
Gröbner
Bases,
Macaulay
Matrices
and
Dubé's
Degree
Bounds
Title: 
Gröbner Bases, Macaulay Matrices and Dubé's Degree Bounds 
Author:

Alexander Maletzky

Submission date: 
20190615 
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 rowreducing
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_MacaulayAFP,
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://isaafp.org/entries/Groebner_Macaulay.html},
Formal proof development},
ISSN = {2150914x},
}

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.

