maxFace -- computes the face of a Polyhedron or Cone where a weight attains its maximum

Synopsis

Usage:

F = maxFace(w,P)

F = maxFace(w,C)
Inputs:
- w, a matrix, over ZZ or QQ with only one column representing a weight vector
- P, a convex polyhedron
- C, a convex rational cone
Outputs:
- F, Depending on the input, a Cone or a Polyhedron, the face where w attains its maximum

Description

maxFace computes the face of the given Polyhedron P or Cone C where w attains its maximum.

i1 : P = crossPolytope 3

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

o1 : Polyhedron

i2 : w = matrix {{1},{-1},{0}}

o2 = | 1  |
     | -1 |
     | 0  |

              3       1
o2 : Matrix ZZ  <-- ZZ

i3 : F = maxFace(w,P)

o3 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 1
      number of facets => 2
      number of rays => 0
      number of vertices => 2

o3 : Polyhedron

i4 : vertices F

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

              3       2
o4 : Matrix QQ  <-- QQ

Ways to use maxFace :

maxFace(Matrix,Cone)
maxFace(Matrix,Polyhedron)

For the programmer

The object maxFace is a method function.