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On the complexity of polynomial reduction

Abstract : In this paper, we present a new algorithm for reducing a multivariate polynomial with respect to an autoreduced tuple of other polynomials. In a suitable sparse complexity model, it is shown that the execution time is essentially the same (up to a logarithmic factor) as the time needed to verify that the result is correct. This is a first step towards making advantage of fast sparse polynomial arithmetic for the computation of Gröbner bases.
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https://hal.archives-ouvertes.fr/hal-00658704
Contributor : Joris van der Hoeven Connect in order to contact the contributor
Submitted on : Wednesday, January 11, 2012 - 3:26:43 AM
Last modification on : Wednesday, November 18, 2020 - 10:32:03 PM
Long-term archiving on: : Thursday, April 12, 2012 - 2:22:53 AM

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  • HAL Id : hal-00658704, version 1

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Joris van der Hoeven. On the complexity of polynomial reduction. 2012. ⟨hal-00658704⟩

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