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Computing the Length of Sum of Squares and Pythagoras Element in a Global Field

Darkey-Mensah Mawunyo Kofi, Rothkege Beata

Fundamenta Informaticae

2021

Vol. 184, nr 4

297--306

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.