IneqA334254.ipynb

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       "static PyObject *__pyx_f_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_ProcessRT(PyObject *__pyx_v_t, int __pyx_v_i, int __pyx_v_l, int __pyx_v_nn1, CYTHON_UNUSED int __pyx_skip_dispatch) {\n",
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       "\n",
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       "static char __pyx_doc_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_ProcessRT[] = \" This function recursively extends an input tuple of integers, which represents \\n    a set of sets (more precisily, a formal context), by adding to it an integer i (a new set).\\n    The length of a terminal tuple is constrained by l, while nn1 should be passed as 2**n-1. \\n    The function checks whether the new tuple forms a unique closure system and returns the dictionary of the first elements of\\n    processed tuples as keys and values 1 for clousre system with T1 propery and 0 otherwise.\";\n",
       "static PyObject *__pyx_pw_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_1ProcessRT(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">004</span>:     <span class=\"sd\">&quot;&quot;&quot; This function recursively extends an input tuple of integers, which represents </span></pre>\n",
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       "<pre class='cython code score-0 '>    __pyx_v_r = 0;\n",
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       "<pre class='cython code score-0 '>    __pyx_t_12 = __pyx_v_nn1;\n",
       "    __pyx_t_14 = __pyx_t_12;\n",
       "    for (__pyx_t_15 = (__pyx_v_i + 1); __pyx_t_15 &lt; __pyx_t_14; __pyx_t_15+=1) {\n",
       "      __pyx_v_k = __pyx_t_15;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">045</span>:             <span class=\"c\">#print(&quot;Process(t,k,l-1,tuples,nn1)&quot;)</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">046</span>:             <span class=\"c\">#print(&quot;t&quot;,t,&quot;k&quot;,k)</span></pre>\n",
       "<pre class=\"cython line score-1\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">047</span>:             <span class=\"n\">ucount</span><span class=\"o\">=</span><span class=\"n\">ProcessRT</span><span class=\"p\">(</span><span class=\"n\">t</span><span class=\"p\">,</span><span class=\"n\">k</span><span class=\"p\">,</span><span class=\"n\">l</span><span class=\"o\">-</span><span class=\"mf\">1</span><span class=\"p\">,</span><span class=\"n\">nn1</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-1 '>      __pyx_t_3 = __pyx_f_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_ProcessRT(__pyx_v_t, __pyx_v_k, (__pyx_v_l - 1), __pyx_v_nn1, 0);<span class='error_goto'> if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 47, __pyx_L1_error)</span>\n",
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       "      __pyx_t_3 = 0;\n",
       "</pre><pre class=\"cython line score-43\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">048</span>:             <span class=\"k\">for</span> <span class=\"n\">key</span> <span class=\"ow\">in</span> <span class=\"n\">ucount</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-43 '>      if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_v_ucount)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_v_ucount)) {\n",
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       "</pre><pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">049</span>:                 <span class=\"k\">if</span> <span class=\"n\">key</span> <span class=\"ow\">in</span> <span class=\"n\">count</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-2 '>        __pyx_t_8 = (<span class='pyx_c_api'>__Pyx_PyDict_ContainsTF</span>(__pyx_v_key, __pyx_v_count, Py_EQ)); if (unlikely(__pyx_t_8 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 49, __pyx_L1_error)</span>\n",
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       "        }\n",
       "</pre><pre class=\"cython line score-19\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">050</span>:                     <span class=\"n\">count</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span><span class=\"o\">+=</span><span class=\"n\">ucount</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-19 '>          <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_key);\n",
