Galois groups of second and third order linear differential equations
Journal of Symbolic Computation
Selecting base points for the Schreier-Sims algorithm for matrix groups
Journal of Symbolic Computation
Factorization of differential operators with rational functions coefficients
Journal of Symbolic Computation
Fast evaluation of holonomic functions
Theoretical Computer Science - Special issue on real numbers and computers
Fast evaluation of holonomic functions near and in regular singularities
Journal of Symbolic Computation
Journal of Symbolic Computation
Acceleration of Euclidean algorithm and extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Computations with effective real numbers
Theoretical Computer Science - Real numbers and computers
Quantum automata and algebraic groups
Journal of Symbolic Computation
Efficient accelero-summation of holonomic functions
Journal of Symbolic 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
ACM Communications in Computer Algebra
Finding hyperexponential solutions of linear ODEs by numerical evaluation
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
| Hi-index | 0.00 |
Let L@?K(z)[@?] be a linear differential operator, where K is an effective algebraically closed subfield of C. It can be shown that the differential Galois group of L is generated (as a closed algebraic group) by a finite number of monodromy matrices, Stokes matrices and matrices in local exponential groups. Moreover, there exist fast algorithms for the approximation of the entries of these matrices. In this paper, we present a numeric-symbolic algorithm for the computation of the closed algebraic subgroup generated by a finite number of invertible matrices. Using the above results, this yields an algorithm for the computation of differential Galois groups, when computing with a sufficient precision. Even though there is no straightforward way to find a ''sufficient precision'' for guaranteeing the correctness of the end result, it is often possible to check a posteriori whether the end result is correct. In particular, we present a non-heuristic algorithm for the factorization of linear differential operators.