# Publications

Most of my papers are available in electronic form from the list below.

Usually, I put preliminary versions on arXiv. You can be informed of new ones by subscribing to this rss feed.

## 2024

- V. Neiger, B. Salvy, É. Schost, and G. Villard, “Faster Modular Composition,”
*Journal of the ACM*, vol. 71, no. 2, pp. 1–79, 2024. - J.-M. Muller and B. Salvy, “Effective Quadratic Error Bounds for Floating-Point Algorithms Computing the Hypotenuse Function,” arXiv, May 2024.
- M. Masson, D. Arzelier, F. Bréhard, M. Joldes, and B. Salvy, “Fast and reliable computation of the instantaneous orbital collision probability,”
*Journal of Guidance, Control, and Dynamics*, vol. 47, no. 8, pp. 1660–1673, 2024. - A. Ibrahim and B. Salvy, “Positivity certificates for linear recurrences,” in
*Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)*, 2024, pp. 982–994. - H. Brochet and B. Salvy, “Reduction-Based Creative Telescoping for Definite Summation of D-finite Functions,”
*Journal of Symbolic Computation*, vol. 125, pp. 21 pages, 2024. - A. Bostan, T. Rivoal, and B. Salvy, “Minimization of differential equations and algebraic values of E-functions,”
*Mathematics of Computation*, vol. 93, no. 347, pp. 1427–1472, 2024.

## 2023

- N. Brisebarre and B. Salvy, “Differential-Difference Properties of Hypergeometric Series,”
*Proceedings of the American Mathematical Society*, vol. 151, no. 6, pp. 2603–2617, 2023.

## 2022

- Y. Bugeaud, A. Dujella, W. Fang, T. Pejković, and B. Salvy, “Absolute root separation,”
*Experimental Mathematics*, vol. 31, no. 3, pp. 805–812, 2022.

## 2021

- S. Melczer and B. Salvy, “Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems,”
*Journal of Symbolic Computation*, vol. 103, pp. 234–279, 2021. - A. Bostan, T. Rivoal, and B. Salvy, “Explicit degree bounds for right factors of linear differential operators,”
*Bulletin of the London Mathematical Society*, vol. 53, no. 1, pp. 53–62, 2021.

## 2020

- J. Dahne and B. Salvy, “Computation of Tight Enclosures for Laplacian Eigenvalues,”
*SIAM J. Sci. Comput.*, vol. 42, no. 5, pp. A3210–A3232, 2020.

## 2019

- B. Salvy, “Linear Differential Equations as a Data-Structure,”
*Foundations of Computational Mathematics*, vol. 19, no. 5, pp. 1071–1112, 2019.

## 2018

- B. Salvy, “Recursive Combinatorial Structures: Enumeration, Probabilistic Analysis and Random Generation,” in
*35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)*, Dagstuhl, Germany, 2018, vol. 96, pp. 1:1–1:5. - A. Bostan, F. Chyzak, P. Lairez, and B. Salvy, “Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions,” in
*ISSAC’18—Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation*, 2018, pp. 95–102.

## 2017

- Y. Bugeaud, A. Dujella, T. Pejkovic, and B. Salvy, “Absolute real root separation,”
*The American Mathematical Monthly*, vol. 124, no. 10, pp. 930–936, Dec. 2017. - A. Bostan, P. Lairez, and B. Salvy, “Multiple binomial sums,”
*Journal of Symbolic Computation*, vol. 80, pp. 351–386, 2017. - A. Bostan, L. Dumont, and B. Salvy, “Algebraic Diagonals and Walks: Algorithms, Bounds, Complexity,”
*Journal of Symbolic Computation*, vol. 83, pp. 68–92, 2017. - A. Bostan
*et al.*,*Algorithmes Efficaces en Calcul Formel*. Palaiseau: Frédéric Chyzak (auto-édit.), 2017.

## 2016

- R. Serra, D. Arzelier, M. Joldes, J.-B. Lasserre, A. Rondepierre, and B. Salvy, “Fast and accurate computation of orbital collision probability for short-term encounters,”
*Journal of Guidance, Control, and Dynamics*, vol. 39, no. 5, pp. 1009–1021, 2016. - S. Melczer and B. Salvy, “Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables,” in
*ISSAC’16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation*, New York, NY, USA, 2016, pp. 333–340. - A. Bostan, L. Dumont, and B. Salvy, “Efficient Algorithms for Mixed Creative Telescoping,” in
*ISSAC’16—Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation*, 2016, pp. 127–134.

## 2015

- S. Maulat and B. Salvy, “Formulas for Continued Fractions: An Automated Guess and Prove Approach,” in
*ISSAC’15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation*, New York, NY, USA, 2015, pp. 275–282. - A. Bostan, L. Dumont, and B. Salvy, “Algebraic Diagonals and Walks,” in
*ISSAC’15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation*, New York, NY, USA, 2015, pp. 77–84. - M. Bardet, J.-C. Faugère, and B. Salvy, “On the Complexity of the F5 Gröbner basis Algorithm,”
*Journal of Symbolic Computation*, vol. 70, pp. 49–70, 2015.

## 2014

- R. Serra, D. Arzelier, M. Joldes, J.-B. Lasserre, A. Rondepierre, and B. Salvy, “A New Method to Compute the Probability of Collision for Short-term Space Encounters,” in
*AIAA/AAS Astrodynamics Specialist Conference*, 2014, pp. 1–7. - A. Bostan, K. Raschel, and B. Salvy, “Non-D-finite excursions in the quarter plane,”
*Journal of Combinatorial Theory, Series A*, vol. 121, pp. 45–63, 2014.

## 2013

- B. Salvy, “Philippe Flajolet and Symbolic Computation.” Preprint. To appear in Philippe Flajolet’s collected works., 2013.
- B. Salvy, “Asymptotics of linear divide-and-conquer recurrences.” Summary of Philippe Dumas’ talk at the Flajolet seminar, IHP., pp. 1–8, 2013.
- A. Bostan, P. Lairez, and B. Salvy, “Creative telescoping for rational functions using the Griffiths-Dwork method,” in
*ISSAC ’13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation*, 2013, pp. 93–100. - M. Bardet, J.-C. Faugère, B. Salvy, and P.-J. Spaenlehauer, “On the Complexity of Solving Quadratic Boolean Systems,”
*Journal of Complexity*, vol. 29, no. 1, pp. 53–75, 2013.

## 2012

- C. Pivoteau, B. Salvy, and M. Soria, “Algorithms for Combinatorial Structures: Well-founded systems and Newton iterations,”
*Journal of Combinatorial Theory, Series A*, vol. 119, pp. 1711–1773, 2012. - A. Bostan, F. Chyzak, Z. Li, and B. Salvy, “Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators,” in
*ISSAC ’12: Proceedings of the twenty-fifth International Symposium on Symbolic and Algebraic Computation*, 2012, pp. 99–106. - A. Bostan, M. F. I. Chowdhury, R. Lebreton, B. Salvy, and É. Schost, “Power Series Solutions of Singular (q)-Differential Equations,” in
*ISSAC ’12: Proceedings of the twenty-fifth International Symposium on Symbolic and Algebraic Computation*, 2012, pp. 107–114.

## 2011

- J.-G. Dumas, L. Fousse, and B. Salvy, “Simultaneous modular reduction and Kronecker substitution for small finite fields,”
*Journal of Symbolic Computation*, vol. 46, no. 7, pp. 823–840, 2011. - F. Chyzak, J. H. Davenport, C. Koutschan, and B. Salvy, “On Kahan’s Rules for Determining Branch Cuts,” in
*Proceedings of the 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2011)*, 2011, pp. 47–51.