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       "          __pyx_t_11 = <span class='pyx_c_api'>__Pyx_PyDict_GetItem</span>(__pyx_v_count, __pyx_t_1);<span class='error_goto'> if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 50, __pyx_L1_error)</span>\n",
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       "          <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">051</span>:                 <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-8\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">052</span>:                     <span class=\"n\">count</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span><span class=\"o\">=</span><span class=\"n\">ucount</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-8 '>        /*else*/ {\n",
       "          __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyObject_GetItem</span>(__pyx_v_ucount, __pyx_v_key);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 52, __pyx_L1_error)</span>\n",
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       "        }\n",
       "        __pyx_L17:;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">053</span>:             <span class=\"c\">#if r&lt;0: print(&quot;r&quot;,r)</span></pre>\n",
       "<pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">054</span>:         <span class=\"k\">return</span> <span class=\"n\">count</span></pre>\n",
       "<pre class='cython code score-2 '>    <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "    <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_count);\n",
       "    __pyx_r = __pyx_v_count;\n",
       "    goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">055</span>:     <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">056</span>:         <span class=\"c\">#print(tuples)</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">057</span>:         <span class=\"c\">#tuples.append(tuple(t))</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">058</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">059</span>: </pre>\n",
       "<pre class=\"cython line score-14\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">060</span>:         <span class=\"k\">print</span><span class=\"p\">(</span><span class=\"s\">&quot;Branch process&quot;</span><span class=\"p\">,</span><span class=\"n\">t</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">])</span></pre>\n",
       "<pre class='cython code score-14 '>  /*else*/ {\n",
       "    __pyx_t_3 = <span class='pyx_c_api'>__Pyx_GetItemInt</span>(__pyx_v_t, 0, long, 1, __Pyx_PyInt_From_long, 0, 0, 1);<span class='error_goto'> if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 60, __pyx_L1_error)</span>\n",
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       "    <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_1, 1, __pyx_t_3);\n",
       "    __pyx_t_3 = 0;\n",
       "    __pyx_t_3 = <span class='pyx_c_api'>__Pyx_PyObject_Call</span>(__pyx_builtin_print, __pyx_t_1, NULL);<span class='error_goto'> if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 60, __pyx_L1_error)</span>\n",
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       "    <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_3); __pyx_t_3 = 0;\n",
       "</pre><pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">061</span>:         <span class=\"k\">return</span> <span class=\"n\">count</span></pre>\n",
       "<pre class='cython code score-2 '>    <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "    <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_count);\n",
       "    __pyx_r = __pyx_v_count;\n",
       "    goto __pyx_L0;\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">062</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">063</span>: </pre>\n",
