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

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

o1 : Polyhedron

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

o2 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 3
      number of rays => 0
      number of vertices => 3

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 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o5 : Polyhedron

i6 : isFace(Q,P)

o6 = true

Ways to use isFace:

isFace(Cone,Cone)
isFace(Polyhedron,Polyhedron)

For the programmer

The object isFace is a method function.

The source of this document is in OldPolyhedra.m2:5651:0.