Details:
Title  Around the numeric–symbolic computation of differential Galois groups  Author(s)  Joris van der Hoeven  Type  Article in Journal  Abstract  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 nonheuristic algorithm for the factorization of linear differential operators.  Keywords  Differential Galois group, Algebraic group, Algorithm, Accelerosummation, Stokes multipliers  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717106000745 
Language  English  Journal  Journal of Symbolic Computation  Volume  42  Number  1–2  Pages  236  264  Year  2007  Note  Effective Methods in Algebraic Geometry (MEGA 2005)  Edition  0  Translation 
No  Refereed 
No 
