| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/francy/notebooks/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 17.3.2023 mit Größe 47 kB |
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Quelle orbital-graphs.ipynb Sprache: unbekannt |
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{ "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 ] }, "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": [ { "data": { "application/vnd.francy+json": "{\"canvas\" : {\"graph\" : {\"collapsed\" : true,\"id\" }, "execution_count": 6, "metadata": { "application/vnd.francy+json": {} }, "output_type": "execute_result" } ], "source": [ "# This seems to work quite ok\n", "DrawOrbitalGraph(ogs[1]);" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/vnd.francy+json": "{\"canvas\" : {\"graph\" : {\"collapsed\" : true,\"id\" }, "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), ] }, "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": [ { "data": { "application/vnd.francy+json": "{\"canvas\" : {\"graph\" : {\"collapsed\" : true,\"id\" |