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OldPolyhedra :: smallestFace

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

Synopsis

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

Ways to use smallestFace :

For the programmer

The object smallestFace is a method function.