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TitleIdealization of modules in computer algebra
Author(s) Martin Kreuzer, Lorenzo Robbiano
TypeArticle in Conference Proceedings
AbstractBased on an explicit description of the idealization of a graded
submodule of a graded free module, we examine the behaviour of
Gröbner bases and minimal homogeneous systems of generators under
this process. Then we show how one can idealize a homogeneous
presentation. Using this theory, we present a unified description
of several strategies for computing minimal homogeneous presentations
and minimal graded free resolutions, in particular of the vertical
and horizontal strategies. We obtain a simple and compact algorithm
for computing minimal graded free resolutions degree-by-degree
which lands itself well to further optimizations.
Keywordsidealization, Gröbner basis, homogeneous presentation, minimal graded free resolution
Length17
File
LanguageEnglish
SeriesNATO Science Series III
Pages226-243
PublisherIOS Press
AddressAmsterdam
Year2005
EditorS. Cojocaru, G. Pfister and V. Ufnarovski
Edition0
Translation No
Refereed No
BookComputational Non-Commutative and Commutative Algebraic Geometry
ConferencenameNATO Workshop 2004 (Chisinau/Moldavia)
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