# Gröbner Bases, Macaulay Matrices and Dubé's Degree Bounds

 Title: Gröbner Bases, Macaulay Matrices and Dubé's Degree Bounds Author: Alexander Maletzky Submission date: 2019-06-15 Abstract: This entry formalizes the connection between Gröbner bases and Macaulay matrices (sometimes also referred to as generalized Sylvester matrices'). In particular, it contains a method for computing Gröbner bases, which proceeds by first constructing some Macaulay matrix of the initial set of polynomials, then row-reducing this matrix, and finally converting the result back into a set of polynomials. The output is shown to be a Gröbner basis if the Macaulay matrix constructed in the first step is sufficiently large. In order to obtain concrete upper bounds on the size of the matrix (and hence turn the method into an effectively executable algorithm), Dubé's degree bounds on Gröbner bases are utilized; consequently, they are also part of the formalization. BibTeX: @article{Groebner_Macaulay-AFP, author = {Alexander Maletzky}, title = {Gröbner Bases, Macaulay Matrices and Dubé's Degree Bounds}, journal = {Archive of Formal Proofs}, month = jun, year = 2019, note = {\url{https://isa-afp.org/entries/Groebner_Macaulay.html}, Formal proof development}, ISSN = {2150-914x}, }` License: BSD License Depends on: Groebner_Bases Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.