volume -- computes the volume of a polytope

Synopsis

Usage:

v = volume P
Inputs:
- P, a convex polyhedron, , which must be compact
Outputs:
- v, a rational number

Description

volume computes the volume of a polytope. To do this, it triangulates the polytope first. The volume of a simplex is |det(v_1-v_0,..,v_n-v_0)|/n!, where v_0,..,v_n are the vertices of the simplex.

i1 : P = crossPolytope 3

o1 = P

o1 : Polyhedron

i2 : volume P

     4
o2 = -
     3

o2 : QQ

Ways to use volume :

volume(Polyhedron)

For the programmer

The object volume is a method function.