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On Regular and Logarithmic Solutions of Ordinary Linear Differential Systems
TLDR
We present an approach to construct all the regular solutions of systems of linear ordinary differential equations using the desingularization algorithm of Abramov & Bronstein (2001) as an auxiliary tool. Expand
  • 17
  • 2
Denominators of rational solutions of linear difference systems of an arbitrary order
TLDR
An algorithm for finding a universal denominator of rational solutions of a system of linear difference equations with polynomial coefficients is proposed. Expand
  • 18
  • 1
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On singular points of solutions of linear differential systems with polynomial coefficients
We consider systems of linear ordinary differential equations containing m unknown functions of a single variable x. The coefficients of the systems are polynomials over a field k of characteristicExpand
  • 15
Factorization of Polynomials and GCD Computations for Finding Universal Denominators
TLDR
We discuss the algorithms which, given a linear difference equation with rational function coefficients over a field k of characteristic 0, compute a polynomial U(x) ∈ k[x] (a universal denominator) such that the denominator of each of rational solutions (if exist) of the given equation dividesU(x). Expand
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Rational solutions of linear difference equations: Universal denominators and denominator bounds
TLDR
Complexities of some well-known algorithms for finding rational solutions of linear difference equations with polynomial coefficients are studied. Expand
  • 18
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On full rank differential systems with power series coefficients
TLDR
We define the width of a given full rank system S with formal power series coefficients as the smallest non-negative integer w such that any l -truncation of S with l ⩾ w is a full Rank system. Expand
  • 13
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Search for Polynomial Solutions of Linear Functional Systems by Means of Induced Recurrences
  • D. E. Khmelnov
  • Mathematics, Computer Science
  • Programming and Computer Software
  • 1 March 2004
TLDR
The problem of searching for polynomial solutions of linear functional (differential, difference, and q-difference) equations is considered. Expand
  • 15
Linear differential and difference systems: EGδ- and EGσ- eliminations
TLDR
We consider systems of the form (1) where ξ ∈ and E is the shift operator: Ey(x) = y(x + 1). Expand
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Regular solutions of linear differential systems with power series coefficients
TLDR
The following problem is considered: given a system of linear ordinary differential equations of arbitrary order with power series coefficients, to recognize whether it has regular solutions at point 0 and, if it does, find them. Expand
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Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients
TLDR
Construction of Laurent, regular, and formal (exponential–logarithmic) solutions of full-rank linear ordinary differential systems with the coefficients given by infinite, rather than truncated, series. Expand
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