Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions

Gregoire Lecerf

doi:10.1145/345542.345633

Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions

Gregoire Lecerf

Research output: Contribution to conference › Paper › peer-review

28 Citations (Scopus)

Abstract

Let f₁, ..., f_s be polynomials in n variables over a field of characteristic zero and d be the maximum of their total degree. We propose a new probabilistic algorithm for computing a geometric resolution of each equidimensional part of the variety defined by the system f₁ = ··· = f_s = 0. The returned resolutions are encoded by means of Straight-Line Programs and the complexity of the algorithm is polynomial in a geometric degree of the system. In the worst case this complexity is asymptotically polynomial in sdⁿ.

Original language	English
Pages	209-216
Number of pages	8
DOIs	https://doi.org/10.1145/345542.345633
Publication status	Published - 1 Jan 2000
Event	Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000) - St Andrews, UK Duration: 7 Aug 2000 → 9 Aug 2000

Conference

Conference	Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000)
City	St Andrews, UK
Period	7/08/00 → 9/08/00

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10.1145/345542.345633

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AB - Let f1, ..., fs be polynomials in n variables over a field of characteristic zero and d be the maximum of their total degree. We propose a new probabilistic algorithm for computing a geometric resolution of each equidimensional part of the variety defined by the system f1 = ··· = fs = 0. The returned resolutions are encoded by means of Straight-Line Programs and the complexity of the algorithm is polynomial in a geometric degree of the system. In the worst case this complexity is asymptotically polynomial in sdn.

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Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions

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