Computations in cubic function fields of characteristic three

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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.

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This work demonstrates calculations of genus and discriminant in cubic function fields, suggesting methods for ideal arithmetic.

Bauer et al. (2013) studied this question.

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