A factorization algorithm for linear ordinary differential equations
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients
Journal of Symbolic Computation
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
On solutions of linear ordinary differential equations in their coefficient field
Journal of Symbolic Computation
Linear ordinary differential equations: breaking through the order 2 barrier
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Galois groups of second and third order linear differential equations
Journal of Symbolic Computation
Liouvillian and algebraic solutions of second and third order linear differential equations
Journal of Symbolic Computation
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
An algorithm for computing exponential solutions of first order linear differential systems
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On factorization of nonlinear ordinary differential equations
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
An Algorithm for Nonparametric Decomposition of Differential Polynomials
Programming and Computing Software
Factoring zero-dimensional ideals of linear partial differential operators
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Factorization of the Heun's differential operator
Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
Factorization of linear differential operators in exponential extensions
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computer algebra handbook
Factoring systems of linear PDEs with finite-dimensional solution spaces
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Decomposition of differential polynomials with constant coefficients
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Solving third order linear differential equations in terms of second order equations
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Solving differential equations in terms of bessel functions
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
2-descent for second order linear differential equations
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Hi-index | 0.00 |
We describe an efficient algorithm for computing the associated equations appearing in the Beke-Schlesinger factorisation method for linear ordinary differential operators. This algorithm, which is based on elementary operations with sets of integers, can be easily implemented for operators of any order, produces several possible associated equations, of which only the simplest can be selected for solving, and often avoids the degenerate case, where the order of the associated equation is less than in the generic case. We conclude with some fast heuristics that can produce some factorisations while using only linear computations.