       "<pre class=\"cython line score-45\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">064</span>: <span class=\"k\">def</span> <span class=\"nf\">isClosed</span><span class=\"p\">(</span><span class=\"n\">t</span><span class=\"p\">,</span><span class=\"n\">g</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-45 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_3isClosed(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static char __pyx_doc_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_2isClosed[] = \"Checks whether g is closed in t.\";\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_3isClosed = {\"isClosed\", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_3isClosed, METH_VARARGS|METH_KEYWORDS, __pyx_doc_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_2isClosed};\n",
       "static PyObject *__pyx_pw_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_3isClosed(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  PyObject *__pyx_v_t = 0;\n",
       "  PyObject *__pyx_v_g = 0;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"isClosed (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_t,&amp;__pyx_n_s_g,0};\n",
       "    PyObject* values[2] = {0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        CYTHON_FALLTHROUGH;\n",
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       "        CYTHON_FALLTHROUGH;\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_t)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_g)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"isClosed\", 1, 2, 2, 1); <span class='error_goto'>__PYX_ERR(0, 64, __pyx_L3_error)</span>\n",
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       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"isClosed\") &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 64, __pyx_L3_error)</span>\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 2) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "    }\n",
       "    __pyx_v_t = values[0];\n",
       "    __pyx_v_g = values[1];\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"isClosed\", 1, 2, 2, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); <span class='error_goto'>__PYX_ERR(0, 64, __pyx_L3_error)</span>\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_f107e2abde8e9e051114cf74f90b54e3.isClosed\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_f107e2abde8e9e051114cf74f90b54e3_2isClosed(__pyx_self, __pyx_v_t, __pyx_v_g);\n",
       "  int __pyx_lineno = 0;\n",
       "  const char *__pyx_filename = NULL;\n",
       "  int __pyx_clineno = 0;\n",
       "\n",
       "  /* function exit code */\n",
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       "<pre class='cython code score-6 '>      __pyx_t_5 = <span class='py_c_api'>PyNumber_And</span>(__pyx_v_h, __pyx_v_res);<span class='error_goto'> if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 73, __pyx_L1_error)</span>\n",
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       "<pre class='cython code score-10 '>      __pyx_t_9 = (<span class='pyx_c_api'>__Pyx_PyDict_ContainsTF</span>(__pyx_v_key, __pyx_v_merged, Py_EQ)); if (unlikely(__pyx_t_9 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 109, __pyx_L1_error)</span>\n",
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       "      __pyx_t_7 = <span class='pyx_c_api'>__Pyx_PyObject_GetItem</span>(__pyx_v_dic, __pyx_v_key);<span class='error_goto'> if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 109, __pyx_L1_error)</span>\n",
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       "      if (__pyx_t_8) {\n",
       "/* … */\n",
       "        goto __pyx_L7;\n",
       "      }\n",
       "</pre><pre class=\"cython line score-19\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">110</span>:                 <span class=\"n\">merged</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span><span class=\"o\">+=</span><span class=\"n\">dic</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-19 '>        <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_key);\n",
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       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_11); __pyx_t_11 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">111</span>:             <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-8\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">112</span>:                 <span class=\"k\">if</span> <span class=\"n\">dic</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span><span class=\"o\">==</span><span class=\"mf\">1</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-8 '>      /*else*/ {\n",
