/usr/share/polymake/demo/random.ipynb is in polymake-common 3.2r2-3.
This file is owned by root:root, with mode 0o644.
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"cells": [
{
"attachments": {},
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"source": [
"# Random Constructions\n",
"\n",
"## Random points on the unit sphere\n",
"\n",
"The easiest way to randomly construct a polytope is by sampling points on the unit sphere. The following chooses 100 points on the units sphere in 3-space.\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1\n",
"\n"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"$p1=rand_sphere(3,100);\n",
"print $p1->SIMPLICIAL;"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"With probability one such polytopes are simplicial.\n",
"\n",
"## Random polytopes with are neither simplicial nor simple\n",
"\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 0\n",
"30 166 264 128\n",
"\n"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"($d,$m,$n) = (4,50,30);\n",
"$p1=rand_sphere($d,$m);\n",
"$p2=polarize($p1);\n",
"$p3=new Polytope(POINTS=>rand_vert($p2->VERTICES,$n));\n",
"print $p3->SIMPLICIAL, \" \", $p3->SIMPLE, \"\\n\", $p3->F_VECTOR;"
]
}
],
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