| 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 24 kB |
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{
"cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0; margin-left: 5%\">\n", "<h1 style=\"text-align: left;\">Francy - An Interactive Discrete Mathematics Framework for "</div>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0\">\n", " <div style=\"text-align: left; float: left;\">\n", " <h2>Manuel Martins</h2>\n", " <h3>Universidade Aberta, Lisbon - Portugal</h3>\n", " <h4>manuelmachadomartins@gmail.com</h4>\n", " </div>\n", " <div style=\"text-align: left; float: right;\">\n", " <h2>Markus Pfeiffer</h2>\n", " <h3>University of St Andrews, St Andrews - Scotland</h3>\n", " <h4>markus.pfeiffer@morphism.de</h4>\n", " </div>\n", "</div>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0\">\n", "<h1 style=\"text-align: center\">Agenda</h1>\n", "\n", "<h3>\n", " <ol type=\"1\">\n", " <li>Motivation</li>\n", " <li>Solution</li>\n", " <li>Features</li>\n", " <li>Hands-on</li>\n", " <li>Future</li>\n", " </ol>\n", "</h3>\n", "</div>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0\">\n", "<h1 style=\"text-align: center\">1. Motivation</h1>\n", "\n", "<h3><ul><li>Francy arose from the necessity of having a lightweight framework for building intera "\n", "<h2 style=\"text-align: left; margin-left: 10%\">1.1 What is Francy?</h2>\n", "\n", "<h3>\n", "<ul>\n", " <li>an interface to draw graphics using objects;</li>\n", " <li>based on simple concepts of drawing and graph theory;</li>\n", " <li>2 components:</li>\n", " <ol type=\"1\">\n", " <li>a GAP package that is responsible for the semantic representation of graphics;</li>\n", " <li>a GUI library that is responsible for generating the actual interactive graphical represe " </ol>\n", "</ul>\n", "</h3>\n", "</div>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0\">\n", "<h1 style=\"text-align: center\">2. Solution</h1>\n", "\n", "<h2 style=\"text-align: left; margin-left: 10%\">2.1 GAP Package</h2>\n", "\n", "<h3>\n", "<ul>\n", " <li>provides a semantic representation of graphics is provided by a thin layer.</li>\n", " <li>uses JSON, a lightweight, text-based, language-independent data interchange format.</l " <li>follows a JSON Schema, and is identified with the application/vnd.francy+json MIME type.< "</ul>\n", "</h3>\n", "\n", "<h2 style=\"text-align: left; margin-left: 10%\">2.2 GUI Library - Javascript</h2>\n", "\n", "<h3>\n", "<ul>\n", " <li>based on d3.js, for rendering the semantic representation produced by the GAP package;</li> " <li>this library is distributed both as a browser module and as a Jupyter extension.</li>\n", "</ul>\n", "</h3>\n", "\n", "<h2 style=\"text-align: left; margin-left: 10%\">2.3 Jupyter GAP Kernel</h2>\n", "\n", "<h3>\n", "<ul>\n", " <li>pure GAP package that implements the Jupyter Kernel specification;</li>\n", " <li>\"glues\" everything together.</li>\n", "</ul>\n", "</h3>\n", "\n", "<h3>\n", "The Jupyter extension can be used in Jupyter Notebooks or Jupyter Lab, using the Jupyter GAP Ke "</h3>\n", "<h3>\n", "This creates an abstraction and allows the development of new GUI libraries, \n", "using different data rendering dependencies or even different programming languages, inde "</h3>\n", "</div>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 0 0\">\n", "<h1 style=\"text-align: center\">3. Features</h1>\n", "\n", "<h3>\n", "<ul>\n", " <li>allows the creation of directed and undirected graphs, trees, line charts, bar charts and s " <li>enables interaction with graphical objects by clicking, selecting, dragging and zooming "</ul>\n", "</h3>\n", "<h2 style=\"text-align: left; margin-left: 10%\">3.1 How to install</h2>\n", "</div>\n", "\n", "### 1. download latest release and extract the GAP package to GAP packages directory\n", "\n", "```bash\n", "user@local:~$ wget https://github.com/mcmartins/francy/archive/v0.8.2.tar.gz && \\\n" " mkdir -p $GAPROOT/pkg/francy && \\\n", " tar xzvf v0.8.2.tar.gz -C $GAPROOT/pkg/francy francy-0.8.2/gap\n", "```\n", "\n", "### 2. install latest jupyter extension using pip and install on Jupyter lab and/or notebook\ "\n", "```bash\n", "user@local:~$ pip install jupyter_francy\n", "user@local:~$ jupyter lab build # for JupyterLab\n", "user@local:~$ jupyter nbextension enable --py --sys-prefix jupyter_francy # for Notebook "```\n", "<div style=\"display: block; margin: 0 0 50px 0\"/>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0\">\n", "<h1 style=\"text-align: center\">4. Hands-on</h1>\n", "</div>" ] }, { "cell_type": "code", "execution_count": null, "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(\"francy\");\n", "LoadPackage(\"digraph\");" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "function( G ) ... end" ] }, "execution_count": 3, "metadata": { "text/plain": "" }, "output_type": "execute_result" } ], "source": [ "FrancyDigraphs := function(G)\n", " local as, d, v, e, graph, nodes, m, IsGroupSimple, canvas, i, graphviz;\n", "\n", " as := AllSubgroups(G);\n", "\n", " d := Digraph(as, {H, K} -> IsSubgroup(H, K));;\n", " v := DigraphVertices(d);;\n", " e := DigraphEdges(d);;\n", "\n", " graph := Graph(GraphType.DIRECTED);;\n", " canvas := Canvas(Concatenation(\"Subgroups Digraph of \", String(G)));;\n", " Add(canvas, graph);;\n", "\n", " nodes := [];;\n", "\n", " m := FrancyMessage(FrancyMessageType.INFO, \"Simple Groups\", \n", " \"A group is simple if it is nontrivial and has no nontrivial normal subgroups.\");;\n", " \n", " IsGroupSimple := function(i)\n", " Add(canvas, m);;\n", " if IsSimpleGroup(as[i]) then\n", " Add(canvas, FrancyMessage(\"Simple\", Concatenation(\"The vertex \", \n", " String(i), \", representing the subgroup \", String(as[i]), \", is simple.\")));;\n", " else\n", " Add(canvas, FrancyMessage(\"Not Simple\", Concatenation(\"The vertex \", \n", " String(i), \", representing the subgroup \", String(as[i]), \", is not simple.\")));;\n", " fi;;\n", " return Draw(canvas);\n", " end;;\n", "\n", " for i in v do\n", " nodes[i] := Shape(ShapeType.CIRCLE, String(i));;\n", " Add(nodes[i], Menu(\"Simple\", Callback(IsGroupSimple, [i])));;\n", " Add(graph, nodes[i]);;\n", " od;;\n", "\n", " for i in e do\n", " Add(graph, Link(nodes[i[1]], nodes[i[2]]));;\n", " od;;\n", " \n", " graphviz := FrancyRenderer(FrancyRendererType.GRAPHVIZ_DOT);\n", " Add(canvas, graphviz);\n", "\n", " return Draw(canvas);\n", "end;" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<pc group of size 4 with 2 generators>" ] }, "execution_count": 4, "metadata": { "text/plain": "" }, "output_type": "execute_result" } ], "source": [ "G := DihedralGroup(4);" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<!-- Generated by graphviz version 2.43.0 (0)\n", " -->\n", "<!-- Title: hgn Pages: 1 -->\n", "<svg width=\"220pt\" height=\"188pt\"\n", " viewBox=\"0.00 0.00 220.06 188.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n" "<title>hgn</title>\n", "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-184 216.06,-184 216.0 "<!-- 1 -->\n", "<g id=\"node1\" class=\"node\">\n", "<title>1</title>\n", "<ellipse fill=\"none\" stroke=\"black\" cx=\"68.06\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n "<text text-anchor=\"middle\" x=\"68.06\" y=\"-14.3\" font-family=\"Times,serif\" font "</g>\n", "<!-- 1->1 -->\n", "<g id=\"edge1\" class=\"edge\">\n", "<title>1->1</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M82.11,-29.76C92.98,-34.15 104.06,-30.23 104 "<polygon fill=\"black\" stroke=\"black\" points=\"91.38,-1.12 82.11,-6.24 92.55,-8.02 "</g>\n", "<!-- 2 -->\n", "<g id=\"node2\" class=\"node\">\n", "<title>2</title>\n", "<ellipse fill=\"none\" stroke=\"black\" cx=\"32.06\" cy=\"-90\" rx=\"18\" ry=\"18\"/>\n "<text text-anchor=\"middle\" x=\"32.06\" y=\"-86.3\" font-family=\"Times,serif\" font "</g>\n", "<!-- 2->1 -->\n", "<g id=\"edge2\" class=\"edge\">\n", "<title>2->1</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M40.05,-73.46C44.58,-64.67 50.33,-53.48 55.4 "<polygon fill=\"black\" stroke=\"black\" points=\"58.64,-44.99 60.1,-34.49 52.41,-41. 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"<polygon fill=\"black\" stroke=\"black\" points=\"127.38,-73.12 118.11,-78.24 128.55, "</g>\n", "<!