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       "      __pyx_L7:;\n",
       "</pre><pre class=\"cython line score-8\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">113</span>:                     <span class=\"n\">merged</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span><span class=\"o\">=</span><span class=\"n\">dic</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-8 '>          __pyx_t_13 = <span class='pyx_c_api'>__Pyx_PyObject_GetItem</span>(__pyx_v_dic, __pyx_v_key);<span class='error_goto'> if (unlikely(!__pyx_t_13)) __PYX_ERR(0, 113, __pyx_L1_error)</span>\n",
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       "          <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_13); __pyx_t_13 = 0;\n",
       "</pre><pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">114</span>:     <span class=\"k\">return</span> <span class=\"n\">merged</span></pre>\n",
       "<pre class='cython code score-2 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_merged);\n",
       "  __pyx_r = __pyx_v_merged;\n",
       "  goto __pyx_L0;\n",
       "</pre></div></body></html>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "execution_count": 2,
     "metadata": {},
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   ],
   "source": [
    "%%cython --annotate\n",
    "from math import log \n",
    "\n",
    "cpdef ProcessRT(t,int i,int l,int nn1):\n",
    "    \"\"\" This function recursively extends an input tuple of integers, which represents \n",
    "    a set of sets (more precisily, a formal context), by adding to it an integer i (a new set).\n",
    "    The length of a terminal tuple is constrained by l, while nn1 should be passed as 2**n-1. \n",
    "    The function checks whether the new tuple forms a unique closure system and returns the dictionary of the first elements of\n",
    "    processed tuples as keys and values 1 for clousre system with T1 propery and 0 otherwise.\"\"\"\n",
    "    \n",
    "    count={}\n",
    "    t=t[:]\n",
    "    cdef int P\n",
    "    cdef int lent=len(t)\n",
    "\n",
    "    \n",
    "    #checking whether the context is reducible\n",
    "    for j in range(lent-1,-1,-1):\n",
    "        P=i\n",
    "        #print(\"t[j],i\",t[j],i,t[j]&i,)\n",
    "        tji=t[j]&i\n",
    "        if tji in t[0:j]:\n",
    "            return count\n",
    "            \n",
    "        if tji==t[j]:\n",
    "            #print(\"t[j],i\",t[j],i,t[j]&i,)\n",
    "            for h in range(j+1,lent):\n",
    "                if t[j]&t[h]==t[j]:\n",
    "                    P=P&t[h]\n",
    "                    if P==t[j]:                        \n",
    "                        return count\n",
    "    t.append(i)\n",
    "\n",
    "    #checking T1 property\n",
    "    if Check(t,nn1):\n",
    "        count[(lent+1,tuple(t))]=1\n",
    "    else:\n",
    "        count[(lent+1,tuple(t))]=0\n",
    "\n",
    "    #recursive call\n",
    "    cdef unsigned long long r\n",
    "    #print(l)\n",
    "    if l!=0:\n",
    "        r=0\n",
    "        for k in range(i+1,nn1):\n",
    "            #print(\"Process(t,k,l-1,tuples,nn1)\")\n",
    "            #print(\"t\",t,\"k\",k)\n",
    "            ucount=ProcessRT(t,k,l-1,nn1)\n",
    "            for key in ucount:\n",
    "                if key in count:\n",
    "                    count[key]+=ucount[key]\n",
    "                else:\n",
    "                    count[key]=ucount[key]\n",
    "            #if r<0: print(\"r\",r)\n",
    "        return count\n",
    "    else: \n",
    "        #print(tuples)\n",
    "        #tuples.append(tuple(t))\n",
    "       \n",
    "        \n",
    "        print(\"Branch process\",t[0])\n",
    "        return count\n",
    "\n",
    "    \n",
    "def isClosed(t,g):\n",
    "    \"\"\"Checks whether g is closed in t.\"\"\"\n",
    "    cont=[]\n",
    "    for h in t:\n",
    "        if g&h==g:\n",
    "            cont.append(h)\n",
    "    if len(cont)>0:\n",
    "        res=cont[0]\n",
    "        for h in cont:\n",
    "            res=h&res\n",
