23 citations · 45 across the 17 of their papers we have counts for
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math.CA2013★ 3 cited
Bounding the number of remarkable values via Jouanolou's theorem
Guillaume Chèze
In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar…
math.CA2012
Darboux theory of integrability in the sparse case
Guillaume Chèze
Darboux's theorem and Jouanolou's theorem deal with the existence of first integrals and rational first integrals of a polynomial vector field. These results are given in terms of…
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…