next | previous | forward | backward | up | top | index | toc | Macaulay2 website
OldPolyhedra :: normalCone(Polyhedron,Polyhedron)

normalCone(Polyhedron,Polyhedron) -- computes the normal cone of a face of a polyhedron

Synopsis

Description

The normal cone of a face Q of a polyhedron P is the cone in the normal fan (see normalFan) that corresponds to this face. This is the cone of all vectors attaining their maximum on this face.

i1 : P = hypercube 3

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 6
      number of rays => 0
      number of vertices => 8

o1 : Polyhedron
i2 : Q = convexHull matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}}

o2 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o2 : Polyhedron
i3 : C = normalCone(P,Q)

o3 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 1
      number of facets => 1
      number of rays => 1

o3 : Cone
i4 : rays C

o4 = | 0  |
     | 0  |
     | -1 |

              3        1
o4 : Matrix ZZ  <--- ZZ