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Polyhedra :: areCompatible

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

Synopsis

Description

areCompatible is an extension of commonFace for two Cones and for two Polyhedra. It also checks if the intersection X of X1 and X2 is a face of each and the answer is given by b. Furthermore, the intersection is given for further calculations if the two cones/polyhedra lie in the same ambient space. Otherwise, the empty polyhedron in the ambient space of X1 is given. Note that the input arguments must either both be polyhedra or both be cones.

For example, consider the following three cones

i1 : C1 = coneFromVData matrix {{1,0},{0,1}};
i2 : C2 = coneFromVData matrix {{1,-1},{0,-1}};
i3 : C3 = coneFromVData 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, Cone{...1...})

o4 : Sequence
i5 : areCompatible(C2,C3)

o5 = (true, Cone{...1...})

o5 : Sequence
i6 : areCompatible(C3,C1)

o6 = (false, Cone{...1...})

o6 : Sequence

Ways to use areCompatible :