user_guide:tutorials:latest:random

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 — user_guide:tutorials:latest:random [2020/01/22 09:02] (current) Line 1: Line 1: + ====== Random Constructions ====== + + ===== Random points on the unit sphere ===== + + 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. + + + > $p1=rand_sphere(3,​100);​ + > print$p1->​SIMPLICIAL;​ + true + ​ + With probability one such polytopes are simplicial. + + ===== Random polytopes with are neither simplicial nor simple ===== + + + > ($d,$m,$n) = (4,50,30); + >$p1=rand_sphere($d,​$m);​ + > $p2=polarize($p1);​ + > $p3=new Polytope(POINTS=>​rand_vert($p2->​VERTICES,​$n));​ + > print$p3->​SIMPLICIAL,​ " ", $p3->​SIMPLE,​ "​\n",​$p3->​F_VECTOR;​ + false false + 30 163 256 123 +
• user_guide/tutorials/latest/random.txt