## 2010

- B. Salvy and J. Shackell, “Measured limits and multiseries,”
*Journal of the London Mathematical Society*, vol. 82, no. 3, pp. 747–762, 2010. - M. Mezzarobba and B. Salvy, “Effective Bounds for P-Recursive Sequences,”
*Journal of Symbolic Computation*, vol. 45, no. 10, pp. 1075–1096, Oct. 2010. - P. Flajolet, S. Gerhold, and B. Salvy, “Lindelöf Representations and (Non-)Holonomic Sequences,”
*The Electronic Journal of Combinatorics*, vol. 17, no. 1, pp. 1–28, 2010. - A. Bostan, B. Salvy, and K. Tran, “Generating functions of Chebyshev-like polynomials,”
*International Journal of Number Theory*, vol. 6, no. 7, pp. 1659–1667, 2010. - A. Bostan, B. Salvy, and É. Schost, “Fast conversion algorithms for orthogonal polynomials,”
*Linear Algebra and its Applications*, vol. 432, no. 1, pp. 249–258, Jan. 2010. - A. Benoit, F. Chyzak, A. Darrasse, S. Gerhold, M. Mezzarobba, and B. Salvy, “The Dynamic Dictionary of Mathematical Functions (DDMF),” in
*The Third International Congress on Mathematical Software (ICMS 2010)*, 2010, vol. 6327, pp. 35–41.

## 2009

- P. Clote, E. Kranakis, D. Krizanc, and B. Salvy, “Asymptotics of Canonical and Saturated RNA Secondary Structures,”
*Journal of Bioinformatics and Computational Biology*, vol. 7, no. 5, pp. 869–893, Oct. 2009. - F. Chyzak, M. Kauers, and B. Salvy, “A Non-Holonomic Systems Approach to Special Function Identities,” in
*ISSAC ’09: Proceedings of the twenty-second international symposium on Symbolic and algebraic computation*, 2009, pp. 111–118. - A. Benoit and B. Salvy, “Chebyshev Expansions for Solutions of Linear Differential Equations,” in
*ISSAC ’09: Proceedings of the twenty-second international symposium on Symbolic and algebraic computation*, 2009, pp. 23–30.

## 2008

- C. Pivoteau, B. Salvy, and M. Soria, “Boltzmann Oracle for Combinatorial Systems,” in
*Algorithms, Trees, Combinatorics and Probabilities*, 2008, pp. 475–488. - C. Gomez and B. Salvy, “Calcul Formel,”
*Les Techniques de l’Ingénieur*, vol. Dossier AF1460, pp. 1–20, 2008. - J.-G. Dumas, L. Fousse, and B. Salvy, “Compressed Modular Matrix Multiplication,” in
*Milestones in Computer Algebra (MICA 2008)*, 2008. - A. Bostan, B. Salvy, and É. Schost, “Power Series Composition and Change of Basis,” in
*ISSAC’08: Proceedings of the twenty-first international symposium on Symbolic and algebraic computation*, 2008, pp. 269–276. - A. Bostan, F. Morain, B. Salvy, and É. Schost, “Fast algorithms for computing isogenies between elliptic curves,”
*Mathematics of Computation*, vol. 77, no. 263, pp. 1755–1778, 2008. - J. M. Borwein and B. Salvy, “A proof of a recursion for Bessel moments,”
*Experimental Mathematics*, vol. 17, no. 2, pp. 223–230, 2008.

## 2007

- M. Giusti, G. Lecerf, B. Salvy, and J.-C. Yakoubsohn, “On Location and Approximation of Clusters of Zeroes: Case of Embedding Dimension One,”
*Foundations of Computational Mathematics*, vol. 7, no. 1, pp. 1–58, 2007. - A. Bostan, F. Chyzak, F. Ollivier, B. Salvy, É. Schost, and A. Sedoglavic, “Fast computation of power series solutions of systems of differential equations,” in
*SODA’07*, 2007, pp. 1012–1021. - A. Bostan, F. Chyzak, G. Lecerf, B. Salvy, and É. Schost, “Differential equations for algebraic functions,” in
*ISSAC’07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation*, 2007, pp. 25–32.

