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The complete Generating Function for Gessel Walks is Algebraic
TLDR
We prove that if $g(n; i,j)$ denotes the number of Gessel walks of length $n$ which end at the point $(i,j)\in\set N^2$, then the trivariate generating series $G(t;x,y)x^i y^j t^n$ is an algebraic function. Expand
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Automatic Classification of Restricted Lattice Walks
We propose an experimental mathematics approach leading to the computer-driven discovery of various structural properties of general counting functions coming from enumeration of walks.
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Non-D-finite excursions in the quarter plane
TLDR
We prove that the sequence (e"n^S)"n">="0 of numbers of excursions in the quarter plane corresponding to a nonsingular step set S@?{0,+/-1}^2 with infinite group does not satisfy any nontrivial linear recurrence with polynomial coefficients. Expand
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Polynomial evaluation and interpolation on special sets of points
TLDR
We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. Expand
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Linear Recurrences with Polynomial Coefficients and Application to Integer Factorization and Cartier-Manin Operator
TLDR
We study the complexity of computing one or several terms (not necessarily consecutive) in a recurrence with polynomial coefficients. Expand
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Fast algorithms for computing isogenies between elliptic curves
TLDR
We introduce a new algorithm that computes an isogeny of degree l (l different from the characteristic) in time quasi-linear with respect to l. Expand
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Wronskians and Linear Independence
TLDR
A new and simple proof of the fact that a finite family of analytic functions has a zero Wronskian only if it is linearly dependent. Expand
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Algorithmes Efficaces en Calcul Formel
Le calcul formel traite des objets mathematiques exacts d’un point de vue informatique. Cet ouvrage « Algorithmes efficaces en calcul formel » explore deux directions : la calculabilite et laExpand
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Tellegen's principle into practice
TLDR
We propose explicit transposed versions of polynomial multiplication and division but also new faster algorithms for multipoint evaluation, interpolation and their transposes. Expand
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Solving structured linear systems with large displacement rank
TLDR
Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in [email protected]?(@a^2n) operations, where n is the matrix size, @a is its displacement rank, and @w denotes the omission of logarithmic factors. Expand
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