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We illustrate OSCAR ’s capabilities for computing with polynomial ideals using Gröbner bases. We give a detailed overview of the available Gröbner basis algorithms and provide some practical advice on how to use them. Based on this, we illustrate how to compute real solutions to polynomial systems in OSCAR. We then demonstrate with a range of examples from different areas of mathematics where Gröbner bases come into play when trying to answer computational questions.

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Gröbner Bases for Polynomial Ideals and Applications

  • 章节

  • 发表日期：

    2025年

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  • Christian Eder,
  • Rafael Mohr,
  • Mohab Safey El Din

摘要

We illustrate OSCAR ’s capabilities for computing with polynomial ideals using Gröbner bases. We give a detailed overview of the available Gröbner basis algorithms and provide some practical advice on how to use them. Based on this, we illustrate how to compute real solutions to polynomial systems in OSCAR. We then demonstrate with a range of examples from different areas of mathematics where Gröbner bases come into play when trying to answer computational questions.