23 citations · 45 across the 17 of their papers we have counts for
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cs.SC2010
A recombination algorithm for the decomposition of multivariate rational functions
Guillaume Chèze
In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombinat…
math.CA2010★ 23 cited
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
Guillaume Chèze
In this paper we study planar polynomial differential systems of this form: dX/dt=A(X, Y), dY/dt= B(X, Y), where A,B belongs to Z[X, Y], degA \leq d, degB \leq d, and the height of…
cs.SC2010★ 3 cited
Nearly Optimal Algorithms for the Decomposition of Multivariate Rational Functions and the Extended Lüroth's Theorem
Guillaume Chèze
The extended Lüroth'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(\…