100, 13252, 771, 17, 54, "Output",ExpressionUUID->"e1821211-0047-44dc-9425-9c45f19e5e41",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[508874, 13271, 1142, 29, 110, "Input",ExpressionUUID->"b70c5d5e-37b0-4abd-a2cf-b33a307c83f2",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[510019, 13302, 1365, 37, 71, "Output",ExpressionUUID->"a96321b2-5d18-4b57-bff2-4f95d4f7950d",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[511387, 13341, 1235, 31, 110, "Input",ExpressionUUID->"502b01ab-9d3a-43f4-97cf-d537edf6b81c",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[512625, 13374, 1400, 39, 71, "Output",ExpressionUUID->"6dc8c8e8-c9c4-4bae-baa5-ff309c16f3ca",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[514028, 13415, 2317, 60, 126, "Input",ExpressionUUID->"b5e37d96-1d0f-4d4b-b55c-11f14530b6c7",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[516348, 13477, 414, 9, 45, "Output",ExpressionUUID->"f8b22cb3-9634-496f-b37a-daf767e11c75",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[516765, 13488, 412, 9, 45, "Output",ExpressionUUID->"64de66b5-a0d9-4467-822e-ee851ba5cdd4",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[517180, 13499, 412, 9, 45, "Output",ExpressionUUID->"1d3bc1ca-4f40-4faf-887f-00b1f481a77f",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[517595, 13510, 415, 9, 45, "Output",ExpressionUUID->"abc223f5-2925-4455-bf4f-e845261aefc3",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[518013, 13521, 6785, 192, 504, "Input",ExpressionUUID->"aa44a920-de2c-49d8-87bb-a3181fc83f16",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[524801, 13715, 351, 6, 41, "Output",ExpressionUUID->"801810df-4233-497e-a54c-d80638a617c4",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[525155, 13723, 353, 6, 41, "Output",ExpressionUUID->"a7028458-e848-4628-8439-d93a2df87dfb",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[525511, 13731, 351, 6, 41, "Output",ExpressionUUID->"099dc78d-e355-460a-a620-8b92588f9e88",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[525865, 13739, 350, 6, 41, "Output",ExpressionUUID->"63b7ba3e-3315-4f27-83d4-74d9a9a04f8c",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[526218, 13747, 353, 6, 41, "Output",ExpressionUUID->"6e4d415d-2677-4b14-99d8-e370006049af",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[526574, 13755, 351, 6, 41, "Output",ExpressionUUID->"47af53b3-f2d4-44f4-8dc5-2589eee195ab",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[526928, 13763, 353, 6, 41, "Output",ExpressionUUID->"a6c70b29-055e-489e-a7db-0984baf718ae",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[527284, 13771, 350, 6, 41, "Output",ExpressionUUID->"12063317-9055-43c2-8077-db880d670588",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[527637, 13779, 1656, 48, 113, "Output",ExpressionUUID->"62a1e1ae-9ae1-4445-88ea-1cfe4c62cf14",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[529296, 13829, 427, 10, 52, "Output",ExpressionUUID->"a2c97f3e-d13b-4300-9f04-0a5f12b4f5b4",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[529726, 13841, 1549, 44, 113, "Output",ExpressionUUID->"933e8540-72cf-4208-af33-be9fd733068f",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}],
