smallestFace -- determines the smallest face of the Cone/Polyhedron containing a point

Usage:

C1 = smallestFace(p,C)

P1 = smallestFace(p,P)
Inputs:
- p, a matrix, over ZZ or QQ with only one column representing a point
- C, a convex rational cone
- P, a convex polyhedron
Outputs:
- C1, a convex rational cone, or
- P1, a convex polyhedron

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 = 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

Ways to use smallestFace:

smallestFace(Matrix,Cone)
smallestFace(Matrix,Polyhedron)

For the programmer

The object smallestFace is a method function.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Polyhedra/documentation/old_documentation.m2:2119:0.