# intersection -- computes the intersection of cones, and polyhedra

## Synopsis

• Usage:
P = intersection L
C = intersection(C1,C2)
P = intersection(P1,P2)
• Inputs:
• L, a list, containing any of the inputs below
• C1,
• C2,
• P1,
• P2,
• Outputs:

## 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 intersection :

• "intersection(Cone,Cone)"
• "intersection(Cone,Polyhedron)"
• "intersection(List)"
• "intersection(Polyhedron,Cone)"
• "intersection(Polyhedron,Polyhedron)"
• intersection(Matrix) -- Deprecated variant of {\tt coneFromHData}
• intersection(Matrix,Matrix) -- Deprecated variants of {\tt polyhedronFromHData} and {\tt coneFromHData}
• "intersection(Matrix,Matrix,Matrix,Matrix)" -- see intersection(Matrix,Matrix) -- Deprecated variants of {\tt polyhedronFromHData} and {\tt coneFromHData}
• intersection(RRi,RRi) -- computes intersection of input intervals

## For the programmer

The object intersection is .