Cell[531278, 13887, 425, 10, 52, "Output",ExpressionUUID->"6ea95e4a-98c0-41be-ad70-f159f80e4301",
 CellGroupingRules->{"GroupTogetherGrouping", 10001.}]
}, Closed]],
Cell[CellGroupData[{
Cell[531740, 13902, 236, 4, 55, "Section",ExpressionUUID->"5bac3f92-a7f3-4499-938c-fd5ef8f4f96e",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[531979, 13908, 12534, 306, 530, "Input",ExpressionUUID->"6506df50-5203-4732-af8e-2abc3c7ce3d6",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[544516, 14216, 4151, 126, 326, "Output",ExpressionUUID->"239303f9-ef50-4f26-8ffc-00881d8d2e10",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[548670, 14344, 9710, 252, 772, "Input",ExpressionUUID->"5944b505-9b73-4322-93e8-6b0b06eac3d6",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[558383, 14598, 12027, 331, 292, "Output",ExpressionUUID->"4ea7fdd0-3611-444f-849d-86fd7e68ab6f",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[570413, 14931, 5651, 144, 336, "Input",ExpressionUUID->"9bcdbfbc-ee38-43fe-b505-753f5f9c6438",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}],
Cell[576067, 15077, 5271, 148, 162, "Output",ExpressionUUID->"2a423914-9e12-4985-bbca-7cfcc19e3c8b",
 CellGroupingRules->{"GroupTogetherGrouping", 10002.}]
}, Closed]],
Cell[CellGroupData[{
Cell[581375, 15230, 1170, 29, 104, "Input",ExpressionUUID->"8a315062-9d79-4e7f-9dfe-f54253e00f37"],
Cell[582548, 15261, 1709, 53, 74, "Output",ExpressionUUID->"5fec5823-7eb9-44b7-92e8-d11baaf7433e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[584294, 15319, 554, 12, 105, "Input",ExpressionUUID->"8b3de61d-c738-48bb-a97d-92b6f6c9f992"],
Cell[584851, 15333, 296, 8, 48, "Output",ExpressionUUID->"5cffd79c-1311-4c8b-9c85-5a170b792b62"]
}, Open  ]],
Cell[CellGroupData[{
Cell[585184, 15346, 1175, 29, 107, "Input",ExpressionUUID->"39aba092-3224-41c2-802f-79abd1131fb1"],
Cell[586362, 15377, 1601, 50, 72, "Output",ExpressionUUID->"819bd8c5-ff53-488f-adc6-97753d2e1ebf"]
}, Open  ]],
Cell[CellGroupData[{
Cell[588000, 15432, 633, 18, 44, "Input",ExpressionUUID->"edfe1279-2aab-487c-920c-337528e98699"],
Cell[588636, 15452, 1533, 48, 72, "Output",ExpressionUUID->"72d6d448-72c2-47b5-a894-141c4d56e716"]
}, Open  ]],
Cell[CellGroupData[{
Cell[590206, 15505, 909, 22, 107, "Input",ExpressionUUID->"fda1f1a2-9988-43cf-ba5c-d8e2b083ba42"],
Cell[591118, 15529, 1728, 54, 72, "Output",ExpressionUUID->"7fe9139b-c7fe-4f4c-b0be-97d2d5cc90af"]
}, Open  ]],
Cell[CellGroupData[{
Cell[592883, 15588, 300, 7, 41, "Input",ExpressionUUID->"013d799b-2ad4-4a6b-b1af-d565870aa378"],
Cell[593186, 15597, 917, 29, 72, "Output",ExpressionUUID->"2c7a6c30-70b6-4080-9159-826b0ab6261b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[594140, 15631, 1028, 26, 107, "Input",ExpressionUUID->"839d76c2-309b-42e1-a12f-796165da3501"],
