Algorithms for quadratic forms over global function fields of odd characteristic

TL;DR

This paper adapts algorithms from number fields to global function fields of odd characteristic, enabling the analysis of quadratic forms through isotropy, anisotropic dimension, and field invariants.

Contribution

It introduces new algorithms for quadratic forms over global function fields, extending methods previously used for number fields.

Findings

Algorithms for checking isotropy and hyperbolicity

Method for computing anisotropic part dimension

Algorithms for level and Pythagoras number

Abstract

This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given non-degenerate quadratic form is isotropic or hyperbolic. Next we devise a method for computing the dimension of the anisotropic part of a quadratic form. Finally we present algorithms computing two field invariants: the level and the Pythagoras number.