-- 4 -->\n", "<g id=\"node4\" class=\"node\">\n", "<title>4</title>\n", "<ellipse fill=\"none\" stroke=\"black\" cx=\"176.06\" cy=\"-90\" rx=\"18\" ry=\"18\"/>\ "<text text-anchor=\"middle\" x=\"176.06\" y=\"-86.3\" font-family=\"Times,serif\" fon "</g>\n", "<!-- 4->1 -->\n", "<g id=\"edge6\" class=\"edge\">\n", "<title>4->1</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M161.05,-79.27C142.99,-67.56 112.49,-47.79 9 "<polygon fill=\"black\" stroke=\"black\" points=\"93.25,-31.15 82.95,-28.65 89.44,-37 "</g>\n", "<!-- 4->4 -->\n", "<g id=\"edge7\" class=\"edge\">\n", "<title>4->4</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M190.11,-101.76C200.98,-106.15 212.06,-102. "<polygon fill=\"black\" stroke=\"black\" points=\"199.38,-73.12 190.11,-78.24 200.55, "</g>\n", "<!-- 5 -->\n", "<g id=\"node5\" class=\"node\">\n", "<title>5</title>\n", "<ellipse fill=\"none\" stroke=\"black\" cx=\"68.06\" cy=\"-162\" rx=\"18\" ry=\"18\"/>\ "<text text-anchor=\"middle\" x=\"68.06\" y=\"-158.3\" font-family=\"Times,serif\" fon "</g>\n", "<!-- 5->1 -->\n", "<g id=\"edge8\" class=\"edge\">\n", "<title>5->1</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M52.2,-152.98C36.91,-144.25 14.72,-128.73 5. "<polygon fill=\"black\" stroke=\"black\" points=\"45.48,-35.21 52.2,-27.02 41.84,-29. "</g>\n", "<!-- 5->2 -->\n", "<g id=\"edge9\" class=\"edge\">\n", "<title>5->2</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M60.07,-145.46C55.55,-136.67 49.8,-125.48 44 "<polygon fill=\"black\" stroke=\"black\" points=\"47.72,-113.78 40.03,-106.49 41.49,- "</g>\n", "<!-- 5->3 -->\n", "<g id=\"edge10\" class=\"edge\">\n", "<title>5->3</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M76.05,-145.46C80.58,-136.67 86.33,-125.48 9 "<polygon fill=\"black\" stroke=\"black\" points=\"94.64,-116.99 96.1,-106.49 88.41,-1 "</g>\n", "<!-- 5->4 -->\n", "<g id=\"edge11\" class=\"edge\">\n", "<title>5->4</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M83.08,-151.27C101.14,-139.56 131.64,-119.7 "<polygon fill=\"black\" stroke=\"black\" points=\"154.69,-109.03 161.18,-100.65 150.8 "</g>\n", "<!-- 5->5 -->\n", "<g id=\"edge12\" class=\"edge\">\n", "<title>5->5</title>\n", "<path fill=\"none\" stroke=\"black\" d=\"M82.11,-173.76C92.98,-178.15 104.06,-174.23 "<polygon fill=\"black\" stroke=\"black\" points=\"91.38,-145.12 82.11,-150.24 92.55,- "</g>\n", "</g>\n", "</svg>\n" ] }, "execution_count": 5, "metadata": { "image/svg+xml": { "height": 500, "width": 500 } }, "output_type": "execute_result" } ], "source": [ "JupyterSplashDot(DotDigraph(Digraph(AllSubgroups(G), {H, K} -> IsSubgroup(H, K))));" ] }, { "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": [ "FrancyDigraphs(G);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<h2 style=\"text-align: left; margin-left: 10%\">4.1 More examples</h2>\n", "\n", "<h3>Try these notebooks:</h3>\n", "\n", "1. [Francy Features](francy-features.ipynb)\n", "2. [Subgroup Lattice](subgroup-lattice.ipynb)\n", "3. [Francy Monoids](francy-monoids.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0\">\n", "<h1 style=\"text-align: center\">5. Future</h1>\n", "\n", "<h3>\n", "<ul>\n", " <li>rendering multiple topological graphs on the same canvas.</li>\n", " <li>allow the creation of \"free graphics\" using lines and text.</li>\n", " <li>introduce new concepts like tables for matrices representations.</li>\n", " <li>validate the JSON against its JSON Schema between GAP and GUI.</li>\n", " <li>rendering is done on SVG which might be \"heavy\" when loading huge graphs.</li>\n", "<ul>\n", "</h3>\n", "</div>" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "<hr/>\n", "<div style=\"display: block; margin: 50px 0 50px 0\">\n", "<h1 style=\"text-align: center\">Questions?</h1>\n", "<br/>\n", "<h1 style=\"margin-left: 10%\">Thanks!</h1>\n", "</div>" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "GAP 4", "language": "gap", "name": "gap-4" }, "language_info": { "codemirror_mode": "gap", "file_extension": ".g", "mimetype": "text/x-gap", "name": "GAP 4", "nbconvert_exporter": "", "pygments_lexer": "gap", "version": "4.13dev" } }, "nbformat": 4, "nbformat_minor": 4 } [ Dauer der Verarbeitung: 0.17 Sekunden (vorverarbeitet) ] |
2026-03-28