    "        return res==g\n",
    "    else:\n",
    "        return g==0\n",
    "\n",
    "    \n",
    "def Check(t,nn1):\n",
    "    \"\"\"Checks whether T1 is fulfilled for t.\"\"\"\n",
    "    n=int(log(nn1+1,2))\n",
    "    members=[]\n",
    "    members.extend([2**i for i in range(n)])\n",
    "    for m in members:\n",
    "        if not isClosed(t,m):\n",
    "            return False\n",
    "    return True\n",
    "\n",
    "def merge(r):\n",
    "    \"\"\"This is a value collector for the resulting list of dictionaries\n",
    "    \"\"\"\n",
    "    merged={}\n",
    "    for dic in r:\n",
    "        for key in dic:\n",
    "            if key in merged:\n",
    "                merged[key]+=dic[key]\n",
    "            else:\n",
    "                merged[key]=dic[key]\n",
    "    return merged\n",
    "\n",
    "\n",
    "def merge2(r):\n",
    "    \"\"\"This is a value collector for the resulting list of dictionaries\n",
    "    with non-zero values.\n",
    "    \"\"\"\n",
    "    merged={}\n",
    "    for dic in r:\n",
    "        for key in dic:\n",
    "            if key in merged and dic[key]==1:\n",
    "                merged[key]+=dic[key]\n",
    "            else:\n",
    "                if dic[key]==1:\n",
    "                    merged[key]=dic[key]\n",
    "    return merged"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Counting closure systems from A334254 for n=2, 3, 4, 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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([29], 30, 30, 31)]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "IOPub data rate exceeded.\n",
      "The notebook server will temporarily stop sending output\n",
      "to the client in order to avoid crashing it.\n",
      "To change this limit, set the config variable\n",
      "`--NotebookApp.iopub_data_rate_limit`.\n",
      "\n",
      "Current values:\n",
      "NotebookApp.iopub_data_rate_limit=1000000.0 (bytes/sec)\n",
      "NotebookApp.rate_limit_window=3.0 (secs)\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.42 s, sys: 1.11 s, total: 6.52 s\n",
      "Wall time: 11.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "\n",
    "\n",
    "from multiprocessing import Pool\n",
    "from multiprocessing import cpu_count\n",
    "\n",
    "\n",
    "n=5\n",
    "\n",
    "#computing A334254 for n=5 by levels\n",
    "if __name__ == \"__main__\":\n",
    "    pool = Pool(cpu_count())\n",
    "    \n",
    "    nn1=2**n-1\n",
    "\n",
    "    lt=[]\n",
    "    lk=[]\n",
    "\n",
    "    count={}\n",
    "\n",
    "    \n",
    "    for t in range(nn1):\n",
    " \n",
    "        for i in range(t+1,nn1):\n",
    "            lt.append([t])\n",
    "            lk.append(i)\n",
    "            \n",
    "    ln_2=[nn1-1]* len(lt)\n",
    "    lnn1=[nn1]* len(lt)\n",
    "           \n",
    "    #print(lk)   \n",
    "     \n",
    "    print(list(zip(lt,lk,ln_2,lnn1)))\n",
    "\n",
    "    \n",
    "    #parallel execution of ProcessRT function\n",
    "    res5 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
    "    print(res5.get())# print the list of resulting dictionaries\n",
    "    print(sum(merge(res5.get()).values()))#the number of closure systems w.r.t. T1\n",
    "\n",
    "    pool.close()  # 'TERM'\n",
    "    pool.join()   # 'KILL'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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13)): 0}, {(2, (8, 10)): 0, (3, (8, 10, 11)): 0, (3, (8, 10, 14)): 0}, {(2, (8, 11)): 0, (3, (8, 11, 13)): 0, (3, (8, 11, 14)): 0}, {(2, (8, 12)): 0, (3, (8, 12, 13)): 0, (3, (8, 12, 14)): 0}, {(2, (8, 13)): 0, (3, (8, 13, 14)): 0}, {(2, (8, 14)): 0}, {(2, (9, 10)): 0, (3, (9, 10, 11)): 0, (4, (9, 10, 11, 12)): 0, (3, (9, 10, 12)): 0, (4, (9, 10, 12, 13)): 0, (4, (9, 10, 12, 14)): 0, (3, (9, 10, 13)): 0, (4, (9, 10, 13, 14)): 0, (3, (9, 10, 14)): 0}, {(2, (9, 11)): 0, (3, (9, 11, 12)): 0, (4, (9, 11, 12, 14)): 0, (3, (9, 11, 14)): 0}, {(2, (9, 12)): 0, (3, (9, 12, 13)): 0, (3, (9, 12, 14)): 0}, {(2, (9, 13)): 0, (3, (9, 13, 14)): 0}, {(2, (9, 14)): 0}, {(2, (10, 11)): 0, (3, (10, 11, 12)): 0, (4, (10, 11, 12, 13)): 0, (3, (10, 11, 13)): 0}, {(2, (10, 12)): 0, (3, (10, 12, 13)): 0, (3, (10, 12, 14)): 0}, {(2, (10, 13)): 0, (3, (10, 13, 14)): 0}, {(2, (10, 14)): 0}, {(2, (11, 12)): 0, (3, (11, 12, 13)): 0, (3, (11, 12, 14)): 0}, {(2, (11, 13)): 0, (3, (11, 13, 14)): 0}, {(2, (11, 14)): 0}, {(2, (12, 13)): 0}, {(2, (12, 14)): 0}, {(2, (13, 14)): 0}]\n",
