Singular

Dear all,

is it possible to use Singular to check whether two given multivariate polynomial matrices are similar, with a unimodular similarity matrix?

In the case of univariate polynomial matrices computing the Smith normal form of both matrices answers this question, but the Smith form is not available for more than one variable, and "simply" solving systems of polynomial equations is not feasible.

In case there is no such general algorithm, would it help if the given matrices were of block-matrix form with only monomial entries in the two off-diagonal block-matrices and zero entries in the two block-matrices on the diagonal?

Any hints or ideas would be very much appreciated.

Thank you and kind regards,
Nils