Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Erhard Aichinger

Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Erhard Aichinger

Institute for Algebra

Research output: Working paper and reports › Preprint

Abstract

We provide a self-contained introduction to Gröbner bases of submodules of R[x1,…,xn]^k, where R is a Euclidean domain, and explain how to use these bases to solve linear systems over R[x1,…,xn].

Original language	English
Number of pages	31
Publication status	Published - Jun 2024

Publication series

Name	arXiv.org

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Digital Transformation

Cite this

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abstract = "We provide a self-contained introduction to Gr{\"o}bner bases of submodules of R[x1,…,xn]\textasciicircum{}k, where R is a Euclidean domain, and explain how to use these bases to solve linear systems over R[x1,…,xn].",

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year = "2024",

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PY - 2024/6

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N2 - We provide a self-contained introduction to Gröbner bases of submodules of R[x1,…,xn]^k, where R is a Euclidean domain, and explain how to use these bases to solve linear systems over R[x1,…,xn].

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UR - https://arxiv.org/pdf/2406.06994

M3 - Preprint

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BT - Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

ER -

Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Abstract

Publication series

Fields of science

JKU Focus areas

Other files and links

Equations in universal algebra

Cite this

Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Abstract

Publication series

Fields of science

JKU Focus areas

Other files and links

Projects

Equations in universal algebra

Cite this