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- W2039529828 abstract "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 the degree of the polynomial vector field. Here we show that we can get the same kind of results if we consider the size of a Newton polytope associated to the vector field. Furthermore, we show that in this context the bound is optimal." @default.
- W2039529828 created "2016-06-24" @default.
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- W2039529828 date "2012-10-29" @default.
- W2039529828 modified "2023-10-10" @default.
- W2039529828 title "Darboux theory of integrability in the sparse case" @default.
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