Splitting quaternion algebras over quadratic number fields. (September 2019)

• Record Type: Journal Article
• Authors: Kutas, Péter
• Is Part Of: Journal of symbolic computation. Volume 94(2019)
• Page Start: 173
• Page End: 182
• Publication Date: 2019-09
• Subjects: 68W30 -- 16Z05 -- 11D09; Explicit isomorphism -- Full matrix algebra -- Quadratic form -- Quaternion algebra -- Quadratic number field -- Polynomial-time algorithm; 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.2018.08.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We propose an algorithm for finding zero divisors in quaternion algebras over quadratic number fields, or equivalently, solving homogeneous quadratic equations in three variables over Q ( d ) where d is a square-free integer. The algorithm is randomized and runs in polynomial time if one is allowed to call oracles for factoring integers.