Grégoire Lecerf
PreprintsCoursesManualPhDHDRBooksJournalsProceedingsSoftware

Postal

Address:

Laboratoire d'informatique de l'École polytechnique

(LIX, UMR 7161 CNRS)

Campus de l'École polytechnique

Bâtiment Alan Turing, CS35003

1, rue Honoré d'Estienne d'Orves

91120 Palaiseau

France

Affiliation:

Laboratoire d'informatique de l'École polytechnique

CNRS, École polytechnique, Institut Polytechnique de Paris (91120, Palaiseau, France)

Team:

Algebraic modeling and symbolic computation

Office:

1009

Telephone:

+33(0)1 77 57 80 81

E-mail: gregoire.lecerf@lix.polytechnique.fr

Position:

Full time researcher at CNRS

Directeur de recherche

Habilité à diriger des recherches

Current

Responsibilities:

Past

responsibilities:

Awards:

  • Best Paper Award 2020 of Journal of Complexity (with J. van der Hoeven).

  • Best Paper Award 2016 of Journal of Complexity (with D. Harvey and J. van der Hoeven).

  • ISSAC 2014 Distinguished Software Presentation Award (with J. van der Hoeven).

Preprints [BibTex file]

J. van der Hoeven and G. Lecerf. Faster multi-point evaluation over any field. Technical Report, HAL, 2024. [Preliminary version].

J. van der Hoeven and G. Lecerf. Fast interpolation of sparse multivariate polynomials. Technical Report, HAL, 2023. [Preliminary version].

Course notes [BibTex file]

A. Bostan, F. Chyzak, M. Giusti, R. Lebreton, G. Lecerf, B. Salvy, and É. Schost. Algorithmes efficaces en calcul formel, notes du cours 2-22 du MPRI, version de 2013. [Current version], https://wikimpri.dptinfo.ens-cachan.fr/doku.php?id=cours:c-2-22.

G. Lecerf. Factorisation des polynômes à plusieurs variables (Cours no. II). In G. Chèze, P. Boito, C. Pernet, and M. Safey el Din, editors, Journées nationales de calcul formel, volume 3 of Les cours du CIRM, pages 1–85. Cedram, 2013. https://ccirm.centre-mersenne.org/item/CCIRM_2013__3_1_A2_0.

Manuals [BibTex file]

J. van der Hoeven and G. Lecerf. Mathemagix User Guide. École polytechnique, France, 2013. [Preliminary version].

Ph.D. thesis [BibTex file]

G. Lecerf. Une alternative aux méthodes de réécriture pour la résolution des systèmes algébriques. PhD thesis, École polytechnique, France, 2001. [Published version].

HDR [BibTex file]

G. Lecerf. Algorithmique des polynômes à plusieurs variables : opérations élémentaires, factorisation, élimination. Université Paris-Sud, France, [Published version], 2013.

Books [BibTex file]

Alin Bostan, Frédéric Chyzak, Marc Giusti, Romain Lebreton, Grégoire Lecerf, Bruno Salvy, and Éric Schost. Algorithmes Efficaces en Calcul Formel. Frédéric Chyzak (auto-édit.), Palaiseau, September 2017. 686 pages. Imprimé par CreateSpace. Aussi disponible en version électronique à https://hal.archives-ouvertes.fr/AECF.

Chapters in books [BibTex file]

E. Kaltofen and G. Lecerf. Factorization of multivariate polynomials. In G. L. Mullen and D. Panario, editors, Handbook of Finite Fields, Discrete Mathematics and Its Applications, pages 382–392. Chapman and Hall/CRC, 2013. [Preliminary version].

Articles in journals [BibTex file]

J. van der Hoeven and G. Lecerf. Plane curve germs and contact factorization. Applicable Algebra in Engineering, Communication and Computing, 2024. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Sparse polynomial interpolation: faster strategies over finite fields. Applicable Algebra in Engineering, Communication and Computing, 2024. [Published version], [Preliminary version].

E. Berardini, A. Couvreur, and G. Lecerf. A proof of the Brill–Noether method from scratch. ACM Commun. Comput. Algebra, 57(4):200–229, 2024. [Published version], [Preliminary version].

S. Abelard, A. Couvreur, and G. Lecerf. Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities. Applicable Algebra in Engineering, Communication and Computing, 2022. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Amortized multi-point evaluation of multivariate polynomials. Journal of Complexity, 74:101693, 2022. [Published version], [Preliminary version].

