Checks if two smooth polytopes P and Q are isomorphic, i.e. checks if there exist a unitary matrix A with integer entries and a vector v such that Q=A*P+v. Currently the function only works on smooth polytopes.
i1 : P=convexHull(matrix{{0,1}}); |
i2 : Q=convexHull(matrix{{0,2}}); |
i3 : areIsomorphic(P,Q) o3 = false |
As a standard, areIsomorphic will check if the polytopes are smooth first. This takes some time, so if one is sure that they are smooth then it is possible to suppress this test.
i4 : M = transpose matrix{{0,0,0},{1,0,0},{0,1,0},{0,0,1},{1,1,0},{1,0,1},{0,1,1},{1,1,1}} o4 = | 0 1 0 0 1 1 0 1 | | 0 0 1 0 1 0 1 1 | | 0 0 0 1 0 1 1 1 | 3 8 o4 : Matrix ZZ <--- ZZ |
i5 : P = convexHull(M); |
i6 : time areIsomorphic(P,P); -- used 0.943828 seconds |
i7 : time areIsomorphic(P,P,smoothTest=>false); -- used 0.449556 seconds |