Gröbner Bases Computation and Macaulay Matrices

In my PhD thesis 1965 and the subsequent publication 1970 in Aequationes Mathematicae, I introduced the notion of Grobner bases and proved a characterization theorem for Grobner bases on which an algorithm for constructing Grobner bases can be based. The main idea for the theorem and the algorithm was the notion of "S-polynomials". Most of the subsequent work on the algorithmic theory of Grobner bases, including the implementation of the Grobner bases technology in mathematical software systems like Mathematica, Maple, etc. was based on this approach.