## 2006

- A. Bostan, P. Flajolet, B. Salvy, and É. Schost, “Fast Computation of Special Resultants,”
*Journal of Symbolic Computation*, vol. 41, no. 1, pp. 1–29, Jan. 2006. - A. Bostan, F. Chyzak, T. Cluzeau, and B. Salvy, “Low Complexity Algorithms for Linear Recurrences,” in
*ISSAC’06*, 2006, pp. 31–38.

## 2005

- B. Salvy, “D-Finiteness: Algorithms and Applications,” in
*ISSAC’05*, 2005, pp. 2–3.PDF from ACM (free) doi BibTeX

Abstract for an invited talk. Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, Beijing, July 2005. - M. Giusti, G. Lecerf, B. Salvy, and J.-C. Yakoubsohn, “On Location and Approximation of Clusters of Zeroes of Analytic Functions,”
*Foundations of Computational Mathematics*, vol. 5, no. 3, pp. 257–311, 2005. - P. Flajolet, S. Gerhold, and B. Salvy, “On the non-holonomic character of logarithms, powers, and the nth prime function,”
*The Electronic Journal of Combinatorics*, vol. 11, no. 2, 2005. - F. Chyzak, M. Mishna, and B. Salvy, “Effective Scalar Products of D-finite Symmetric Functions,”
*Journal of Combinatorial Theory. Series A*, vol. 112, no. 1, pp. 1–43, Oct. 2005. - A. Bostan, T. Cluzeau, and B. Salvy, “Fast Algorithms for Polynomial Solutions of Linear Differential Equations,” in
*ISSAC’05*, New York, 2005, pp. 45–52.PDF from ACM (free) doi BibTeX Abstract

Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, July 2005, Beijing, China. - M. Bardet, J.-C. Faugère, B. Salvy, and B.-Y. Yang, “Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems,” in
*MEGA’05*, 2005.

## 2004

- P. Flajolet, B. Salvy, and G. Schaeffer, “Airy Phenomena and Analytic Combinatorics of Connected Graphs,”
*The Electronic Journal of Combinatorics*, vol. 11, no. 1, p. R34, 2004. - A. Bostan, G. Lecerf, B. Salvy, É. Schost, and B. Wiebelt, “Complexity Issues in Bivariate Polynomial Factorization,” in
*Symbolic and Algebraic Computation*, 2004, pp. 42–49. - M. Bardet, J.-C. Faugère, and B. Salvy, “On the Complexity of Gröbner basis computation of Semi-regular Overdetermined algebraic equations,” in
*International Conference on Polynomial System Solving*, 2004, pp. 71–74.

## 2003

- L. Meunier and B. Salvy, “ESF: An Automatically Generated Encyclopedia of Special Functions,” in
*Symbolic and Algebraic Computation*, 2003, pp. 199–205. - A. Bostan, B. Salvy, and É. Schost, “Fast Algorithms for Zero-Dimensional Polynomial Systems Using Duality,”
*Applicable Algebra in Engineering, Communication and Computing*, vol. 14, no. 4, pp. 239–272, 2003.

## 2002

- P. Nicodème, B. Salvy, and P. Flajolet, “Motif Statistics,”
*Theoretical Computer Science*, vol. 287, no. 2, pp. 593–618, 2002. - R. Cori, D. Rossin, and B. Salvy, “Polynomial Ideals for Sandpiles and their Gröbner Bases,”
*Theoretical Computer Science*, vol. 276, no. 1, pp. 1–15, 2002. - F. Chyzak, M. Mishna, and B. Salvy, “Effective D-finite Symmetric Functions,” in
*14th Conference of Formal Power Series and Algebraic Combinatorics*, Melbourne, Australia, 2002, pp. 19.1–19.12.