      "545\n",
      "CPU times: user 67.1 ms, sys: 559 ms, total: 626 ms\n",
      "Wall time: 1.04 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "\n",
    "\n",
    "from multiprocessing import Pool\n",
    "from multiprocessing import cpu_count\n",
    "\n",
    "\n",
    "n=4\n",
    "\n",
    "#computing A334254 for n=4 by levels\n",
    "if __name__ == \"__main__\":\n",
    "    pool = Pool(cpu_count())\n",
    "    \n",
    "    nn1=2**n-1\n",
    "\n",
    "    lt=[]\n",
    "    lk=[]\n",
    "\n",
    "    count={}\n",
    "\n",
    "    \n",
    "    for t in range(nn1):\n",
    " \n",
    "        for i in range(t+1,nn1):\n",
    "            lt.append([t])\n",
    "            lk.append(i)\n",
    "            \n",
    "    ln_2=[nn1-1]* len(lt)\n",
    "    lnn1=[nn1]* len(lt)\n",
    "           \n",
    "    #print(lk)   \n",
    "     \n",
    "    print(list(zip(lt,lk,ln_2,lnn1)))\n",
    "\n",
    "    \n",
    "    #parallel execution of ProcessRT function\n",
    "    res4 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
    "    print(res4.get())# print the list of resulting dictionaries\n",
    "    print(sum(merge(res4.get()).values()))#the number of closure systems w.r.t. T1\n",
    "\n",
    "    pool.close()  # 'TERM'\n",
    "    pool.join()   # 'KILL'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[([0], 1, 6, 7), ([0], 2, 6, 7), ([0], 3, 6, 7), ([0], 4, 6, 7), ([0], 5, 6, 7), ([0], 6, 6, 7), ([1], 2, 6, 7), ([1], 3, 6, 7), ([1], 4, 6, 7), ([1], 5, 6, 7), ([1], 6, 6, 7), ([2], 3, 6, 7), ([2], 4, 6, 7), ([2], 5, 6, 7), ([2], 6, 6, 7), ([3], 4, 6, 7), ([3], 5, 6, 7), ([3], 6, 6, 7), ([4], 5, 6, 7), ([4], 6, 6, 7), ([5], 6, 6, 7)]\n",
      "[{(2, (0, 1)): 0, (3, (0, 1, 3)): 0, (3, (0, 1, 5)): 0}, {(2, (0, 2)): 0, (3, (0, 2, 3)): 0, (3, (0, 2, 6)): 0}, {(2, (0, 3)): 0, (3, (0, 3, 5)): 0, (3, (0, 3, 6)): 0}, {(2, (0, 4)): 0, (3, (0, 4, 5)): 0, (3, (0, 4, 6)): 0}, {(2, (0, 5)): 0, (3, (0, 5, 6)): 0}, {(2, (0, 6)): 0}, {(2, (1, 2)): 0, (3, (1, 2, 3)): 0, (4, (1, 2, 3, 4)): 1, (3, (1, 2, 4)): 1, (4, (1, 2, 4, 5)): 1, (4, (1, 2, 4, 6)): 1, (3, (1, 2, 5)): 0, (4, (1, 2, 5, 6)): 1, (3, (1, 2, 6)): 0}, {(2, (1, 3)): 0, (3, (1, 3, 4)): 0, (4, (1, 3, 4, 6)): 1, (3, (1, 3, 6)): 0}, {(2, (1, 4)): 0, (3, (1, 4, 5)): 0, (3, (1, 4, 6)): 0}, {(2, (1, 5)): 0, (3, (1, 5, 6)): 0}, {(2, (1, 6)): 0}, {(2, (2, 3)): 0, (3, (2, 3, 4)): 0, (4, (2, 3, 4, 5)): 1, (3, (2, 3, 5)): 0}, {(2, (2, 4)): 0, (3, (2, 4, 5)): 0, (3, (2, 4, 6)): 0}, {(2, (2, 5)): 0, (3, (2, 5, 6)): 0}, {(2, (2, 6)): 0}, {(2, (3, 4)): 0, (3, (3, 4, 5)): 0, (3, (3, 4, 6)): 0}, {(2, (3, 5)): 0, (3, (3, 5, 6)): 1}, {(2, (3, 6)): 0}, {(2, (4, 5)): 0}, {(2, (4, 6)): 0}, {(2, (5, 6)): 0}]\n",
      "8\n",
      "CPU times: user 54.6 ms, sys: 496 ms, total: 551 ms\n",
      "Wall time: 847 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "\n",
    "\n",
    "from multiprocessing import Pool\n",
    "from multiprocessing import cpu_count\n",
    "\n",
    "\n",
    "n=3\n",
    "\n",
    "#computing A334254 for n=3 by levels\n",
    "if __name__ == \"__main__\":\n",
    "    pool = Pool(cpu_count())\n",
    "    \n",
    "    nn1=2**n-1\n",
    "\n",
    "    lt=[]\n",
    "    lk=[]\n",
    "\n",
    "    count={}\n",
    "\n",
    "    \n",
    "    for t in range(nn1):\n",
    " \n",
    "        for i in range(t+1,nn1):\n",
    "            lt.append([t])\n",
    "            lk.append(i)\n",
    "            \n",
    "    ln_2=[nn1-1]* len(lt)\n",
    "    lnn1=[nn1]* len(lt)\n",
    "           \n",
    "    #print(lk)   \n",
    "     \n",
    "    print(list(zip(lt,lk,ln_2,lnn1)))\n",
    "\n",
    "    \n",
    "    #parallel execution of ProcessRT function\n",
    "    res3 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
    "    print(res3.get())# print the list of resulting dictionaries\n",
    "    print(sum(merge(res3.get()).values()))#the number of closure systems w.r.t. T1\n",
    "\n",
