2006/05/12 by Eduardo Sáenz‐de‐Cabezón, de Cabezon, Eduardo Saenz
Computer Science · Mathematics · #13D25 #13P99 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0605325
openalex publication_date 2006/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Koszul homology of modules of the polynomial ring R is a central object in commutative algebra.It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case of modules of the form R/I where I is a monomial ideal. So far, some good algorithms have been given in the literature and implemented in different Computer Algebra Systems (e.g. CoCoa, Singular, Macaulay), which compute minimal free resolutions of modules of the form R/I with I an ideal in R, which include the case of I being a monomial ideal as a particular one (a good review is given in \cite Sie). Our goal is to build algorithms especially teargeted to monomial ideals, taking into account the special combinatorial and structural properties of these ideals. This being a first goal, it is also a first step of an alternative approach to the computation of the Koszul homology and minimal free resolutions of polynomial ideals.