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

Function: normalCone
Usage:

C = normalCone(P,Q)
Inputs:
- P, a convex polyhedron
- Q, a convex polyhedron, which must be a face of P
Outputs:
- C, a convex rational cone

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 = P

o1 : Polyhedron

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

o2 = Q

o2 : Polyhedron

i3 : C = normalCone(P,Q)

o3 = C

o3 : Cone

i4 : rays C

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

              3       1
o4 : Matrix ZZ  <-- ZZ

Ways to use this method:

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

The source of this document is in Polyhedra/documentation/old_documentation.m2:2001:0.