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 = P

o1 : Polyhedron

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

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

              3        1
o2 : Matrix ZZ  <--- ZZ

i3 : F = maxFace(w,P)

o3 = F

o3 : Polyhedron

i4 : vertices F

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

              3        2
o4 : Matrix QQ  <--- QQ