2021/11/16 by Przemysław Koprowski, Koprowski, Przemysław
Computer Science · Mathematics · #11E12 #11E25 #11Y40 #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Rings, Modules, and Algebras #Symbolic Computation (cs.SC) #cs.SC #math.NT #msc:11E12 #msc:11E25 #msc:11Y40
paper · pdf · doi:10.48550/arxiv.2111.08558
arxiv created 2021/11/16 · openalex publication_date 2021/11/16 · arxiv updated 2021/11/17 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
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.