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Computing Square Roots in Quaternion Algebras

Koprowski Przemysław

Fundamenta Informaticae

2022

Vol. 190, nr 1

1--15

We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.

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.