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We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some classical results and their constructive counterparts, we showcase the functionality in two examples related to the investigation of the Cohen–Lenstra heuristic for quadratic fields and the Galois module structure of rings of integers.

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Number Theory

  • 章节

  • 发表日期：

    2025年

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  • Claus Fieker,
  • Tommy Hofmann

摘要

We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some classical results and their constructive counterparts, we showcase the functionality in two examples related to the investigation of the Cohen–Lenstra heuristic for quadratic fields and the Galois module structure of rings of integers.