Description
p is considered to be a point in the ambient space of the second argument, so the number of rows of
p must equal the dimension of the ambient space of the second argument. The function computes the smallest face of the second argument that contains
p. If the second argument is a
Polyhedron the output is a
Polyhedron and if it is a
Cone the output is a
Cone. In both cases, if the point is not contained in the second argument then the output is the empty polyhedron.
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 : p = matrix {{1},{0},{0}}
o2 =  1 
 0 
 0 
3 1
o2 : Matrix ZZ < ZZ

i3 : smallestFace(p,P)
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o3 : Polyhedron
