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Reports (Research Report) Year : 2005

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

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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Other [cs.OH]
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Dates and versions

inria-00070516 , version 1 (19-05-2006)

Identifiers

  • HAL Id : inria-00070516 , version 1

Cite

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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