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

DOI10.3233/FI-2021-2100zbMath1490.11120arXiv2102.08741MaRDI QIDQ5862346

Mawunyo Kofi Darkey-Mensah, Beata Rothkegel

Publication date: 9 March 2022

Published in: Fundamenta Informaticae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.08741

zbMATH Keywords

algorithmsquadratic formsPythagoras numberglobal fieldslength of sum of squaresPythagoras element

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Quadratic forms over global rings and fields (11E12) Algebraic number theory computations (11Y40)

Uses Software

• CQF

Cites Work

• A new computational approach to ideal theory in number fields
• Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
• Sums of squares in some integral domains
• An algorithm for sums of squares of real polynomials
• Computing with quadratic forms over number fields
• The Pythagoras number of some affine algebras and local algebras.
• CQF Magma package
• Newton polygons of higher order in algebraic number theory
• Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms
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