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

Usage:

b = contains(C,X)

b = contains(P,X)

b = contains(F,C)

b = contains(L,C)

b = contains(L,P)
Inputs:
- C, a convex rational cone
- P, a convex polyhedron
- F, an instance of the type Fan
- L, a list
- X, either a Cone, a Polyhedron, or a Matrix with only one column giving a point.
Outputs:
- b, a Boolean value, true if the first argument contains the second argument, false otherwise.

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 = P

o1 : Polyhedron

i2 : Q = crossPolytope 3

o2 = Q

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 = coneFromVData 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 = P

o7 : Polyhedron

i8 : contains(C,P)

o8 = true

Ways to use contains:

contains(Cone,Cone)
contains(Cone,Matrix)
contains(Cone,Polyhedron)
contains(Fan,Cone)
contains(List,Cone)
contains(List,Polyhedron)
contains(Polyhedron,Cone)
contains(Polyhedron,Matrix)
contains(Polyhedron,Polyhedron)

For the programmer

The object contains is a method function.

The source of this document is in Polyhedra/documentation/old_documentation.m2:1164:0.