Commutative Algebra and Algebraic Geometry using OSCAR

We give illustrative examples of how the computer algebra system OSCAR can support research in commutative algebra and algebraic geometry. We start with a thorough introduction to Groebner basis techniques, with particular emphasis on the computation of syzygies, then apply these techniques to deal...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Boehm, Janko, Decker, Wolfram, Frank-Olaf Schreyer
Format: Article
Language:English
Subjects:
Computer algebra
Curves
Rings (mathematics)
Online Access:Get full text
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Summary:We give illustrative examples of how the computer algebra system OSCAR can support research in commutative algebra and algebraic geometry. We start with a thorough introduction to Groebner basis techniques, with particular emphasis on the computation of syzygies, then apply these techniques to deal with ideal and ring theoretic concepts such as primary decomposition and normalization, and finally use them for geometric case studies which concern curves and surfaces, both from a local and global point of view.
ISSN:2331-8422