Mathematics – Commutative Algebra
Scientific paper
2006-05-12
Mathematics
Commutative Algebra
Appears in Proceedings of the 10th Rhine Workshop on Computer Algebra
Scientific paper
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.
No associations
LandOfFree
Computing Koszul Homology for Monomial Ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Computing Koszul Homology for Monomial Ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing Koszul Homology for Monomial Ideals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-596592