# incompCones -- returns the pairs of incompatible cones

## Synopsis

• Usage:
Lpairs = incompCones L
Lpairs = incompCones(X,F)
Lpairs = incompCones(F,X)
• Inputs:
• Outputs:

## Description

If incompCones is applied to a list of cones and fans, then it returns the pairs of elements whose intersection is not a face of each. For a cone C and a fan F in the list this means there is at least one generating cone of F whose intersection with C is not a face of each. For two fans in the list this means there is at least one generating cone each such that their intersection is not a face of each. If applied to a pair consisting of a cone and a fan or two fans, then it returns the pairs of cones that do not share a common face.

 i1 : C1 = posHull matrix{{1,0},{1,1}}; i2 : C2 = posHull matrix{{1,0},{0,-1}}; i3 : C3 = posHull matrix{{-1,0},{0,1}}; i4 : C4 = posHull matrix{{1,1},{0,1}}; i5 : C5 = posHull matrix {{1,2},{2,1}}; i6 : L = {C1,C2,C3,C4,C5}; i7 : Lpairs = incompCones L o7 = {({ambient dimension => 2 }, {ambient dimension => 2 dimension of lineality space => 0 dimension of lineality space => dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 ------------------------------------------------------------------------ }), ({ambient dimension => 2 }, {ambient dimension => 2 0 dimension of lineality space => 0 dimension of lineality space dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 ------------------------------------------------------------------------ })} => 0 o7 : List i8 : Lpairs == {(C1,C4),(C1,C5)} o8 = false

## Ways to use incompCones :

• "incompCones(Cone,Fan)"
• "incompCones(Fan,Cone)"
• "incompCones(Fan,Fan)"
• "incompCones(List)"

## For the programmer

The object incompCones is .