Intrinsic Factorization of Ideals in Dedekind Domains

Darkey-Mensah, Mawunyo Kofi; Koprowski, Przemysław

doi:10.3233/fi-2019-1865

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2021

2022

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“…(1) Factorization of (fractional) ideals in global fields. There are a couple of methods for achieving this (see e.g., [4,6]). At the moment of writing the fastest ideal factorization method known to the author is the one described in [11].…”

Section: Introductionmentioning

confidence: 99%

Solving sums of squares in global fields

Koprowski¹

2021

Preprint

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The problem of writing a totally positive element as a sum of squares has a long history in mathematics, going back to Bachet and Lagrange. While for some specific rings (like integers or polynomials over the rationals), there are known methods for decomposing an element into a sum of squares, in general, for many other important rings and fields, the problem is still widely open. In this paper, we present an explicit algorithm for decomposing an element of an arbitrary global field (either a number field or a global function field) into a sum of squares of minimal length.

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Section: Introductionmentioning

confidence: 99%