Conjugacy of integral matrices

is_GLZ_conjugate(A::MatElem, B::MatElem) -> Bool, MatElem

Given two integral or rational matrices, determine whether there exists an invertible integral matrix $T$ with $TA = BT$. If true, the second argument is such a matrix $T$. Otherwise, the second argument is unspecified.

julia> A = matrix(ZZ, 4, 4, [ 0, 1,  0, 0,
                             -4, 0,  0, 0,
                              0, 0,  0, 1,
                              0, 0, -4, 0]);

julia> B = matrix(ZZ, 4, 4,  [ 0, 1,  4,  0,
                              -4, 0,  0, -4,
                               0, 0,  0,  1,
                               0, 0, -4,  0]);

julia> fl, T = is_GLZ_conjugate(A, B);

julia> isone(abs(det(T))) && T * A == B * T
true