incompCones -- returns the pairs of incompatible cones

Synopsis

• Usage:

  Lpairs = incompCones L

  Lpairs = incompCones(X,F)

  Lpairs = incompCones(F,X)

• Inputs:
  • L, a list
  • F, an instance of the type Fan
  • X, Cone or Fan
• Outputs:
  • Lpairs, a list

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 = coneFromVData matrix{{1,0},{1,1}};

i2 : C2 = coneFromVData matrix{{1,0},{0,-1}};

i3 : C3 = coneFromVData matrix{{-1,0},{0,1}};

i4 : C4 = coneFromVData matrix{{1,1},{0,1}};

i5 : C5 = coneFromVData matrix {{1,2},{2,1}};

i6 : L = {C1,C2,C3,C4,C5};

i7 : Lpairs = incompCones L

o7 = {(C1, C5), (C4, C5)}

o7 : List

i8 : Lpairs == {(C1,C4),(C1,C5)}

o8 = false