    "    pool.close()  # 'TERM'\n",
    "    pool.join()   # 'KILL'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[([0], 1, 2, 3), ([0], 2, 2, 3), ([1], 2, 2, 3)]\n",
      "[{(2, (0, 1)): 0}, {(2, (0, 2)): 0}, {(2, (1, 2)): 1}]\n",
      "1\n",
      "CPU times: user 82.6 ms, sys: 481 ms, total: 563 ms\n",
      "Wall time: 927 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "\n",
    "\n",
    "from multiprocessing import Pool\n",
    "from multiprocessing import cpu_count\n",
    "\n",
    "\n",
    "n=2\n",
    "\n",
    "#computing A334254 for n=3 by levels\n",
    "if __name__ == \"__main__\":\n",
    "    pool = Pool(cpu_count())\n",
    "    \n",
    "    nn1=2**n-1\n",
    "\n",
    "    lt=[]\n",
    "    lk=[]\n",
    "\n",
    "    count={}\n",
    "\n",
    "    \n",
    "    for t in range(nn1):\n",
    " \n",
    "        for i in range(t+1,nn1):\n",
    "            lt.append([t])\n",
    "            lk.append(i)\n",
    "            \n",
    "    ln_2=[nn1-1]* len(lt)\n",
    "    lnn1=[nn1]* len(lt)\n",
    "           \n",
    "    #print(lk)   \n",
    "     \n",
    "    print(list(zip(lt,lk,ln_2,lnn1)))\n",
    "\n",
    "    \n",
    "    #parallel execution of ProcessRT function\n",
    "    res2 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
    "    print(res2.get())# print the list of resulting dictionaries\n",
    "    print(sum(merge(res2.get()).values()))#the number of closure systems w.r.t. T1\n",
    "\n",
    "    pool.close()  # 'TERM'\n",
    "    pool.join()   # 'KILL'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Inequivalent closure systems (formal contexts) with respect to set permutations.\n",
    "\n",
    "### Cases from n=2 to 5 are given. For n=0,1, a(0)=1 (empty set) and a(1)=2 ({1} and {{},1})."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PermBit(bit,perm):\n",
    "    out=0\n",
    "    for i in range(len(perm)):\n",
    "        if (bit>>i) & 1==1:\n",
    "            out=out | (1<<perm[i])\n",
    "    return out\n",
    "\n",
    "def PermTuple(t,perm):\n",
    "    ret=[]\n",
    "    for bit in t:\n",
    "        ret.append(PermBit(bit,perm))\n",
    "    return tuple(ret)\n",
    "\n",
    "\n",
    "def isLectLess(a,b):\n",
    "    #is A lectically smaller than B?\n",
    "    for i in range(len(a)):\n",
    "        if a[i]==b[i]:\n",
    "            pass\n",
    "        elif a[i]<b[i]:\n",
    "            return True\n",
    "        else:\n",
    "            return False\n",
    "    return True\n",
    "        \n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isLectLess((1,2,3),(1,2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isLectLess((1,2,3),(1,3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isLectLess((1,3,4),(1,2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import permutations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=3\n",
    "Perms=list(permutations(range(n)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "d3=merge2(res3.get())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "T3=[]\n",
    "for key in d3.keys():\n",
    "    T3.append(key[1])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, 3, 4),\n",
       " (1, 2, 4),\n",
       " (1, 2, 4, 5),\n",
       " (1, 2, 4, 6),\n",
       " (1, 2, 5, 6),\n",
       " (1, 3, 4, 6),\n",
       " (2, 3, 4, 5),\n",
       " (3, 5, 6)]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 4, 5, 2)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PermTuple(T3[0],Perms[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1, 2)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Perms[0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "ineqT3=[]\n",
    "\n",
    "\n",
    "for t in T3:\n",
    "    mode=True\n",
    "    for p in Perms:\n",
    "        pt=sorted(PermTuple(t,p))\n",
    "        if isLectLess(t,pt):\n",
    "            pass\n",
    "        else:\n",
    "            mode=False\n",
    "            break\n",
    "            \n",
    "    if mode: \n",
    "        ineqT3.append(t)\n",
    "            \n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, 3, 4), (1, 2, 4), (1, 2, 5, 6), (3, 5, 6)]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ineqT3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=4\n",
