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Commutative Algebra and Algebraic Geometry using OSCAR

Year: 2024

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2404.12085

Authors: Boehm, Janko, Decker, Wolfram, Schreyer, Frank-Olaf

Institutions: University of Kaiserslautern, Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, Saarland University

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G251152387, TRR 195: Symbolische Werkzeuge in der Mathematik und ihre Anwendung, G87478678

OpenAlex ID: W4394973585

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