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• W3103289733 abstract "The extended Luroth's Theorem says that if the transcendence degree of $KK(mathsf{f}_1,dots,mathsf{f}_m)/KK$ is 1 then there exists $f in KK(underline{X})$ such that $KK(mathsf{f}_1,dots,mathsf{f}_m)$ is equal to $KK(f)$. In this paper we show how to compute $f$ with a probabilistic algorithm. We also describe a probabilistic and a deterministic algorithm for the decomposition of multivariate rational functions. The probabilistic algorithms proposed in this paper are softly optimal when $n$ is fixed and $d$ tends to infinity. We also give an indecomposability test based on gcd computations and Newton's polytope. In the last section, we show that we get a polynomial time algorithm, with a minor modification in the exponential time decomposition algorithm proposed by Gutierez-Rubio-Sevilla in 2001." @default.
• W3103289733 created "2020-11-23" @default.
• W3103289733 creator A5058294598 @default.
• W3103289733 date "2010-08-01" @default.
• W3103289733 modified "2023-10-10" @default.
• W3103289733 title "Nearly optimal algorithms for the decomposition of multivariate rational functions and the extended Lüroth Theorem" @default.
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• W3103289733 doi "https://doi.org/10.1016/j.jco.2010.05.001" @default.
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