Binary Cubic Forms and Cubic Number Fields

K. Belabas - H. Cohen

The aim of this paper is to present in a naïve manner a small part of the theory of binary cubic forms and in particular its application to cubic number fields. Most of the results are due to Davenport-Heilbronn ([5],[6]), but the algorithmic applications seem to be new.

• A list of mathactivations
• A list of related links

• General Binary Forms
• Binary Cubic Forms and Cubic Number Fields
• Algorithmic Characterization of the set U
• The Heilbronn-Davenport Theorem
  • Remarks
• Real cubic fields
  • Remark
• Complex cubic fields
• Implementation and results
• References
• About this document ...