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Computing syzygies of homogeneous polynomials using linear algebra

Date

2014

Authors

Hodges, Tim, author
Bates, Dan, advisor
Peterson, Chris, committee member
Böhm, A. P. Willem, committee member

Journal Title

Journal ISSN

Volume Title

Abstract

Given a ideal generated by polynomials ƒ1,...,ƒn in polynomial ring of m variables a syzygy is an n-tuple α1,.., αn, & αi in our polynomial ring of m variables such that our n-tuple holds the orthogonal property on the generators above. Syzygies can be computed by Buchberger's algorithm for computing Gröbner Bases. However, Gröbner bases have been computationally impractical as the number of variables and number of polynomials increase. The aim of this thesis is to describe a way to compute syzygies without the need for Grobner bases but still retrieve some of the same information as Gröbner bases. The approach is to use the monomial structure of the polynomials in our generating set to build syzygies using Nullspace computations.

Description

2014 Spring.
Includes bibliographical references.

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Subject

algebraic geometry
syzygy
linear algebra
homogenous polynomials

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