Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
From MaRDI portal
Publication:2431341
DOI10.1016/j.jco.2010.10.004zbMath1215.65040arXiv1009.2876OpenAlexW3102593879MaRDI QIDQ2431341
Publication date: 13 April 2011
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1009.2876
Computation of special functions and constants, construction of tables (65D20) Other functions defined by series and integrals (33E20) Numerical approximation and evaluation of special functions (33F05)
Related Items
Symbolic computations of first integrals for polynomial vector fields ⋮ The Poincaré problem, algebraic integrability and dicritical divisors ⋮ On symbolic integration of algebraic functions ⋮ An efficient method for computing Liouvillian first integrals of planar polynomial vector fields ⋮ Computation of invariant curves and identifying the type of critical point ⋮ Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields ⋮ On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D ⋮ A recombination algorithm for the decomposition of multivariate rational functions ⋮ Catching Tangent Curves in Fields of Lines
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A lifting and recombination algorithm for rational factorization of sparse polynomials
- A new algorithm for finding rational first integrals of polynomial vector fields
- The number of reducible hypersurfaces in a pencil. -- Erratum
- Factoring bivariate sparse (lacunary) polynomials
- Reducibility of rational functions in several variables
- Algebraic solutions of plane vector fields
- Multiplicity of invariant algebraic curves in polynomial vector fields
- Factoring polynomials over global fields
- Fast parallel absolute irreducibility testing
- Equations de Pfaff algébriques
- Factoring polynomials with rational coefficients
- Practical improvement of the divide-and-conquer eigenvalue algorithms
- M. N. Lagutinskij (1871-1915): A misunderstood mathematician
- Reducibility of polynomials \(f(x,y)\) modulo \(p\)
- Reducibility of polynomials in two variables
- Computing closed form solutions of first order ODEs using the Prelle- Singer procedure
- An extension of the Prelle-Singer method and a Maple implementation
- Factoring multivariate integral polynomials
- A rational approach to the Prelle-Singer algorithm
- Darboux integrability and the inverse integrating factor.
- On the complexity of deciding connectedness and computing Betti numbers of a complex algebraic variety
- Lifting and recombination techniques for absolute factorization
- Algebraic solutions of holomorphic foliations: an algorithmic approach
- Algebraic closure of a rational function
- On some open problems in planar differential systems and Hilbert's 16th problem
- Qualitative theory of planar differential systems
- Invariant algebraic surfaces of the Rikitake system
- Elementary First Integrals of Differential Equations
- Rikitake system: analytic and Darbouxian integrals
- Sharp precision in Hensel lifting for bivariate polynomial factorization
- Darboux integrability and algebraic invariant surfaces for the Rikitake system
- Reduzibilität ebener Kurven.
- Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization
- On the parallel Risch Algorithm (II)
- Polynomial Factorization and Nonrandomness of Bits of Algebraic and Some Transcendental Numbers
- Liouvillian First Integrals of Differential Equations
- On Computing the Exact Determinant of Matrices with Polynomial Entries
- Invariant algebraic curves and conditions for a centre
- On the nonexistence, existence and uniqueness of limit cycles
- A method to tackle first-order ordinary differential equations with Liouvillian functions in the solution
- Analysing the structure of the integrating factors for first-order ordinary differential equations with Liouvillian functions in the solution
- Complexity issues in bivariate polynomial factorization
- Factoring multivariate polynomials via partial differential equations
- Translates of Polynomials
- Factoring Polynomials Over Large Finite Fields
- Vector fields, invariant varieties and linear systems.
