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A Note on NUCOMP

Author: Alfred J. van der Poorten
Journal: Math. Comp. 72 (2003), 1935-1946
MSC (2000): Primary 11Y40, 11E16, 11R11
Published electronically: April 29, 2003
MathSciNet review: 1986813
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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 $10^7$.

References [Enhancements On Off] (What's this?)

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Additional Information

Alfred J. van der Poorten
Affiliation: ceNTRe for Number Theory Research, 1 Bimbil Pl. Killara, New South Wales 2071, Australia

Keywords: Binary quadratic form, composition
Received by editor(s): January 10, 2002
Published electronically: April 29, 2003
Additional Notes: The author was supported in part by a grant from the Australian Research Council
Article copyright: © Copyright 2003 American Mathematical Society