August 17, 2025

Computations in cubic function fields of characteristic three

Key Points

The field discriminant and genus are successfully calculated for cubic function fields in characteristic three, indicating important algebraic properties.
Explicit algorithms are provided for ideal arithmetic, enabling efficient computation within the ideal class group of certain cubic function fields.
An integral basis is defined for the maximal order of cubic function fields, enhancing the understanding of their algebraic structure.
The research highlights the significance of cubic curves, revealing connections to computational methods in algebra.

Abstract

This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an integral basis for the maximal order of these function fields, we are able to calculate the field discriminant and the genus. We also give explicit algorithms for ideal arithmetic which for certain cubic function fields give rise to composition and reduction algorithms for computing in the associated ideal class group.

Bookmark

Cite This Study

Bauer et al. (Mon,) studied this question.

synapsesocial.com/papers/68a370e80a429f7973333217 https://doi.org/https://doi.org/10.55016/ojs/cdm.v8i1.61907

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Bookmark