Add OrbitalGraph for a group and a base-pair

gap-packages · Oct 16, 2021 · c282ea0 · c282ea0
1 parent af82d83
commit c282ea0
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Showing 3 changed files with 53 additions and 11 deletions.
diff --git a/gap/OrbitalGraphs.gd b/gap/OrbitalGraphs.gd
@@ -80,10 +80,13 @@ DeclareOperation("OrbitalGraphs", [IsPermGroup, IsInt]);
 # TODO: Implement constructing the orbital graph with a given base pair
 #! @BeginGroup orbital
 #! @Returns An orbital graph
-#! @Arguments G, u, v
+#! @Arguments G, basepair, n
 #! @Description
 #!   TODO.
-DeclareOperation("OrbitalGraph", [IsPermGroup, IsPosInt, IsPosInt]);
+DeclareOperation("OrbitalGraph", [IsPermGroup, IsHomogeneousList, IsPosInt]);
+#! @Arguments G, basepair, points
+DeclareOperation("OrbitalGraph", [IsPermGroup, IsHomogeneousList,
+                                  IsHomogeneousList]);
 #! @EndGroup
 #! @Group orbital
 #! @Arguments G, basepair

diff --git a/gap/OrbitalGraphs.gi b/gap/OrbitalGraphs.gi
@@ -113,6 +113,45 @@ function(G, points)
 end);
 
 
+# Individual orbital graphs
+
+InstallMethod(OrbitalGraph, "for a permutation group and homogenous list",
+[IsPermGroup, IsHomogeneousList],
+function(G, basepair)
+    if not (Length(basepair) = 2 and ForAll(basepair, IsPosInt)) then
+        ErrorNoReturn("the second argument <basepair> must be a pair of ",
+                      "positive integers");
+    fi;
+    return OrbitalGraph(G, basepair,
+                        Maximum(NrMovedPoints(G), Maximum(basepair)));
+end);
+
+InstallMethod(OrbitalGraph,
+"for a permutation group, homogeneous list, and pos int",
+[IsPermGroup, IsHomogeneousList, IsPosInt],
+function(G, basepair, max)
+    return OrbitalGraph(G, basepair, [1 .. max]);
+end);
+
+InstallMethod(OrbitalGraph,
+"for a permutation group and two homogeneous lists",
+[IsPermGroup, IsHomogeneousList, IsHomogeneousList],
+function(G, basepair, points)
+    local D;
+    if not ForAll(points, IsPosInt) then
+        ErrorNoReturn("the third argument <points> must be... TODO");
+    elif not (Length(basepair) = 2 and IsSubset(points, basepair)) then
+        ErrorNoReturn("the second argument <basepair> must be... TODO");
+    fi;
+    # FIXME This is naive, and doesn't respect <points>
+    D := DigraphByEdges(Orbit(G, basepair, OnPairs), Maximum(points));
+    SetFilterObj(D, IsOrbitalGraphOfGroup);
+    SetUnderlyingGroup(D, G);
+    SetBasePair(D, basepair);
+    return D;
+end);
+
+
 # Transformation semigroups
 
 InstallMethod(OrbitalGraphs, "for a transformation semigroup",

diff --git a/tst/orbitalgraphs01.tst b/tst/orbitalgraphs01.tst
@@ -18,23 +18,23 @@ gap> OrbitalGraphs(D8);
     , <self-paired orbital graph of D8 on 4 vertices 
     with base-pair (1,2), 8 arcs> ]
 
-# doc/_Chapter_Orbital_graphs.xml:95-98
+# doc/_Chapter_Orbital_graphs.xml:97-100
 gap> true;
 true
 
-# doc/_Chapter_Orbital_graphs.xml:129-132
+# doc/_Chapter_Orbital_graphs.xml:131-134
 gap> true;
 true
 
-# doc/_Chapter_Orbital_graphs.xml:148-151
+# doc/_Chapter_Orbital_graphs.xml:150-153
 gap> true;
 true
 
-# doc/_Chapter_Orbital_graphs.xml:167-170
+# doc/_Chapter_Orbital_graphs.xml:169-172
 gap> true;
 true
 
-# doc/_Chapter_Orbital_graphs.xml:199-211
+# doc/_Chapter_Orbital_graphs.xml:201-213
 gap> OrbitalClosure(PSL(2,5)) = SymmetricGroup(6);
 true
 gap> C6 := CyclicGroup(IsPermGroup, 6);;
@@ -47,7 +47,7 @@ gap> IsConjugate(SymmetricGroup(6),
 >                closure, WreathProduct(Group([(1,2)]), Group([(1,2,3)])));
 true
 
-# doc/_Chapter_Orbital_graphs.xml:227-236
+# doc/_Chapter_Orbital_graphs.xml:229-238
 gap> OrbitalIndex(PSL(2,5));
 12
 gap> OrbitalIndex(PGL(2,5));
@@ -57,23 +57,23 @@ gap> OrbitalIndex(AlternatingGroup(6));
 gap> OrbitalIndex(DihedralGroup(IsPermGroup, 6));
 1
 
-# doc/_Chapter_Orbital_graphs.xml:263-270
+# doc/_Chapter_Orbital_graphs.xml:265-272
 gap> IsOrbitalGraphRecognisable(QuaternionGroup(IsPermGroup, 8));
 true
 gap> IsOGR(AlternatingGroup(8));
 false
 gap> IsOGR(TrivialGroup(IsPermGroup));
 true
 
-# doc/_Chapter_Orbital_graphs.xml:294-301
+# doc/_Chapter_Orbital_graphs.xml:296-303
 gap> IsStronglyOrbitalGraphRecognisable(CyclicGroup(IsPermGroup, 8));
 true
 gap> IsStronglyOGR(QuaternionGroup(IsPermGroup, 8));
 false
 gap> IsStronglyOGR(TrivialGroup(IsPermGroup));
 true
 
-# doc/_Chapter_Orbital_graphs.xml:325-332
+# doc/_Chapter_Orbital_graphs.xml:327-334
 gap> IsAbsolutelyOrbitalGraphRecognisable(DihedralGroup(IsPermGroup, 8));
 true
 gap> IsAbsolutelyOGR(CyclicGroup(IsPermGroup, 8));