## Mawunyo Kofi Darkey-Mensah ; Beata Rothkegel - Computing the Length of Sum of Squares and Pythagoras Element in a Global Field

fi:7200 - Fundamenta Informaticae, March 10, 2022, Volume 184, Issue 4
Computing the Length of Sum of Squares and Pythagoras Element in a Global Field

Authors: Mawunyo Kofi Darkey-Mensah ; Beata Rothkegel

This paper presents algorithms for computing the length of a sum of squares and a Pythagoras element in a global field $K$ of characteristic different from $2$. In the first part of the paper, we present algorithms for computing the length in a non-dyadic and dyadic (if $K$ is a number field) completion of $K$. These two algorithms serve as subsidiary steps for computing lengths in global fields. In the second part of the paper we present a procedure for constructing an element whose length equals the Pythagoras number of a global field, termed a Pythagoras element.

Volume: Volume 184, Issue 4
Published on: March 10, 2022
Accepted on: August 13, 2021
Submitted on: February 18, 2021
Keywords: Mathematics - Number Theory,11Y16, 11E12