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areCompatible -- checks if the intersection of two cones is a face of each

Synopsis

Description

areCompatible is an extension of commonFace for Cones. It also checks if the intersection C of C1 and C2 is a face of each and the answer is given by b. Furthermore, the intersection is given for further calculations if the two cones lie in the same ambient space. Otherwise, the empty polyhedron in the ambient space of C1 is given.

For example, consider the following three cones

i1 : C1 = posHull matrix {{1,0},{0,1}};
i2 : C2 = posHull matrix {{1,-1},{0,-1}};
i3 : C3 = posHull matrix {{1,-1},{2,-1}};

These might form a fan, but if we check if they are compatible, we see they are not:

i4 : areCompatible(C1,C2)

o4 = (true, {ambient dimension => 2           })
             dimension of lineality space => 0
             dimension of the cone => 1
             number of facets => 1
             number of rays => 1

o4 : Sequence
i5 : areCompatible(C2,C3)

o5 = (true, {ambient dimension => 2           })
             dimension of lineality space => 0
             dimension of the cone => 1
             number of facets => 1
             number of rays => 1

o5 : Sequence
i6 : areCompatible(C3,C1)

o6 = (false, {ambient dimension => 2           })
              dimension of lineality space => 0
              dimension of the cone => 2
              number of facets => 2
              number of rays => 2

o6 : Sequence

Ways to use areCompatible :