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OldPolyhedra :: contains

contains -- checks if the first argument contains the second argument

Synopsis

Description

contains determines if the first argument contains the second argument. Both arguments have to lie in the same ambient space. When the first argument is a Cone or Polyhedron, it tests if the equations of the first argument are satisfied by the generating points/rays of the second argument.

For example, we can check if the 3 dimensional crosspolytope contains the hypercube or the other way around:

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 = crossPolytope 3

o2 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 8
      number of rays => 0
      number of vertices => 6

o2 : Polyhedron
i3 : contains(Q,P)

o3 = false
i4 : contains(P,Q)

o4 = true

We can also check if the hypercube lies in the positive orthant.

i5 : C = posHull matrix {{1,0,0},{0,1,0},{0,0,1}};
i6 : contains(C,P)

o6 = false
i7 : P = affineImage(P,matrix{{1},{1},{1}})

o7 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 6
      number of rays => 0
      number of vertices => 8

o7 : Polyhedron
i8 : contains(C,P)

o8 = true

Ways to use contains :

For the programmer

The object contains is a method function.