A Gröbner basis technique for Padé approximation

We consider solving for a and b the congruence a=bh mod I, where a, b and h are (multivariable) polynomials and I is a polynomial ideal. This is a generalization of the well-known problem of Pade approximation of which decoding Hensel codes is a special case. We show how Grobner bases of modules may be used to generalize the Euclidean algorithm method of solution of the 1-variable problem.