Adam Chapman ; Ilan Levin - Alternating Roots of Polynomials over Cayley-Dickson Algebras

cm:11514 - Communications in Mathematics, October 26, 2023, Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024") - https://doi.org/10.46298/cm.11514
Alternating Roots of Polynomials over Cayley-Dickson AlgebrasArticle

Authors: Adam Chapman ; Ilan Levin

    We introduce the notions of alternating roots of polynomials and alternating polynomials over a Cayley-Dickson algebra, and prove a connection between the alternating roots of a given polynomial and the roots of the corresponding alternating polynomial over the Cayley-Dickson doubling of the algebra. We also include a detailed Octave code for the computation of alternating roots over Hamilton's quaternions.


    Volume: Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
    Published on: October 26, 2023
    Accepted on: July 7, 2023
    Submitted on: June 29, 2023
    Keywords: Mathematics - Rings and Algebras,Mathematics - Number Theory,Primary: 17A20, Secondary: 17A45, 17A75, 17D05, 11R52

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