Polyhedron * Polyhedron -- computes the direct product of two polyhedra

Synopsis

Operator: *
Usage:

Q = P1 * P2
Inputs:
- P1, a convex polyhedron
- P2, a convex polyhedron
Outputs:
- Q, a convex polyhedron

Description

Computes the direct product of P1 and P2.This is the polyhedron {(x,y) | x in P1, y in P2}, in the direct product of the ambient spaces.

See also directProduct.

i1 : P1 = convexHull matrix {{1,-1,0,0},{0,0,1,-1}}

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o1 : Polyhedron

i2 : P2 = convexHull matrix {{1},{-1}}

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 0
      number of facets => 1
      number of rays => 0
      number of vertices => 1

o2 : Polyhedron

i3 : P = P1 * P2

o3 = {ambient dimension => 4           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o3 : Polyhedron

i4 : vertices P

o4 = | -1 1  0  0  |
     | 0  0  -1 1  |
     | 1  1  1  1  |
     | -1 -1 -1 -1 |

              4       4
o4 : Matrix QQ  <-- QQ

Ways to use this method:

Polyhedron * Polyhedron -- computes the direct product of two polyhedra