minFace -- computes the face of a Polyhedron or Cone where a weight attains its minimum

• Usage:

  F = minFace(w,P)

  F = minFace(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 minimum

i1 : P = hypercube 3

o1 = P

o1 : Polyhedron

i2 : w = matrix {{1},{2},{0}}

o2 = | 1 |
     | 2 |
     | 0 |

              3       1
o2 : Matrix ZZ  <-- ZZ

i3 : F = minFace(w,P)

o3 = F

o3 : Polyhedron

i4 : vertices F

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

              3       2
o4 : Matrix QQ  <-- QQ