The anisotropic part of a quadratic form over a number field. (March 2023)

• Record Type: Journal Article
• Authors: Koprowski, Przemysław; Rothkegel, Beata
• Is Part Of: Journal of symbolic computation. Volume 115(2023)
• Page Start: 39
• Page End: 52
• Publication Date: 2023-03
• Subjects: 11Y40 -- 68W30 -- 11E12; Quadratic forms -- Isotropy -- Number fields; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.07.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: It is well known that every non-degenerate quadratic form admits a decomposition into an orthogonal sum of its anisotropic part and a hyperbolic form. This decomposition is unique up to isometry. In this paper we present an algorithm for constructing an anisotropic part of a given form with coefficients in an arbitrary number field.