    "\n",
    "Perms=list(permutations(range(n)))\n",
    "\n",
    "d4=merge2(res4.get())\n",
    "\n",
    "\n",
    "T4=[]\n",
    "for key in d4.keys():\n",
    "    T4.append(key[1])\n",
    "\n",
    "\n",
    "ineqT4=[]\n",
    "for t in T4:\n",
    "    mode=True\n",
    "    for p in Perms:\n",
    "        pt=sorted(PermTuple(t,p))\n",
    "        if isLectLess(t,pt):\n",
    "            pass\n",
    "        else:\n",
    "            mode=False\n",
    "            break\n",
    "            \n",
    "            \n",
    "    if mode: \n",
    "        ineqT4.append(t)\n",
    "              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, 3, 4, 7, 8),\n",
       " (1, 2, 3, 4, 8),\n",
       " (1, 2, 3, 4, 8, 12),\n",
       " (1, 2, 3, 4, 11, 12),\n",
       " (1, 2, 4, 7, 8),\n",
       " (1, 2, 4, 7, 8, 11),\n",
       " (1, 2, 4, 8),\n",
       " (1, 2, 4, 9, 10),\n",
       " (1, 2, 4, 9, 10, 11),\n",
       " (1, 2, 4, 9, 10, 11, 12),\n",
       " (1, 2, 4, 9, 10, 12),\n",
       " (1, 2, 4, 9, 10, 13),\n",
       " (1, 2, 4, 9, 10, 13, 14),\n",
       " (1, 2, 4, 9, 11, 14),\n",
       " (1, 2, 4, 9, 14),\n",
       " (1, 2, 4, 11, 13, 14),\n",
       " (1, 2, 5, 10, 12),\n",
       " (1, 2, 5, 10, 12, 13),\n",
       " (1, 2, 5, 10, 13, 14),\n",
       " (1, 2, 7, 11, 12),\n",
       " (1, 3, 6, 7, 10, 12),\n",
       " (1, 3, 6, 10, 12),\n",
       " (1, 3, 6, 10, 12, 14),\n",
       " (1, 3, 6, 11, 12),\n",
       " (1, 3, 6, 11, 12, 14),\n",
       " (1, 6, 7, 10, 11, 12),\n",
       " (1, 6, 7, 10, 12),\n",
       " (1, 6, 7, 10, 13),\n",
       " (1, 6, 10, 12),\n",
       " (1, 6, 10, 12, 14),\n",
       " (1, 6, 10, 13),\n",
       " (1, 6, 10, 13, 14),\n",
       " (1, 6, 11, 13, 14),\n",
       " (3, 5, 6, 7, 9, 10),\n",
       " (3, 5, 6, 7, 9, 10, 12),\n",
       " (3, 5, 6, 9, 10),\n",
       " (3, 5, 6, 9, 10, 12),\n",
       " (3, 5, 6, 9, 10, 13),\n",
       " (3, 5, 6, 9, 10, 13, 14),\n",
       " (3, 5, 6, 9, 11, 14),\n",
       " (3, 5, 6, 9, 14),\n",
       " (3, 5, 6, 11, 13, 14),\n",
       " (3, 5, 7, 9, 14),\n",
       " (3, 5, 7, 10, 12),\n",
       " (3, 5, 7, 10, 12, 14),\n",
       " (3, 5, 9, 14),\n",
       " (3, 5, 10, 12),\n",
       " (3, 5, 10, 13, 14),\n",
       " (3, 5, 11, 13, 14),\n",
       " (7, 11, 13, 14)]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ineqT4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ineqT4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=5\n",
    "\n",
    "Perms=list(permutations(range(n)))\n",
    "\n",
    "\n",
    "d5=merge2(res5.get())\n",
    "\n",
    "\n",
    "T5=[]\n",
    "for key in d5.keys():\n",
    "    T5.append(key[1])\n",
    "\n",
    "ineqT5=[]\n",
    "for t in T5:\n",
    "    mode=True\n",
    "    for p in Perms:\n",
    "        pt=sorted(PermTuple(t,p))\n",
    "        if isLectLess(t,pt):\n",
    "            pass\n",
    "        else:\n",
    "            mode=False\n",
    "            break\n",
    "            \n",
    "            \n",
    "    if mode: \n",
    "        ineqT5.append(t)\n",
    "              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7443"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ineqT5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=2\n",
    "\n",
    "Perms=list(permutations(range(n)))\n",
    "\n",
    "\n",
    "d2=merge2(res2.get())\n",
    "\n",
    "\n",
    "T2=[]\n",
    "for key in d2.keys():\n",
    "    T2.append(key[1])\n",
    "\n",
    "ineqT2=[]\n",
    "for t in T2:\n",
    "    mode=True\n",
    "    for p in Perms:\n",
    "        pt=sorted(PermTuple(t,p))\n",
    "        if isLectLess(t,pt):\n",
    "            pass\n",
    "        else:\n",
    "            mode=False\n",
    "            break\n",
    "            \n",
    "            \n",
    "    if mode: \n",
    "        ineqT2.append(t)\n",
    "              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 4, 50, 7443)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ineqT2), len(ineqT3), len(ineqT4), len(ineqT5) #a(2), a(3), a(4), a(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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