Cell[595171, 15659, 1330, 42, 69, "Output",ExpressionUUID->"1bfff447-a672-4aa6-ab1c-76824fd1913a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[596538, 15706, 533, 12, 105, "Input",ExpressionUUID->"b1a5070e-f89d-4589-8165-3ca2b46ede63"],
Cell[597074, 15720, 267, 6, 41, "Output",ExpressionUUID->"cc207088-a09c-4c72-87cc-124b548300ff"]
}, Open  ]],
Cell[CellGroupData[{
Cell[597378, 15731, 1169, 29, 107, "Input",ExpressionUUID->"bc2e4f4e-b4eb-4101-a70d-b6d9672b700c"],
Cell[598550, 15762, 1686, 53, 74, "Output",ExpressionUUID->"e22c200a-9af3-4832-b97c-e23a421fa4b6"]
}, Open  ]],
Cell[CellGroupData[{
Cell[600273, 15820, 1207, 35, 127, "Input",ExpressionUUID->"fda8bf62-c860-4406-9eeb-e8d28d5de66d"],
Cell[601483, 15857, 1199, 38, 79, "Output",ExpressionUUID->"f6e7d302-ad10-480a-9c3f-fc7f033cdb73"]
}, Open  ]],
Cell[CellGroupData[{
Cell[602719, 15900, 667, 17, 63, "Input",ExpressionUUID->"d7d76105-42fe-48a6-b96f-e75884a6c548"],
Cell[603389, 15919, 1067, 33, 69, "Output",ExpressionUUID->"65f4888b-d831-4c0d-8863-dffceac7917c"],
Cell[604459, 15954, 1067, 33, 69, "Output",ExpressionUUID->"3039efab-fdbd-4a35-9d04-ddec522f6c86"]
}, Open  ]],
Cell[CellGroupData[{
Cell[605563, 15992, 1207, 35, 127, "Input",ExpressionUUID->"3de007ba-000d-4e22-b108-2f15af85375b"],
Cell[606773, 16029, 1147, 37, 79, "Output",ExpressionUUID->"62a44277-90c6-462f-b25a-0b86ec0ac81c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[607957, 16071, 667, 17, 63, "Input",ExpressionUUID->"ba718536-1fd3-4ad9-a2d1-5e5a7f00dec1"],
Cell[608627, 16090, 1065, 33, 69, "Output",ExpressionUUID->"e1242f80-1873-4089-98eb-efb17ec9dd09"],
Cell[609695, 16125, 1065, 33, 69, "Output",ExpressionUUID->"deacaef1-2331-4cb1-88f6-24a5190c5f56"]
}, Open  ]],
Cell[CellGroupData[{
Cell[610797, 16163, 1856, 53, 127, "Input",ExpressionUUID->"4cb86ebc-3a6b-46d7-a309-c3dd3ea1bf37"],
Cell[612656, 16218, 5522, 160, 90, "Output",ExpressionUUID->"97176a5f-a0d2-4733-af2c-25769d8e09c7"]
}, Open  ]],
Cell[CellGroupData[{
Cell[618215, 16383, 1143, 27, 168, "Input",ExpressionUUID->"272bf704-1dc4-47f2-b404-c2ce6f030c1d"],
Cell[619361, 16412, 1180, 36, 87, "Output",ExpressionUUID->"38226315-73c6-41e5-acf6-3d092f41821f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[620578, 16453, 1694, 44, 168, "Input",ExpressionUUID->"cb3849c6-1e5a-4c91-b99e-128e3080a317"],
Cell[622275, 16499, 2205, 62, 110, "Output",ExpressionUUID->"95490a46-7167-4883-9a79-71c9e8b3178b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[624517, 16566, 572, 14, 104, "Input",ExpressionUUID->"f586fa4c-3b9f-4ec7-aee4-85368d14a6ac"],
Cell[625092, 16582, 423, 12, 60, "Output",ExpressionUUID->"7f7a5e61-06ab-4dde-a0d0-a20431cd76b0"]
}, Open  ]],
Cell[CellGroupData[{
Cell[625552, 16599, 222, 4, 41, "Input",ExpressionUUID->"f4fc0465-6f62-41bc-a7b2-e12fa06c3de0"],
Cell[625777, 16605, 1206, 36, 87, "Output",ExpressionUUID->"ceda0ad7-9faf-490a-b956-8d5c769b8ac7"]
}, Open  ]],
Cell[CellGroupData[{
Cell[627020, 16646, 1061, 28, 107, "Input",ExpressionUUID->"96c0f043-c5c6-46fe-a7bd-6f07917cb6b9"],
