SSL orbital-graphs.ipynb Sprache: unbekannt

{
"cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo for the OrbitalGraphs GAP package\n",
    "\n",
    "This attempts to draw orbital graphs for groups $G \\leq S_n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 1,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LoadPackage(\"OrbitalGraphs\");\n",
    "LoadPackage(\"Francy\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "function( OG ) ... end"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Input: an orbital graph\n",
    "# Draws orbital graphs\n",
    "\n",
    "DrawOrbitalGraph := function(OG)\n",
    "    local canvas, fgraph, i, e, nodes, graphviz;\n",
    "    \n",
    "    # todo: make it possible to put a caption here\n",
    "    canvas := Canvas(Concatenation(\"Orbital Graph of\", \"\"));\n",
    "    fgraph := Graph(GraphType.DIRECTED);\n",
    "    Add(canvas, fgraph);\n",
    "\n",
    "    nodes := [];\n",
    "\n",
    "    for i in DigraphVertices(OG) do\n",
    "        nodes[i] := Shape(ShapeType.CIRCLE, String(i));;\n",
    "        Add(fgraph, nodes[i]);\n",
    "    od;\n",
    "    for i in [1..Length(nodes)-1] do\n",
    "        e := Link(nodes[i], nodes[i+1]);\n",
    "        SetInvisible(e, true);\n",
    "        Add(fgraph, e);\n",
    "    od;\n",
    "    e := Link(nodes[Length(nodes)], nodes[1]);\n",
    "    SetInvisible(e, true);\n",
    "    Add(fgraph, e);\n",
    "\n",
    "    for e in DigraphEdges(OG) do\n",
    "        Add(fgraph, Link(nodes[e[1]], nodes[e[2]]));\n",
    "    od;\n",
    "    \n",
    "    graphviz := FrancyRenderer(FrancyRendererType.GRAPHVIZ_CIRCO);\n",
    "    Add(canvas, graphviz);\n",
    "\n",
    "    return Draw(canvas);\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Group([ (1,2,3,4,5,6,7,8), (2,8)(3,7)(4,6) ])"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[ <self-paired orbital graph of Group([ (1,2,3,4,5,6,7,8), (2,8)(3,7)(4,6) ])      on 8 vertices with base-pair (1,5), 8 arcs>,   <self-paired orbital graph of Group([ (1,2,3,4,5,6,7,8), (2,8)(3,7)(4,6) ])      on 8 vertices with base-pair (1,2), 16 arcs>,   <self-paired orbital graph of Group([ (1,2,3,4,5,6,7,8), (2,8)(3,7)(4,6) ])      on 8 vertices with base-pair (1,3), 16 arcs>,   <self-paired orbital graph of Group([ (1,2,3,4,5,6,7,8), (2,8)(3,7)(4,6) ])      on 8 vertices with base-pair (1,4), 16 arcs> ]"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G := DihedralGroup(IsPermGroup, 16);\n",
    "ogs := OrbitalGraphs(G);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 6,
     "metadata": {
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   ],
   "source": [
    "# This seems to work quite ok\n",
    "DrawOrbitalGraph(ogs[1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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\"1.2.4\"}"
     },
     "execution_count": 7,
     "metadata": {
      "application/vnd.francy+json": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This, not so much\n",
    "DrawOrbitalGraph(ogs[2]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Group([ (1,2,3), (1,2), (4,5,6,7,8) ])"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[ <orbital graph of Group([ (1,2,3), (1,2), (4,5,6,7,8) ]) on 8 vertices     with base-pair (4,5), 5 arcs>,   <orbital graph of Group([ (1,2,3), (1,2), (4,5,6,7,8) ]) on 8 vertices     with base-pair (4,6), 5 arcs>,   <orbital graph of Group([ (1,2,3), (1,2), (4,5,6,7,8) ]) on 8 vertices     with base-pair (4,7), 5 arcs>,   <orbital graph of Group([ (1,2,3), (1,2), (4,5,6,7,8) ]) on 8 vertices     with base-pair (4,8), 5 arcs>,   <self-paired orbital graph of Group([ (1,2,3), (1,2), (4,5,6,7,8) ]) on     8 vertices with base-pair (1,2), 6 arcs>,   <orbital graph of Group([ (1,2,3), (1,2), (4,5,6,7,8) ]) on 8 vertices     with base-pair (1,4), 15 arcs>,   <orbital graph of Group([ (1,2,3), (1,2), (4,5,6,7,8) ]) on 8 vertices     with base-pair (4,1), 15 arcs> ]"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G := DirectProduct(SymmetricGroup(3), CyclicGroup(IsPermGroup, 5));\n",
    "ogs := OrbitalGraphs(G);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 10,
     "metadata": {
      "application/vnd.francy+json": {}
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   ],
   "source": [
    "DrawOrbitalGraph(ogs[2]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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   "source": [
    "# Maybe slightly more useful?\n",
    "JupyterSplashDot(DotDigraph(ogs[2]));\n",
    "JupyterSplashDot(DotDigraph(ogs[5]));\n",
    "JupyterSplashDot(DotDigraph(ogs[7]));"
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SSL orbital-graphs.ipynb Sprache: unbekannt

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