isFace -- tests if the first argument is a face of the second

Synopsis

• Usage:

  b = isFace(X,Y)

• Inputs:
  • X, a convex rational cone, or Polyhedron
  • Y, an element of the same class as X
• Outputs:
  • b, a Boolean value, true if X is a face of Y, false otherwise

Description

Both arguments must lie in the same ambient space. Then isFace computes all faces of Y with the dimension of X and checks if one of them is X.

i1 : P = hypercube 3

o1 = P

o1 : Polyhedron

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

o2 = Q

o2 : Polyhedron

i3 : isFace(Q,P)

o3 = false

Thus, Q is not a face of P, but we can extend it to a face.

i4 : v = matrix{{1},{-1},{-1}};

              3        1
o4 : Matrix ZZ  <--- ZZ

i5 : Q = convexHull{Q,v}

o5 = Q

o5 : Polyhedron

i6 : isFace(Q,P)

o6 = true