In this paper, we describe a new variation of the interpolation algorithm by Möller, proposed in a way that completely avoids Gröbner bases and does not need a term order, but only a well order on terms. This algorithm takes a set of functionals describing a Macaulay chain, namely, roughly speaking, the functionals are chosen and ordered in such a way that the first functional defines a zero-dimensional ideal and all the sets one gets by adding the functionals one after the other define zero-dimensional ideals as well. Starting from this set, the algorithm describes the zero-dimensional ideals of the Macaulay chain via a basis of the quotient algebra and Auzinger-Stetter matrices.

It is well-known that each effective associative ring with identity is endowed with a Buchberger Theory, id est a notion of Gröbner bases and related algorithms. This note is a sort of Do-It-Yourself manual for setting a Gröbner bases approach to such a ring.