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Sharper Complexity Bounds for Zero-dimensional Gröbner Bases and Polynomial System Solving

Amir Hashemi 1 Daniel Lazard 1
1 SALSA - Solvers for Algebraic Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : In this paper, we improve the bound of complexity of the algorithms on polynomial ideals having complexities polynomial in $d^n$ where $d$ is the maximal degree of input polynomials and $n$ the number of variables. Instead of this bound, we present the more accurate bound $\max{S,D^n}$ where $S$ is the size of the input polynomials in dense representation, and $D$ is the arithmetic mean value of the degrees of input polynomials.
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https://hal.inria.fr/inria-00070516
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Submitted on : Friday, May 19, 2006 - 8:44:10 PM
Last modification on : Friday, February 4, 2022 - 3:13:22 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:23:16 PM

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  • HAL Id : inria-00070516, version 1

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Amir Hashemi, Daniel Lazard. Sharper Complexity Bounds for Zero-dimensional Gröbner Bases and Polynomial System Solving. [Research Report] RR-5491, INRIA. 2005, pp.11. ⟨inria-00070516⟩

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