Computation of a minimal basis of the right null space of a singular multiparameter polynomial matrix

A modification of an algorithm, based on the resultant approach, for computing a minimal basis of the right null space of a singular multiparameter polynomial matrix is suggested. The modification suggested is based on simultaneous computation of bases of the image and kernel of a constant matrix and allows one to reduce computational costs. This modification also permits one to compute a basis of the image of a polynomial matrix. The implementation of the algorithm is illustrated on an example.