• Publications
  • Influence
On Rational Solutions of Systems of Linear Differential Equations
  • M. Barkatou
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 October 1999
TLDR
We propose a new algorithm to compute the set of rational solutions of a system of linear differential equations with coefficients in K(x)logx. Expand
  • 102
  • 7
On the equivalence problem of linear differential systems and its application for factoring completely reducible systems
TLDR
Given two linear di erential systems with rational function coe cients, we give an algorithm to decide whether these two systems are equivalent and to compute the corresponding transformation matrices. Expand
  • 34
  • 7
An Algorithm Computing the Regular Formal Solutions of a System of Linear Differential Equations
TLDR
We propose a method for computing the regular singular formal solutions of a linear differential system in the neighbourhood of a singular point. Expand
  • 62
  • 6
  • PDF
Rational solutions of matrix difference equations: the problem of equivalence and factorization
  • M. Barkatou
  • Mathematics, Computer Science
  • ISSAC '99
  • 1 July 1999
TLDR
Jcu~ (dlcre the ruitt.ions of ClpiLtiOIlS of type (3) llas otlwrs appliwtions [14]. Iu bhis pilper wv(’ shall iwisitlcr ilnd Solve tll(! following more general prol. Bosidrs t.SVHkIllS. Expand
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An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system
  • M. Barkatou
  • Mathematics, Computer Science
  • Applicable Algebra in Engineering, Communication…
  • 2009
TLDR
In this paper we describe an efficient algorithm, fully implemented in the Maple computer algebra system, that computes the exponential part of a formal fundamental matrix solution of a linear differential system having a singularity of pole type at the origin. Expand
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  • 4
Apparent singularities of linear difference equations with polynomial coefficients
TLDR
We prove that one can effectively construct a left multiple with polynomial coefficients of L such that every singularity of L that is not apparent is a t-(resp. l)-singularity of L. Expand
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  • 4
  • PDF
On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity
The notion of irreducible forms of systems of linear differential equations with formal power series coefficients as defined by Moser [Moser, J., 1960. The order of a singularity in Fuchs' theory.Expand
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Computing super-irreducible forms of systems of linear differential equations via moser-reduction: a new approach
TLDR
In this paper, we give a new algorithm for computing, given an arbitrary linear differential system with formal power series coefficients as input, an equivalent system which is super-irreducible. Expand
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Rational solutions of first order linear difference systems
TLDR
We propose an algorithm to compute rational function solutions for a first order system of linear difference equations with rational coefficients that does not require preliminary uncoupling. Expand
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  • 2
  • PDF
An algorithm for computing a companion block diagonal form for a system of linear differential equations
  • M. Barkatou
  • Mathematics, Computer Science
  • Applicable Algebra in Engineering, Communication…
  • 1 September 1993
TLDR
We present a new algorithm for constructing a matrix T such that the transformation Y = TZ reduces the system (1) to an equivalent system (2) where B(x) has the block diagonal form. Expand
  • 32
  • 2