Factorization and root-finding for polynomials over division quaternion algebras

2023/05/03 by Przemysław Koprowski, Koprowski, Przemysław
Computer Science · Mathematics · #11R52 #11Y05 #11Y40 #68W30 #Algebraic and Geometric Analysis #FOS: Computer and information sciences #FOS: Mathematics #I.1.2 #Numerical Methods and Algorithms #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.2305.02072

openalex publication_date 2023/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras, with the single exception of Hamiltonian quaternions for which there are known numerical methods for polynomial root approximation. The sole purpose of the present paper is to present a polynomial factorization algorithm for division quaternion algebras over number fields, together with its adaptation for root finding.

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