Macaulay2 » Documentation
Packages » Polyhedra :: Cone + Polyhedron
next | previous | forward | backward | up | index | toc

# Cone + Polyhedron -- computes the Minkowski sum 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 Minkowski sum of C and P.This is the polyhedron C + P = {c + p | c in C, p in P}. Note that C and P have to lie in the same ambient space.

See also minkowskiSum.

    i1 : C = coneFromVData matrix {{1},{2},{0}}

    o1 = C

    o1 : Cone

    i2 : P = hypercube 3

    o2 = P

    o2 : Polyhedron

    i3 : Q = C + P

    o3 = Q

    o3 : Polyhedron

    i4 : (vertices Q,rays Q)

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

    o4 : Sequence

## Ways to use this method:

- Cone + Polyhedron -- computes the Minkowski sum of a cone and a polyhedron

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Polyhedra/documentation/old_documentation.m2:3333:0.