Counting the number of distinct real roots of certain polynomials by Bezoutian and the Galois groups over the rational number field

Shuichi Otake

    Research output: Contribution to journalArticle

    Abstract

    In this article, we count the number of distinct real roots of certain polynomials in terms of Bezoutian form. As an application, we construct certain irreducible polynomials over the rational number field which have given number of real roots and by the result of Oz Ben-Shimol [On Galois groups of prime degree polynomials with complex roots, Algebra Disc. Math. 2 (2009), pp. 99-107], we obtain an algorithm to construct irreducible polynomials of prime degree p whose Galois groups are isomorphic to Sp or Ap.

    Original languageEnglish
    Pages (from-to)429-441
    Number of pages13
    JournalLinear and Multilinear Algebra
    Volume61
    Issue number4
    DOIs
    Publication statusPublished - 2013 Apr

    Fingerprint

    Irreducible polynomial
    Real Roots
    Galois group
    Number field
    Counting
    Distinct
    Polynomial
    Count
    Isomorphic
    Roots
    Algebra
    Form

    Keywords

    • Bezoutian
    • Galois group
    • irreducible polynomials
    • number of real roots

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Counting the number of distinct real roots of certain polynomials by Bezoutian and the Galois groups over the rational number field. / Otake, Shuichi.

    In: Linear and Multilinear Algebra, Vol. 61, No. 4, 04.2013, p. 429-441.

    Research output: Contribution to journalArticle

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