Algorithms for quadratic forms over global function fields of odd characteristic-Reference-Cited by-同舟云学术

Algorithms for quadratic forms over global function fields of odd characteristic

Published:2021-09 Issue:3 Volume:55 Page:68-72
ISSN:1932-2240
Container-title:ACM Communications in Computer Algebra
language:en
Short-container-title:ACM Commun. Comput. Algebra

Author:

Darkey-Mensah Mawunyo Kofi¹

Affiliation:

1. University of Silesia, Katowice, Poland

Abstract

This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in [4] 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.

Publisher

Association for Computing Machinery (ACM)

Subject

Microbiology (medical),Immunology,Immunology and Allergy

Link

https://dl.acm.org/doi/pdf/10.1145/3511528.3511530

Reference5 articles.

1. The Magma Algebra System I: The User Language

2. Darkey-Mensah , Mawunyo Kofi and Rothkegel , Beata. Computing the Length of Sum of Squares and Pythagoras Element in a Global Field. arXiv preprint arXiv:2102.08741 , 2021 . Darkey-Mensah, Mawunyo Kofi and Rothkegel, Beata. Computing the Length of Sum of Squares and Pythagoras Element in a Global Field. arXiv preprint arXiv:2102.08741, 2021.

3. CQF Magma package

4. Computing with quadratic forms over number fields

5. Lam , Tsit-Yuen Introduction to Quadratic Forms Over Fields . American Mathematical Society 2005 . Lam, Tsit-Yuen Introduction to Quadratic Forms Over Fields. American Mathematical Society 2005.

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