Macaulay2 » Documentation
Packages » OldPolyhedra :: Cone * Polyhedron
next | previous | forward | backward | up | index | toc

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

- Operator: *
- Usage:
    `Q = C * P`
- Inputs:
  - C, a convex rational cone
  - P, a convex polyhedron
- Outputs:
  - Q, a convex polyhedron

## Description

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

See also directProduct.

    i1 : C = posHull matrix {{1,2},{2,1}}

    o1 = {ambient dimension => 2           }
          dimension of lineality space => 0
          dimension of the cone => 2
          number of facets => 2
          number of rays => 2

    o1 : Cone

    i2 : P =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 : Q = C * P

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

    o4 : Sequence

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:7751:0.