Search Results - "LECERF, Grégoire"

Even faster integer multiplication by Harvey, David, van der Hoeven, Joris, Lecerf, Grégoire

“…We give a new algorithm for the multiplication of n-bit integers in the bit complexity model, which is asymptotically faster than all previously known…”
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Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities by Abelard, Simon, Couvreur, Alain, Lecerf, Grégoire

“…We revisit the seminal Brill–Noether algorithm for plane curves with ordinary singularities. Our new approach takes advantage of fast algorithms for…”
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On the Complexity Exponent of Polynomial System Solving by van der Hoeven, Joris, Lecerf, Grégoire

“…We present a probabilistic Las Vegas algorithm for solving sufficiently generic square polynomial systems over finite fields. We achieve a nearly quadratic…”
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Sparse polynomial interpolation: faster strategies over finite fields by van der Hoeven, Joris, Lecerf, Grégoire

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Univariate polynomial factorization over finite fields with large extension degree by Hoeven, Joris van der, Lecerf, Grégoire

“…The best known asymptotic bit complexity bound for factoring univariate polynomials over finite fields grows with d 1.5 + o ( 1 ) for input polynomials of…”
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Fast amortized multi-point evaluation by van der Hoeven, Joris, Lecerf, Grégoire

“…The efficient evaluation of multivariate polynomials at many points is an important operation for polynomial system solving. Kedlaya and Umans have recently…”
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Fast computation of generic bivariate resultants by van der Hoeven, Joris, Lecerf, Grégoire

“…We prove that the resultant of two “sufficiently generic” bivariate polynomials over a finite field can be computed in quasi-linear expected time, using a…”
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Computing Riemann–Roch spaces via Puiseux expansions by Abelard, Simon, Berardini, Elena, Couvreur, Alain, Lecerf, Grégoire

“…Computing large Riemann–Roch spaces for plane projective curves still constitutes a major algorithmic and practical challenge. Seminal applications concern the…”
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On the bit-complexity of sparse polynomial and series multiplication by van der Hoeven, Joris, Lecerf, Grégoire

“…In this paper we present various algorithms for multiplying multivariate polynomials and series. All algorithms have been implemented in the C++ libraries of…”
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Deterministic root finding over finite fields using Graeffe transforms by Grenet, Bruno, van der Hoeven, Joris, Lecerf, Grégoire

“…We design new deterministic algorithms, based on Graeffe transforms, to compute all the roots of a polynomial which splits over a finite field F q . Our…”
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Polynomial root finding over local rings and application to error correcting codes by Berthomieu, Jérémy, Lecerf, Grégoire, Quintin, Guillaume

“…This article is devoted to algorithms for computing all the roots of a univariate polynomial with coefficients in a complete commutative Noetherian unramified…”
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New recombination algorithms for bivariate polynomial factorization based on Hensel lifting by Lecerf, Grégoire

“…We present new faster deterministic and probabilistic recombination algorithms to compute the irreducible decomposition of a bivariate polynomial via the…”
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Improved dense multivariate polynomial factorization algorithms by Lecerf, Grégoire

“…We present new deterministic and probabilistic algorithms that reduce the factorization of dense polynomials from several variables to one variable. The…”
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Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations by BERTHOMIEU, JÉRÉMY, LECERF, GRÉGOIRE

“…In this article we present a new algorithm for reducing the usual sparse bivariate factorization problems to the dense case. This reduction simply consists of…”
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Degeneracy Loci and Polynomial Equation Solving by Bank, Bernd, Giusti, Marc, Heintz, Joos, Lecerf, Grégoire, Matera, Guillermo, Solernó, Pablo

“…Let V be a smooth, equidimensional, quasi-affine variety of dimension r over C , and let F be a ( p × s ) matrix of coordinate functions of C [ V ] , where s ≥…”
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Evaluating Straight-Line Programs over Balls by Van Der Hoeven, Joris, Lecerf, Gregoire

“…Interval arithmetic achieves numerical reliability for a wide range of applications, at the price of a performance penalty. For applications to homotopy…”
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Fast separable factorization and applications by Lecerf, Grégoire

“…In this paper we show that the separable decomposition of a univariate polynomial can be computed in softly optimal time, in terms of the number of arithmetic…”
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Sharp precision in Hensel lifting for bivariate polynomial factorization by LECERF, Grégoire

“…Popularized by Zassenhaus in the seventies, several algorithms for factoring polynomials use a so-called lifting and recombination scheme. Concerning bivariate…”
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Lifting and recombination techniques for absolute factorization by Chèze, Guillaume, Lecerf, Grégoire

“…In the vein of recent algorithmic advances in polynomial factorization based on lifting and recombination techniques, we present new faster algorithms for…”
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Faster FFTs in Medium Precision by Van Der Hoeven, Joris, Lecerf, Gregoire

“…In this paper, we show how to speed up the computation of fast Fourier transforms over complex numbers for "medium" precisions, typically in the range from 100…”
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