## 2001

- B. Salvy, “Even-Odd Set Partitions, Saddle-Point Method and Wyman Admissibility,” Institut National de Recherche en Informatique et en Automatique, Research Report 4201, 2001.
- L. Meunier and B. Salvy, “Automatically Generated Encyclopedia of Special Functions,” in
*Mathematical Knowledge Management*, 2001. - M. Giusti, G. Lecerf, and B. Salvy, “A Gröbner Free Alternative for Polynomial System Solving,”
*Journal of Complexity*, vol. 17, no. 1, pp. 154–211, Mar. 2001.

## 2000

- M. Giusti, K. Hägele, G. Lecerf, J. Marchand, and B. Salvy, “Computing the Dimension of a Projective Variety: the Projective Noether Maple Package,”
*Journal of Symbolic Computation*, vol. 30, no. 3, pp. 291–307, Sep. 2000.

## 1999

- B. Salvy and J. Shackell, “Symbolic Asymptotics: Multiseries of Inverse Functions,”
*Journal of Symbolic Computation*, vol. 27, no. 6, pp. 543–563, 1999. - P. Nicodème, B. Salvy, and P. Flajolet, “Motif Statistics,” in
*Algorithms – ESA’99*, 1999, no. 1643, pp. 194–211.

## 1998

- B. Salvy and J. Shackell, “Symbolic Asymptotics: Functions of Two Variables, Implicit Functions,”
*Journal of Symbolic Computation*, vol. 25, no. 3, pp. 329–349, Mar. 1998. - P. Flajolet and B. Salvy, “Euler Sums and Contour Integral Representations,”
*Experimental Mathematics*, vol. 7, no. 1, pp. 15–35, 1998. - F. Chyzak and B. Salvy, “Non-commutative Elimination in Ore Algebras Proves Multivariate Holonomic Identities,”
*Journal of Symbolic Computation*, vol. 26, no. 2, pp. 187–227, 1998.

## 1997

- L. Habsieger and B. Salvy, “On Integer Chebyshev Polynomials,”
*Mathematics of Computation*, vol. 66, no. 218, pp. 763–770, 1997. - P. Flajolet and B. Salvy, “The SIGSAM Challenges: Symbolic Asymptotics in Practice,”
*SIGSAM Bulletin*, vol. 31, no. 4, pp. 36–47, Dec. 1997.

## 1996

- D. Richardson, B. Salvy, J. Shackell, and J. Van der Hoeven, “Asymptotic Expansions of exp-log Functions,” in
*Symbolic and Algebraic Computation*, New York, 1996, pp. 309–313. - X. Gourdon and B. Salvy, “Effective asymptotics of linear recurrences with rational coefficients,”
*Discrete Mathematics*, vol. 153, no. 1–3, pp. 145–163, 1996.

## 1995

- J. Shackell and B. Salvy, “Asymptotic Forms and Algebraic Differential Equations,”
*Journal of Symbolic Computation*, vol. 20, no. 2, pp. 169–177, 1995. - B. Salvy and S. Y. Slavyanov, “A Combinatorial Problem in the Classification of Second-Order Linear ODE’s,” Institut National de Recherche en Informatique et en Automatique, Research Report 2600, 1995.
- S. P. Lipshitz, T. C. Scott, and B. Salvy, “On the Acoustic Impedance of Baffled Strip Radiators,”
*Journal of the Audio Engineering Society*, vol. 43, no. 7/8, pp. 573–580, Jul. 1995. - C. Gomez, B. Salvy, and P. Zimmermann,
*Calcul formel : mode d’emploi. Exemples en Maple*. Masson, 1995. - P. Flajolet and B. Salvy, “Computer Algebra Libraries for Combinatorial Structures,”
*Journal of Symbolic Computation*, vol. 20, no. 5-6, pp. 653–671, 1995. - P. Flajolet, G. Labelle, L. Laforest, and B. Salvy, “Hypergeometrics and the cost structure of quadtrees,”
*Random Structures & Algorithms*, vol. 7, no. 2, pp. 117–144, 1995. - P. Dumas and B. Salvy, “Maple and the Putnam Competition,”
*The Maple Technical Newsletter*, vol. 2, no. 2, pp. 63–68, 1995.

