Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields

DOI10.1090/mcom/3007zbMath1335.34002arXiv1310.2778OpenAlexW1896102805MaRDI QIDQ2792368

Alin Bostan, Thomas Cluzeau, Guillaume Chèze, Jacques-Arthur Weil

Publication date: 9 March 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.2778

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Symbolic computation and algebraic computation (68W30) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (9)

Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces ⋮ Symbolic computations of first integrals for polynomial vector fields ⋮ An efficient method for computing Liouvillian first integrals of planar polynomial vector fields ⋮ Rational Integrability of the Maxwell–Bloch System ⋮ Bounding the number of remarkable values via Jouanolou's theorem ⋮ RationalFirstintegrals ⋮ On planar polynomial vector fields with elementary first integrals ⋮ On the computation of Darboux first integrals of a class of planar polynomial vector fields ⋮ Catching Tangent Curves in Fields of Lines

Uses Software

• gfun
• Maple

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrability of plane quadratic vector fields
• A new algorithm for finding rational first integrals of polynomial vector fields
• On the total order of reducibility of a pencil of algebraic plane curves
• On the Poincaré problem for foliations of general type
• On multivariate rational function decomposition
• Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
• The number of reducible hypersurfaces in a pencil. -- Erratum
• Reducibility of rational functions in several variables
• Algebraic solutions of plane vector fields
• On the integrable rational Abel differential equations
• Polynomial inverse integrating factors for quadratic differential systems
• Equations de Pfaff algébriques
• Elementary first integrals and algebraic invariant curves of differential equations
• Reducibility of polynomials in two variables
• A rational approach to the Prelle-Singer algorithm
• Darboux integrability and the inverse integrating factor.
• On the Poincaré problem
• The Poincaré problem in the nondicritical case
• Bounding the number of remarkable values via Jouanolou's theorem
• Rational first integrals in the Darboux theory of integrability in \(\mathbb C^n\)
• Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
• Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
• On the remarkable values of the rational first integrals of polynomial vector fields
• Algebraic solutions of holomorphic foliations: an algorithmic approach
• Algebraic closure of a rational function
• Qualitative theory of planar differential systems
• A recombination algorithm for the decomposition of multivariate rational functions
• Elementary First Integrals of Differential Equations
• Noether forms for the study of non-composite rational functions and their spectrum
• Sharp precision in Hensel lifting for bivariate polynomial factorization
• Reduzibilität ebener Kurven.
• Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization
• Liouvillian First Integrals of Differential Equations
• Fast Algorithms for Manipulating Formal Power Series
• A Uniform Approach for the Fast Computation of Matrix-Type Padé Approximants
• GFUN
• Solving second-order ordinary differential equations by extending the Prelle-Singer method
• Complexity issues in bivariate polynomial factorization
• Translates of Polynomials
• Algebraic general solutions of algebraic ordinary differential equations
• Solving second order linear differential equations with Klein's theorem
• On Quadratic Approximation
• Vector fields, invariant varieties and linear systems.

This page was built for publication: Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields