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

Synopsis

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