Quelle ICMS_2018.ipynb
Sprache: unbekannt
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"<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 GAP</h1>\n",
"</div>"
]
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"<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>"
]
},
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"<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>"
]
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"<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 interactive graphics, generated from GAP, running primarily on the web, primarily in a Jupyter Notebook.</li></ul></h3>\n",
"\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 representation.</li>\n",
" </ol>\n",
"</ul>\n",
"</h3>\n",
"</div>"
]
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"<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.</li>\n",
" <li>follows a JSON Schema, and is identified with the application/vnd.francy+json MIME type.</li>\n",
"</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>\n",
" <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 Kernel and the MIME type application/vnd.francy+json to render the document.\n",
"</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, independently of the GAP package.\n",
"</h3>\n",
"</div>"
]
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"<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 scatter charts;</li>\n",
" <li>enables interaction with graphical objects by clicking, selecting, dragging and zooming;</li>\n",
"</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 $GAPROOT/pkg/francy francy-0.8.2/gap\n",
"```\n",
"\n",
"### 2. install latest jupyter extension using pip and install on Jupyter lab and/or notebook\n",
"\n",
"```bash\n",
"user@local:~$ 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",
"```\n",
"<div style=\"display: block; margin: 0 0 50px 0\"/>"
]
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"<hr/>\n",
"<div style=\"display: block; margin: 50px 0 50px 0\">\n",
"<h1 style=\"text-align: center\">4. Hands-on</h1>\n",
"</div>"
]
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"LoadPackage(\"francy\");\n",
"LoadPackage(\"digraph\");"
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"function( G ) ... end"
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"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;"
]
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"<pc group of size 4 with 2 generators>"
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"G := DihedralGroup(4);"
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"<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)"
]
},
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"<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>"
]
},
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"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>"
]
},
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[ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet)
]
|
2026-04-02
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