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

• Operator: +
• Usage:
C = C1 + C2
• Inputs:
• C1,
• C2,
• Outputs:

## 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.

 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