• Publications
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Non-Commutative Elimination in Ore Algebras Proves Multivariate Identities
Many computations involving special functions, combinatorial sequences or theirq-analogues can be performed using linear operators and simple arguments on the dimension of related vector spaces. InExpand
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An extension of Zeilberger's fast algorithm to general holonomic functions
  • F. Chyzak
  • Computer Science, Mathematics
  • Discret. Math.
  • 1 April 2000
TLDR
We extend Zeilberger's fast algorithm for definite hypergeometric summation to non-hypergeometric holonomic sequences. Expand
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Effective algorithms for parametrizing linear control systems over Ore algebras
TLDR
We give effective algorithms which check whether or not a linear control system over some Ore algebra is controllable, parametrizable, flat or π-free. Expand
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OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems
In the seventies, the study of transfer matrices of time-invariant linear systems of ordinary differential equations (ODEs) led to the development of the polynomial approach [20, 22, 44]. InExpand
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The ABC of Creative Telescoping - Algorithms, Bounds, Complexity
  • F. Chyzak
  • Computer Science, Mathematics
  • 14 April 2014
TLDR
Creative telescoping is an algorithmic principle that has been developed since the 1990s in combinatorics and computer algebra in order to compute with parametrised sums and integrals, whether it be to find explicit forms or to justify identities in sums or integrals. Expand
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A Randomized Algorithm for Approximate String Matching
TLDR
We give a randomized algorithm in deterministic time O(Nlog  M) for estimating the score vector of matches between a text string of length N and a patternstring of length M, and the number of matches is counted for each position. Expand
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Fonctions holonomes en calcul formel
Cette these montre comment le calcul formel permet la manipulation d'une grande classe de suites et fonctions solutions d'operateurs lineaires, la classe des fonctions holonomes. Celle-ci contient deExpand
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  • 4
Differential equations for algebraic functions
TLDR
It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Expand
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  • 3
  • PDF
A non-holonomic systems approach to special function identities
TLDR
We extend Zeilberger's approach to special function identities to cases that are not holonomic. Expand
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  • 3
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Products of ordinary differential operators by evaluation and interpolation
TLDR
It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. Expand
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  • 3
  • PDF
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