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 |