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OldPolyhedra :: Polyhedron * Cone

Polyhedron * Cone -- computes the direct product of a polyhedron and a cone

Synopsis

Description

Computes the direct product of P and C. This is the polyhedron {(p,c) | p in P, x in C}, in the direct product of the ambient spaces.

See also directProduct.

i1 : P =convexHull matrix {{1},{-1}}

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 0
      number of facets => 1
      number of rays => 0
      number of vertices => 1

o1 : Polyhedron
i2 : C = posHull matrix {{1,2},{2,1}}

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of the cone => 2
      number of facets => 2
      number of rays => 2

o2 : Cone
i3 : Q = P * C

o3 = {ambient dimension => 4           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 3
      number of rays => 2
      number of vertices => 1

o3 : Polyhedron
i4 : (vertices Q,rays Q)

o4 = (| 1  |, | 0 0 |)
      | -1 |  | 0 0 |
      | 0  |  | 2 1 |
      | 0  |  | 1 2 |

o4 : Sequence