S. Abelard, E. Berardini, A. Couvreur, and G. Lecerf. Computing Riemann–Roch spaces via Puiseux expansions. Journal of Complexity, 73:101666, 2022. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Univariate polynomial factorization over finite fields with large extension degree. Applicable Algebra in Engineering, Communication and Computing, 35:121–149, 2024. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Fast amortized multi-point evaluation. Journal of Complexity, 67:101574, 2021. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. On sparse interpolation of rational functions and gcds. ACM Commun. Comput. Algebra, 55(1):1–12, 2021. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Ultimate complexity for numerical algorithms. ACM Commun. Comput. Algebra, 54(1):1–13, 2020. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Fast computation of generic bivariate resultants. Journal of Complexity, 62:101499, 2021. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Directed evaluation. Journal of Complexity, 60:101498, 2020. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. On the complexity exponent of polynomial system solving. Found. Comput. Math., 21:1–57, 2021. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Fast multivariate multi-point evaluation revisited. Journal of Complexity, 56:101405, 2020. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Accelerated tower arithmetic. Journal of Complexity, 55:101402, 2019. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Modular composition via factorization. Journal of Complexity, 48:36–68, 2018. [Published version], [Preliminary version].

G. Lecerf. On the complexity of the Lickteig–Roy subresultant algorithm. J. Symbolic Comput., 92:243–268, 2019. [Published version], [Preliminary version].

David Harvey, Joris van der Hoeven, and Grégoire Lecerf. Faster polynomial multiplication over finite fields. Journal of the ACM, 63(6), 2017. Article 52. [Published version], [Preliminary version].

David Harvey, Joris van der Hoeven, and Grégoire Lecerf. Even faster integer multiplication. Journal of Complexity, 36:1–30, 2016. [Published version], [Preliminary version].

Grégoire Lecerf and Joelle Saadé. A short survey on Kantorovich-like theorems for Newton's method. ACM Commun. Comput. Algebra, 50(1):1–11, 2016. [Preliminary version].

Joris van der Hoeven, Grégoire Lecerf, and Guillaume Quintin. Modular SIMD arithmetic in Mathemagix. ACM Transactions on Mathematical Software, 43(1), 2016. Article 5. [Published version], [Preliminary version].

Bruno Grenet, Joris van der Hoeven, and Grégoire Lecerf. Deterministic root finding over finite fields using Graeffe transforms. Applicable Algebra in Engineering, Communication and Computing, 27(3):237–257, 2016. [Published version], [Preliminary version].

Joris van der Hoeven and Grégoire Lecerf. Sparse polynomial interpolation in practice. ACM Commun. Comput. Algebra, 48(4), 2014. In section "ISSAC 2014 Software Presentations. [Preliminary version].

B. Bank, M. Giusti, J. Heintz, G. Lecerf, G. Matera, and P. Solernó. Degeneracy loci and polynomial equation solving. Foundations of Computational Mathematics, 15(1):159–184, 2015. [Preliminary version].

J. van der Hoeven, A. Grozin, M. Gubinelli, G. Lecerf, F. Poulain, and D. Raux. GNU TeXmacs: a scientific editing platform. ACM SIGSAM Communications in Computer Algebra, 47(2):59–62, 2013. [Preliminary version].

J. Berthomieu, G. Lecerf, and G. Quintin. Polynomial root finding over local rings and application to error correcting codes. Applicable Algebra in Engineering, Communication and Computing, 24(6):413–443, 2013. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. On the bit-complexity of sparse polynomial and series multiplication. J. Symbolic Comput., 50:227–254, 2013. [Published version], [Preliminary version].

J. Berthomieu and G. Lecerf. Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations. Math. Comp., 81(279), 2012. [Published version], [Preliminary version].

J. van der Hoeven, G. Lecerf, B. Mourain, Ph. Trébuchet, J. Berthomieu, D. Diatta, and A. Mantzaflaris. Mathemagix, the quest of modularity and efficiency for symbolic and certified numeric computation. ACM SIGSAM Communications in Computer Algebra, 177(3), 2011. In Section "ISSAC 2011 Software Demonstrations", edited by M. Stillman, p. 166–188. [Preliminary version].

J. Berthomieu, J. van der Hoeven, and G. Lecerf. Relaxed algorithms for p-adic numbers. Journal de théorie des nombres de Bordeaux, 23(3), 2011. [Published version], [Preliminary version].

G. Lecerf. New recombination algorithms for bivariate polynomial factorization based on Hensel lifting. Applicable Algebra in Engineering, Communication and Computing, 21(2):151–176, 2010. [Published version], [Preliminary version].

G. Lecerf. Fast separable factorization and applications. Applicable Algebra in Engineering, Communication and Computing, 19(2):135–160, 2008. [Published version], [Preliminary version].

C. Durvye and G. Lecerf. A concise proof of the Kronecker polynomial system solver from scratch. Expositiones Mathematicae, 26(2), 2007. [Published version], [Preliminary version].

