A factorization algorithm for linear ordinary differential equations
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Integration of elementary functions
Journal of Symbolic Computation
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients
Journal of Symbolic Computation
The Risch differential equation on an algebraic curve
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Linear ordinary differential equations: breaking through the order 2 barrier
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
D'Alembertian solutions of linear differential and difference equations
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
An improved algorithm for factoring linear ordinary differential operators
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
D'Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other)
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
Solving linear ordinary differential equations over C (x, e∫ f(x)dx)
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Computing the Galois group of a polynomial using linear differential equations
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Linear differential operators for polynomial equations
Journal of Symbolic Computation
Polynomial solutions for first order ODEs with constant coefficients
ACM SIGSAM Bulletin
Hyperexponential solutions of finite-rank ideals in orthogonal ore rings
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Solving difference equations whose coefficients are not transcendental
Theoretical Computer Science
Integration in finite terms of non-liouvillian functions
ACM Communications in Computer Algebra
Polynomial general solutions for first order autonomous ODEs
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
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We describe a rational algorithm for finding the denominator of any solution of a linear ordinary differential equation in its coefficient field. As a consequence, there is now a rational algorithm for finding all such solutions when the coefficients can be built up from the rational functions by finitely many algebraic and primitive adjunctions. This also eliminates one of the computational bottlenecks in algorithms that either factor or search for Liouvillian solutions of such equations with Liouvillian coefficients.