A note on nucomp

Alfred J. Van der Poorten*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    This note is a detailed explanation of Shanks-Atkin NUCOMP -composition and reduction carried out "simultaneously" - for all quadratic fields, that is, including real quadratic fields. That explanation incidentally deals with various "exercises" left for confirmation by the reader in standard texts. Extensive testing in both the numerical and function field cases by Michael J Jacobson, Jr, reported elsewhere, confirms that NUCOMP as here described is in fact efficient for composition both of indefinite and of definite forms once the parameters are large enough to compensate for NUCOMP's extra overhead. In the numerical indefinite case that efficiency is a near doubling in speed already exhibited for discriminants as small as 10 7.

    Original languageEnglish
    Pages (from-to)1935-1946
    Number of pages12
    JournalMathematics of Computation
    Volume72
    Issue number244
    DOIs
    Publication statusPublished - Oct 2003

    Keywords

    • Binary quadratic form
    • Composition

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