Cell[628084, 16676, 1254, 41, 74, "Output",ExpressionUUID->"69aeb040-3010-4078-b659-7f414208b438"]
}, Open  ]],
Cell[CellGroupData[{
Cell[629375, 16722, 825, 22, 105, "Input",ExpressionUUID->"200a393b-eceb-4346-a507-5290f1d937bd"],
Cell[630203, 16746, 984, 32, 69, "Output",ExpressionUUID->"78f39757-5c3f-4e79-b2ac-3340083325f6"]
}, Open  ]],
Cell[CellGroupData[{
Cell[631224, 16783, 950, 25, 105, "Input",ExpressionUUID->"06457696-f40e-43a6-afa9-d6d982d906f3"],
Cell[632177, 16810, 1307, 42, 74, "Output",ExpressionUUID->"e4e5fa17-40e6-41a1-8f91-c90ef13bd767"]
}, Open  ]],
Cell[CellGroupData[{
Cell[633521, 16857, 271, 6, 41, "Input",ExpressionUUID->"23a6a1de-888a-468e-a403-7e2ad9ceb627"],
Cell[633795, 16865, 2174, 70, 74, "Output",ExpressionUUID->"822f41c0-b891-4075-90df-35b966dc2ad0"]
}, Open  ]],
Cell[CellGroupData[{
Cell[636006, 16940, 349, 8, 41, "Input",ExpressionUUID->"35305c84-937f-404f-a055-0650c0446fe0"],
Cell[636358, 16950, 919, 29, 72, "Output",ExpressionUUID->"0d401eea-bcfd-4813-b27c-2bec07867418"]
}, Open  ]],
Cell[CellGroupData[{
Cell[637314, 16984, 597, 17, 44, "Input",ExpressionUUID->"7c16df9c-ab97-48d6-b064-589fcd6048f4"],
Cell[637914, 17003, 1440, 45, 72, "Output",ExpressionUUID->"b3fe0dc4-4b91-41b6-8f88-946d90efdb91"]
}, Open  ]],
Cell[CellGroupData[{
Cell[639391, 17053, 1069, 28, 107, "Input",ExpressionUUID->"830126f3-8963-490b-b2a9-912a6e70cd81"],
Cell[640463, 17083, 2794, 89, 74, "Output",ExpressionUUID->"8921fd0c-44c1-4760-8bf6-2bdf1d8b68ce"]
}, Open  ]],
Cell[CellGroupData[{
Cell[643294, 17177, 1273, 38, 88, "Input",ExpressionUUID->"d47310b2-3a90-4089-8131-6ce2b7afb3e6"],
Cell[644570, 17217, 1580, 50, 74, "Output",ExpressionUUID->"909c735b-1a0c-43ff-9548-aa1522498bf0"],
Cell[646153, 17269, 1582, 50, 74, "Output",ExpressionUUID->"533fa4b7-1688-4e26-b36d-6c3274386504"],
Cell[647738, 17321, 1299, 42, 74, "Output",ExpressionUUID->"f2514173-4c57-4ab8-ac07-088dad3b2855"]
}, Open  ]],
Cell[CellGroupData[{
Cell[649074, 17368, 1791, 45, 128, "Input",ExpressionUUID->"c4095b8f-f136-4f60-aee7-fa3facae4933"],
Cell[650868, 17415, 1726, 53, 69, "Output",ExpressionUUID->"b8174b3e-b25e-4629-9fd4-92d067a8292c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[652631, 17473, 455, 13, 63, "Input",ExpressionUUID->"2693132c-7441-4d29-862a-1d763be2475b"],
Cell[653089, 17488, 645, 20, 69, "Output",ExpressionUUID->"7e8a7a3c-3cdb-466e-8b45-31b151180b83"],
Cell[653737, 17510, 997, 32, 69, "Output",ExpressionUUID->"85e275b6-094d-48f5-ab98-9464ea87698e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[654771, 17547, 486, 11, 105, "Input",ExpressionUUID->"47603c4f-e336-4622-8a93-0c5468b950d2"],
Cell[655260, 17560, 971, 32, 69, "Output",ExpressionUUID->"b40c0884-45b2-49c5-8d94-0fbadaf3ba0e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[656268, 17597, 294, 7, 41, "Input",ExpressionUUID->"fbfd08a6-f080-4785-b224-3069ea676b89"],
Cell[656565, 17606, 2174, 70, 74, "Output",ExpressionUUID->"3dbe6c1c-36e1-4451-8dff-2674e4903799"]
}, Open  ]],
Cell[CellGroupData[{
Cell[658776, 17681, 1512, 44, 109, "Input",ExpressionUUID->"f178ba5a-1b5d-45cd-ad22-e54441d7c4c1"],