## 1994

- B. Salvy and P. Zimmermann, “Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable,”
*ACM Transactions on Mathematical Software*, vol. 20, no. 2, pp. 163–177, 1994. - B. Salvy, “Fast Computation of Some Asymptotic Functional Inverses,”
*Journal of Symbolic Computation*, vol. 17, no. 3, pp. 227–236, 1994.

## 1993

- B. Salvy, “Efficient programming in Maple: a case study,”
*SIGSAM Bulletin*, vol. 27, no. 2, pp. 1–12, Apr. 1993. - M. Petkovšek and B. Salvy, “Finding all hypergeometric solutions of linear differential equations,” in
*ISSAC’93*, New York, 1993, pp. 27–33. - X. Gourdon and B. Salvy, “Computing one million digits of \sqrt2,”
*The Maple Technical Newsletter*, vol. 10, pp. 66–71, 1993. - X. Gourdon and B. Salvy, “Asymptotics of linear recurrences with rational coefficients,” in
*Formal Power Series and Algebraic Combinatorics*, 1993, pp. 253–266. - P. Flajolet and B. Salvy, “A Finite Sum of Products of Binomial Coefficients,”
*SIAM Review*, vol. 35, no. 4, pp. 645–646, 1993. - P. Flajolet, X. Gourdon, and B. Salvy, “Sur une famille de polynômes issus de l’analyse numérique,”
*Gazette des Mathématiciens*, vol. 55, pp. 67–78, Jan. 1993. - M. Bronstein and B. Salvy, “Full Partial Fraction Decomposition of Rational Functions,” in
*ISSAC’93*, New York, 1993, pp. 157–160.

## 1992

- B. Salvy and J. Shackell, “Asymptotic expansions of functional inverses,” in
*Symbolic and Algebraic Computation*, New York, 1992, pp. 130–137. - B. Salvy, “General Asymptotic Scales and Computer Algebra,” in
*Asymptotic and Numerical Methods for Partial Differential Equations, Critical Parameters and Domain Decomposition*, 1992. - F. Bergeron, P. Flajolet, and B. Salvy, “Varieties of Increasing Trees,” in
*CAAP’92*, 1992, vol. 581, pp. 24–48.

## 1991

- B. Salvy, “Asymptotique automatique et fonctions génératrices,” Thèse de Doctorat, École polytechnique, 1991.
- B. Salvy, “Three ways to get Stirling’s formula in Maple,”
*The Maple Technical Newsletter*, vol. 5, pp. 32–42, 1991. - B. Salvy, “Examples of automatic asymptotic expansions,”
*SIGSAM Bulletin*, vol. 25, no. 2, pp. 4–17, Apr. 1991. - P. Flajolet, B. Salvy, and P. Zimmermann, “Automatic Average-case Analysis of Algorithms,”
*Theoretical Computer Science*, vol. 79, no. 1, pp. 37–109, 1991.

## 1989

- P. Flajolet, B. Salvy, and P. Zimmermann, “Lambda-Upsilon-Omega: An Assistant Algorithms Analyzer,” in
*Applied Algebra, Algebraic Algorithms and Error-Correcting Codes*, 1989, vol. 357, pp. 201–212. - P. Flajolet, B. Salvy, and P. Zimmermann, “Lambda-Upsilon-Omega: The 1989 CookBook,” Institut National de Recherche en Informatique et en Automatique, Research Report 1073, 1989.

## 1988

- B. Salvy, “Fonctions génératrices et asymptotique automatique,” Université Paris XI, Rapport de DEA, 1988.

## 1987

- B. Salvy, “Calcul automatique du développement asymptotique lorsque leur rang tend vers l’infini des coefficients des développements en série de Laurent de certaines fonctions génératrices,” École polytechnique, Rapport d’option, 1987.