23 citations · 45 across the 17 of their papers we have counts for
4 papers · 1 filter
Symbolic Computations of First Integrals for Polynomial Vector Fields
Guillaume Chèze, Thierry Combot
In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for…
Efficient Algorithms for Computing Rational First Integrals and Darboux Polynomials of Planar Polynomial Vector Fields
Alin Bostan, Guillaume Chèze, Thomas Cluzeau +1
We present fast algorithms for computing rational first integrals with bounded degree of a planar polynomial vector field. Our approach is inspired by an idea of Ferragut and Giaco…
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…
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(\…