G. Chèze and G. Lecerf. Lifting and recombination techniques for absolute factorization. Journal of Complexity, 23(3):380–420, 2007. [Published version], [Preliminary version].

G. Lecerf. Improved dense multivariate polynomial factorization algorithms. Journal of Symbolic Computation, 42(4):477–494, 2007. [Published version], [Preliminary version].

M. Giusti, G. Lecerf, B. Salvy, and J.-C. Yakoubsohn. On location and approximation of clusters of zeros: Case of embedding dimension one. Foundations of Computational Mathematics, 7(1):1–49, 2007. [Published version], [Preliminary version].

G. Lecerf. Sharp precision in Hensel lifting for bivariate polynomial factorization. Mathematics of Computation, 75:921–933, 2006. [Published version], [Preliminary version].

M. Giusti, G. Lecerf, B. Salvy, and J.-C. Yakoubsohn. On location and approximation of clusters of zeros of analytic functions. Foundations of Computational Mathematics, 5(3):257–311, 2005. [Published version], [Preliminary version].

G. Lecerf and É. Schost. Fast multivariate power series multiplication in characteristic zero. SADIO Electronic Journal on Informatics and Operations Research, 5(1):1–10, September 2003. [Preliminary version].

G. Lecerf. Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers. Journal of Complexity, 19(4):564–596, 2003. [Published version], [Preliminary version].

G. Lecerf. Quadratic Newton iteration for systems with multiplicity. Foundations of Computational Mathematics, 2(3):247–293, 2002. [Published version], [Preliminary version].

M. Giusti, G. Lecerf, and B. Salvy. A Gröbner free alternative for polynomial system solving. Journal of Complexity, 17(1):154–211, 2001. [Published version], [Preliminary version].

M. Giusti, K. Hägele, G. Lecerf, J. Marchand, and B. Salvy. The projective Noether Maple package: computing the dimension of a projective variety. J. Symbolic Comput., 30(3):291–307, 2000. [Published version], [Preliminary version].

Articles in conference proceedings [BibTex file]

J. van der Hoeven and G. Lecerf. Amortized bivariate multi-point evaluation. In M. Mezzarobba, editor, Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation, ISSAC '21, page 179–185, New York, NY, USA, 2021. ACM Press. [Published version], [Preliminary version].

S. Abelard, A. Couvreur, and G. Lecerf. Sub-quadratic time for Riemann–Roch spaces: case of smooth divisors over nodal plane projective curves. In A. Mantzaflaris, editor, Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ISSAC '20, pages 14–21, New York, NY, USA, 2020. ACM Press. [Published version], [Preliminary version].

J. van der Hoeven, R. Larrieu, and G. Lecerf. Implementing fast carryless multiplication. In J. Blömer, I. S. Kotsireas, T. Kutsia, and D. E. Simos, editors, Mathematical Aspects of Computer and Information Sciences, pages 121–136, Cham, 2017. Springer International Publishing. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Composition modulo powers of polynomials. In M. Blurr, editor, Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '17, pages 445–452, New York, NY, USA, 2017. ACM. [Published version], [Preliminary version].

J. van der Hoeven, G. Lecerf, and D. Raux. Preserving syntactic correctness while editing mathematical formulas. In I. S. Kotsireas and E. Martínez-Moro, editors, Applications of Computer Algebra. Kalamata, Greece, July 20–23 2015, volume 197 of Springer Proceedings in Mathematics & Statistics, pages 459–471. Springer International Publishing, 2017. [Preliminary version].

D. Harvey, J. van der Hoeven, and G. Lecerf. Fast polynomial multiplication over 𝔽260. In M. Rosenkranz, editor, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16, pages 255–262, New York, NY, USA, 2016. ACM. [Published version], [Preliminary version].

Joris van der Hoeven and Grégoire Lecerf. Evaluating straight-line programs over balls. In Paolo Montuschi, Michael Schulte, Javier Hormigo, Stuart Oberman, and Nathalie Revol, editors, 2016 IEEE 23nd Symposium on Computer Arithmetic, pages 142–149. IEEE, 2016. [Preliminary version].

J. van der Hoeven and G. Lecerf. Faster FFTs in medium precision. In A. Tisserand and J. Villalba, editors, IEEE 22nd Symposium on Computer Arithmetic, pages 75–82. IEEE, 2015. [Published version], [Preliminary version].

B. Grenet, J. van der Hoeven, and G. Lecerf. Randomized root finding over finite FFT-fields using tangent Graeffe transforms. In D. Robertz, editor, Proc. ISSAC '15, pages 197–204. ACM, 2015. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. Interfacing Mathemagix with C++. In M. Monagan, G. Cooperman, and M. Giesbrecht, editors, Proc. ISSAC '13, pages 363–370. ACM, 2013. [Published version], [Preliminary version].

