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# Cone + Cone -- computes the Minkowski sum of two cones

- Operator: +
- Usage:
    `C = C1 + C2`
- Inputs:
  - C1, a convex rational cone
  - C2, a convex rational cone
- Outputs:
  - C, a convex rational cone

## Description

Computes the Minkowski sum of C1 and C2. This is the cone C1 + C2 = {x + y | x in C1, y in C2}. Note that C1 and C2 have to lie in the same ambient space.

See also minkowskiSum.

    i1 : C1 = posHull matrix {{1,2,3},{2,3,1},{3,1,2}}

    o1 = {ambient dimension => 3           }
          dimension of lineality space => 0
          dimension of the cone => 3
          number of facets => 3
          number of rays => 3

    o1 : Cone

    i2 : C2 = posHull matrix {{1},{0},{0}}

    o2 = {ambient dimension => 3           }
          dimension of lineality space => 0
          dimension of the cone => 1
          number of facets => 1
          number of rays => 1

    o2 : Cone

    i3 : C = C1 + C2

    o3 = {ambient dimension => 3           }
          dimension of lineality space => 0
          dimension of the cone => 3
          number of facets => 4
          number of rays => 4

    o3 : Cone

    i4 : rays C

    o4 = | 1 2 3 1 |
         | 0 3 1 2 |
         | 0 1 2 3 |

                  3       4
    o4 : Matrix ZZ  <-- ZZ

## Ways to use this method:

- Cone + Cone -- computes the Minkowski sum of two cones

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:7880:0.