**Type Name:**`PC`**Structure:****Description:**- ``Polynomials with cofactors w.r.t. an ordered set of
polynomials''. are polynomials such that
holds for given (ordered) polynomials .

An operation for polynomials is generalized for polynomials with cofactors in the following way:

Hence, whenever a new polynomial with cofactors is the result of a sequence of operations, Equation (1) still holds for the result. For instance, the result of

*the calculation of an S-polynomial and reducing it w.r.t. an ordered set of polynomials*is the normal form of the S-polynomial plus a representation in terms of the initial polynomials.

Thu Sep 3 14:50:07 MDT 1998