Algebraic closure of a rational function

DOI10.1007/BF02972683zbMath1121.13301OpenAlexW2108871824MaRDI QIDQ2457730

Jean Moulin Ollagnier

Publication date: 23 October 2007

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02972683

Mathematics Subject Classification ID

Derivations and commutative rings (13N15) Transcendental field extensions (12F20) Computational aspects in algebraic geometry (14Q99)

Related Items (8)

On the saturation of subfields of invariants of finite groups ⋮ Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time ⋮ Counting decomposable multivariate polynomials ⋮ On pairs of commuting derivations of the polynomial ring in one or two variables ⋮ Bounding the number of remarkable values via Jouanolou's theorem ⋮ Nearly optimal algorithms for the decomposition of multivariate rational functions and the extended Lüroth theorem ⋮ Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields ⋮ A recombination algorithm for the decomposition of multivariate rational functions

Cites Work

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• Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence
• Dedekind subrings of \(k[x_1,\dots,x_n\) are rings of polynomials]
• Rings of Constants of the Formk[f]

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