next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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

Synopsis

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 = intersection(matrix{{-1,0},{1,0},{0,-1},{-1,-1},{1,-1}},matrix{{2},{2},{-1},{0},{0}}) 

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 5
      number of rays => 1
      number of vertices => 4

o1 : Polyhedron
i2 : C = tailCone P

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of the cone => 1
      number of facets => 1
      number of rays => 1

o2 : Cone
i3 : rays C

o3 = | 0 |
     | 1 |

              2        1
o3 : Matrix QQ  <--- QQ

Ways to use tailCone :