J. van der Hoeven and G. Lecerf. On the complexity of multivariate blockwise polynomial multiplication. In J van der Hoeven and M. van Hoeij, editors, Proc. ISSAC '12, pages 211–218. ACM, 2012. [Published version], [Preliminary version].

G. Lecerf. Mathemagix: towards large scale programming for symbolic and certified numeric computations. In K. Fukuda, J. van der Hoeven, M. Joswig, and N. Takayama, editors, Mathematical Software - ICMS 2010, Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010, volume 6327 of Lecture Notes in Computer Science, pages 329–332. Springer, 2010. [Published version].

A. Bostan, F. Chyzak, G. Lecerf, B. Salvy, and E. Schost. Differential equations for algebraic functions. In Proc. ISSAC '07. ACM, 2007. [Published version], [Preliminary version].

A. Bostan, G. Lecerf, B. Salvy, É. Schost, and B. Wiebelt. Complexity issues in bivariate polynomial factorization. In J. Schicho, editor, Proc. ISSAC '04, pages 42–49. ACM, 2004. [Published version], [Preliminary version].

A. Bostan, G. Lecerf, and É. Schost. Tellegen's principle into practice. In Hoon Hong, editor, Proc. ISSAC '03, pages 37–44. ACM, 2003. [Published version], [Preliminary version].

G. Lecerf. Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions. In C. Traverso, editor, Proc. ISSAC '00, pages 209–216. ACM, 2000. [Published version].

Software [BibTex file]

G. Lecerf. Ponctual participations to GNU TeXmacs: Doxygen interface, Mathemagix interface, GnuPG interface. [Software location].

J. van der Hoeven and G. Lecerf. Justinline, a Mathemagix library for dynamic compilation and tuning of low level algorithms, 2015. [Software location].

J. van der Hoeven and G. Lecerf. Runtime, a Mathemagix library for dynamic compilation, 2015. [Software location].

G. Lecerf. Factorix, a Mathemagix library for polynomial factorization, 2013. [Software location].

G. Lecerf. Geomsolvex, a Mathemagix library for geometric polynomial system solving, 2012. [Software location].

J. van der Hoeven and G. Lecerf. The Mathemagix interpreter MMI, 2011. [Software location].

G. Lecerf. Mathemagix interface to the BLAD library, 2011. [Software location].

G. Lecerf. Mathemagix interface to the PARI library, 2011. [Software location].

G. Lecerf. Mathemagix interface to the FGb library, 2010. [Software location].

G. Lecerf and G. Quintin. Finitefieldz, a Mathemagix library for finite fields, 2010. [Software location].

J. van der Hoeven and G. Lecerf. Multimix, a Mathemagix library for multivariate polynomials and series, 2009. [Software location].

G. Lecerf. Lattiz, a Mathemagix library for lattice reduction, 2009. [Software location].

J. van der Hoeven, G. Lecerf, and B. Mourrain. Automagix, automatic generation of Mathemagix configuration files, 2008. [Software location].

J. van der Hoeven and G. Lecerf. Algebramix, a Mathemagix library for univariate polynomials, series, and matrices, 2007. [Software location].

J. van der Hoeven and G. Lecerf. Numerix, a Mathemagix library for large integers, modular integers, floating point numbers, intervals, and balls, 2007. [Software location].

G. Lecerf. Emacs mode to Mathemagix: syntax highlighting and indentation, 2007. [Software location].

G. Lecerf. A Magma library for separable factorization, 2007. Not maintained. [Software location].

G. Chèze and G. Lecerf. A Magma library for bivariate absolute factorization, 2005. Not maintained. [Software location].

W. Decker, G. Lecerf, and G. Pfister. absfact.lib, a Singular library for absolute factorization, 2005. [Software location].

G. Lecerf and É. Schost. Experimental Tellegen support for NTL, 2003. Not maintained. [Software location].

G. Lecerf and X. Suraud. Experimental MathML for Magma, 2002. Not maintained.

G. Lecerf. Kronecker, a Magma library for geometric polynomial solving, 1999-2002. With contributions of Schost, Lehmann, and Suraud. Not maintained. [Software location].

M. Giusti, G. Lecerf, J. Marchand, and B. Salvy. The projective Noether package, in Maple, for computing the dimension of a projective algebraic variety, 1997. Not maintained.

G. Lecerf. The dynamic real closure, Axiom library, 1996. Not maintained. [Software location].

Directeur de publication : Grégoire Lecerf, laboratoire d'informatique de l'École polytechnique (LIX). Bâtiment Alan Turing, CS35003

1, rue Honoré d'Estienne d'Orves. 91120 Palaiseau, France