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 = P o1 : Polyhedron |
i2 : p = matrix {{1},{0},{0}} o2 = | 1 | | 0 | | 0 | 3 1 o2 : Matrix ZZ <--- ZZ |
i3 : smallestFace(p,P) o3 = Polyhedron{...1...} o3 : Polyhedron |