Cell[660291, 17727, 1491, 46, 72, "Output",ExpressionUUID->"be7963ee-f0ea-4471-9859-b49595d0eceb"],
Cell[661785, 17775, 941, 29, 72, "Output",ExpressionUUID->"a8d51062-689a-4bdb-b8e2-83adb90a5dc8"],
Cell[662729, 17806, 1607, 50, 74, "Output",ExpressionUUID->"3491cf6f-a241-4620-9ac4-72ee57b2a24c"],
Cell[664339, 17858, 1326, 42, 74, "Output",ExpressionUUID->"d5b45fab-08a6-4141-9826-e2f61d222b46"]
}, Open  ]],
Cell[CellGroupData[{
Cell[665702, 17905, 2174, 56, 130, "Input",ExpressionUUID->"1cfda121-6020-4d90-b093-95ec1bfe886f"],
Cell[667879, 17963, 1653, 52, 69, "Output",ExpressionUUID->"0143aed6-8a20-4d6a-9a65-629bfc5130dd"]
}, Open  ]],
Cell[CellGroupData[{
Cell[669569, 18020, 456, 13, 63, "Input",ExpressionUUID->"bb06d70b-c7a4-4414-bc3c-4c65dac1e19a"],
Cell[670028, 18035, 647, 20, 69, "Output",ExpressionUUID->"5d72d3d8-fe4a-4714-a916-fcdbcd9c6537"],
Cell[670678, 18057, 997, 32, 69, "Output",ExpressionUUID->"e0241d85-0b83-419e-802e-42be0e62cbc7"]
}, Open  ]],
Cell[CellGroupData[{
Cell[671712, 18094, 271, 6, 41, "Input",ExpressionUUID->"3342a31b-39f0-46fd-80a4-8d886277a027"],
Cell[671986, 18102, 2582, 82, 74, "Output",ExpressionUUID->"2ede799b-fa1d-4c6d-8e8f-723d7133f911"]
}, Open  ]],
Cell[CellGroupData[{
Cell[674605, 18189, 665, 19, 65, "Input",ExpressionUUID->"6d358fc1-8d81-4cbe-b969-9a98c84ea821"],
Cell[675273, 18210, 1353, 43, 72, "Output",ExpressionUUID->"35401713-47c3-46c4-bce1-14217387bf57"],
Cell[676629, 18255, 2756, 84, 75, "Output",ExpressionUUID->"98eed14a-a93a-4528-8c08-e12b1d20453a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[679422, 18344, 1028, 27, 107, "Input",ExpressionUUID->"9cb875b7-879e-425c-96e8-e99bcc07a7ad"],
Cell[680453, 18373, 3188, 102, 74, "Output",ExpressionUUID->"e5c02a3e-6fde-49d9-913b-b7c17e926466"]
}, Open  ]],
Cell[CellGroupData[{
Cell[683678, 18480, 2174, 64, 153, "Input",ExpressionUUID->"cf7aab64-97cb-4ac8-acbb-799e6b36b6c6"],
Cell[685855, 18546, 1540, 47, 72, "Output",ExpressionUUID->"02cc51f4-fcf8-4704-8fcb-3ec3e6b166e1"],
Cell[687398, 18595, 1373, 43, 74, "Output",ExpressionUUID->"c8b57273-f960-4adf-a54d-894f4cc90ea9"],
Cell[688774, 18640, 1652, 51, 74, "Output",ExpressionUUID->"8d3cd9c2-149a-40d7-9942-bbe49f6c5ebf"],
Cell[690429, 18693, 1538, 47, 72, "Output",ExpressionUUID->"5290135c-344a-403c-919b-2bda3ecfd934"],
Cell[691970, 18742, 990, 30, 72, "Output",ExpressionUUID->"cdd45f7f-e676-4c1a-955d-3b205676242a"],
Cell[692963, 18774, 1373, 43, 74, "Output",ExpressionUUID->"9dc87395-ac2b-454e-975f-149d7eeaef00"]
}, Open  ]],
Cell[CellGroupData[{
Cell[694373, 18822, 2551, 69, 130, "Input",ExpressionUUID->"7b277787-2cbe-4012-9d58-a0ad0cbb4a62"],
Cell[696927, 18893, 1282, 41, 69, "Output",ExpressionUUID->"33c46d35-4f87-4c86-9fb6-0fc3e7984917"]
}, Open  ]],
Cell[CellGroupData[{
Cell[698246, 18939, 609, 13, 210, "Input",ExpressionUUID->"460dcf6e-11c0-4731-95ac-f3b1f9bb71ae"],
Cell[698858, 18954, 9016, 264, 238, "Output",ExpressionUUID->"23df47b7-bc50-4d52-9250-b0a5efe6afa9"]
}, Open  ]]
}
]
*)