intersect -- computes the intersection of cones, and polyhedra

Usage:

P = intersection L

C = intersection(C1,C2)

P = intersection(P1,P2)
Inputs:
- L, a list, containing any of the inputs below
- C1, a convex rational cone
- C2, a convex rational cone
- P1, a convex polyhedron
- P2, a convex polyhedron
Outputs:
- P, a convex polyhedron
- C, a convex rational cone

Description

If two polyhedra or two cones are inserted, then the intersection of both arguments is computed if both arguments lie in the same ambient space. If both arguments are cones then the output is again a cone. Otherwise intersection returns a polyhedron.

If intersection is called for a list L, then the list may contain a combination of the following in any order.

i1 : C = hypercube 2

o1 = C

o1 : Polyhedron

i2 : S = simplex 2

o2 = S

o2 : Polyhedron

i3 : CS = intersection(C,S)

o3 = CS

o3 : Polyhedron

Ways to use intersect:

intersect(Cone,Cone)
intersect(Cone,Polyhedron)
intersect(List) -- see intersect -- compute an intersection
intersect(Polyhedron,Cone)
intersect(Polyhedron,Polyhedron)
intersect(Sequence) -- see intersect -- compute an intersection
intersect(Ideal) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersect(Module) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersect(Module,Module) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersect(Matrix) -- Deprecated variant of {\tt coneFromHData}
intersect(Matrix,Matrix) -- Deprecated variants of {\tt polyhedronFromHData} and {\tt coneFromHData}
intersect(Matrix,Matrix,Matrix,Matrix) -- see intersect(Matrix,Matrix) -- Deprecated variants of {\tt polyhedronFromHData} and {\tt coneFromHData}
intersect(RRi) -- intersection of input intervals
intersect(RRi,RRi) -- see intersect(RRi) -- intersection of input intervals
intersect(Set,Set) -- set intersection

For the programmer

The object intersect is an associative binary method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Polyhedra/documentation/old_documentation.m2:558:0.