Algorithms for quadratic forms over global function fields of odd characteristic

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.