tailCone -- computes the tail/recession cone of a polyhedron

Synopsis

• Usage:

  C = tailCone P

• Inputs:
  • P, a convex polyhedron
• Outputs:
  • C, a convex rational cone

Description

Every polyhedron P can be uniquely decomposed into the sum of a polytope and a cone, the tail or recession cone of P. Thus, it is the cone generated by the non-compact part, i.e. the rays and the lineality space of P. If P is a polytope then the tail cone is the origin in the ambient space of P.

i1 : P = polyhedronFromHData(matrix{{-1,0},{1,0},{0,-1},{-1,-1},{1,-1}},matrix{{2},{2},{-1},{0},{0}}) 

o1 = P

o1 : Polyhedron

i2 : C = tailCone P

o2 = C

o2 : Cone

i3 : rays C

o3 = | 0 |
     | 1 |

              2        1
o3 : Matrix ZZ  <--- ZZ