Modern computer algebra
On solutions of linear functional systems
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs
SIAM Journal on Matrix Analysis and Applications
Algorithms for regular solutions of higher-order linear differential systems
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Fraction-free row reduction of matrices of Ore polynomials
Journal of Symbolic Computation
Higher-order linear differential systems with truncated coefficients
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Computing closed form solutions of integrable connections
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
On k-simple forms of first-order linear differential systems and their computation
Journal of Symbolic Computation
Linear differential and difference systems: EGδ- and EGσ- eliminations
Programming and Computing Software
Regular solutions of linear differential systems with power series coefficients
Programming and Computing Software
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We propose a direct algorithm for computing regular formal solutions of a given higher-order linear differential system near a singular point. With such a system, we associate a matrix polynomial and we say that the system is simple if the determinant of this matrix polynomial does not identically vanish. In this case, we show that the algorithm developed in Barkatou et al. (2009) can be applied to compute a basis of the regular formal solutions space. Otherwise, we develop an algorithm which, given a non-simple system, computes an auxiliary simple one from which the regular formal solutions space of the original system can be recovered. We also give the arithmetic complexity of our algorithms.