Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

• 1A. Bostan, M. Bousquet-Mélou, M. Kauers, S. Melczer.
  
  On 3-dimensional lattice walks confined to the positive octant, in: Annals of Combinatorics, October 2016, 36 p, First Online: 14 October 2016. [ DOI : 10.1007/s00026-016-0328-7 ]
  
  https://hal.archives-ouvertes.fr/hal-01063886
• 2A. Bostan, F. Chyzak, M. Van Hoeij, M. Kauers, L. Pech.
  
  Hypergeometric Expressions for Generating Functions of Walks with Small Steps in the Quarter Plane, in: European Journal of Combinatorics, 2016, 29 p. [ DOI : 10.1016/j.ejc.2016.10.010 ]
  
  https://hal.inria.fr/hal-01332175
• 3A. Bostan, L. Dumont, B. Salvy.
  
  Algebraic Diagonals and Walks: Algorithms, Bounds, Complexity, in: Journal of Symbolic Computation, 2016. [ DOI : 10.1016/j.jsc.2016.11.006 ]
  
  https://hal.archives-ouvertes.fr/hal-01244914
• 4A. Bostan, I. Kurkova, K. Raschel.
  
  A human proof of Gessel's lattice path conjecture, in: Transactions of the American Mathematical Society, 2016, vol. 369, n^o 2, February 2017, pp. 1365-1393, Published electronically: April 14, 2016.
  
  https://hal.archives-ouvertes.fr/hal-00858083
• 5A. Bostan, P. Lairez, B. Salvy.
  
  Multiple binomial sums, in: Journal of Symbolic Computation, 2016. [ DOI : 10.1016/j.jsc.2016.04.002 ]
  
  https://hal.archives-ouvertes.fr/hal-01220573
• 6P. Lairez.
  
  Computing periods of rational integrals, in: Mathematics of Computation, November 2016, vol. 85, pp. 1719-1752. [ DOI : 10.1090/mcom/3054 ]
  
  https://hal.inria.fr/hal-00981114
• 7A. Mahboubi.
  
  An Induction Principle over Real Numbers, in: Archive for Mathematical Logic, 2016. [ DOI : 10.1007/s00153-016-0513-8 ]
  
  https://hal.inria.fr/hal-01376054
• 8A. Mahboubi.
  
  Machine-checked mathematics, in: Nieuw Archief voor Wiskunde, September 2016, vol. 5/17, n^o 3, 5 p.
  
  https://hal.inria.fr/hal-01363284

International Conferences with Proceedings

• 9K. Bhargavan, A. Delignat-Lavaud, C. Fournet, A. Gollamudi, G. Gonthier, N. Kobeissi, N. Kulatova, A. Rastogi, T. Sibut-Pinote, N. Swamy, S. Zanella-Béguelin.
  
  Formal Verification of Smart Contracts: Short Paper, in: ACM Workshop on Programming Languages and Analysis for Security, Vienna, Austria, October 2016. [ DOI : 10.1145/2993600.2993611 ]
  
  https://hal.inria.fr/hal-01400469
• 10A. Bostan, X. Caruso, É. Schost.
  
  Computation of the Similarity Class of the $p$-Curvature, in: ISSAC 2016, Waterloo, ON, Canada, ACM Press, July 2016, pp. 111–118. [ DOI : 10.1145/2930889.2930897 ]
  
  https://hal.archives-ouvertes.fr/hal-01321043
• 11A. Bostan, G. Christol, P. Dumas.
  
  Fast Computation of the $N$th Term of an Algebraic Series over a Finite Prime Field, in: ISSAC '16, Waterloo, Ontario, Canada, July 2016. [ DOI : 10.1145/2930889.2930904 ]
  
  https://hal.inria.fr/hal-01389421
• 12A. Bostan, L. Dumont, B. Salvy.
  
  Efficient Algorithms for Mixed Creative Telescoping, in: ISSAC 2016, Waterloo, Canada, Proceedings ISSAC'16, pp. 127–134, ACM Press, 2016., July 2016, 8 p. [ DOI : 10.1145/2930889.2930907 ]
  
  https://hal.inria.fr/hal-01317940
• 13A. Mahboubi, G. Melquiond, T. Sibut-Pinote.
  
  Formally Verified Approximations of Definite Integrals, in: Interactive Theorem Proving, Nancy, France, J. C. Blanchette, S. Merz (editors), Lecture Notes in Computer Science, August 2016, vol. 9807. [ DOI : 10.1007/978-3-319-43144-4_17 ]
  
  https://hal.inria.fr/hal-01289616

Scientific Books (or Scientific Book chapters)

• 14A. Bostan, F. Chyzak, M. Giusti, R. Lebreton, G. Lecerf, B. Salvy, E. Schost.
  
  Algorithmes Efficaces en Calcul Formel, January 2017, Cette version est la prépublication de l'ouvrage du même nom à paraître dans la collection https://hal.archives-ouvertes.fr/AECF/.
  
  https://hal.inria.fr/hal-01431717

Internal Reports

• 15G. Gonthier, A. Mahboubi, E. Tassi.
  
  A Small Scale Reflection Extension for the Coq system, Inria Saclay Ile de France, 2016, n^o RR-6455.
  
  https://hal.inria.fr/inria-00258384

Other Publications

• 16A. Bostan.
  
  Algebraicity and transcendence of power series: combinatorial and computational aspects, August 2016, Lecture.
  
  https://hal.inria.fr/cel-01391907
• 17F. Chyzak, T. Dreyfus, P. Dumas, M. Mezzarobba.
  
  Computing solutions of linear Mahler equations, 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01418653
• 18P. Dumas.
  
  Divide-and-Conquer Algebra and Analysis : Lecture given at Journées ALÉA 2016, March 2016, 80 p, Lecture.
  
  https://hal.inria.fr/cel-01388741
• 19H. Lombardi, A. Mahboubi.
  
  Théories géométriques pour l'algèbre des nombres réels, January 2017, working paper or preprint.
  
  https://hal.inria.fr/hal-01426164
• 20S. Maddah, M. A. Barkatou.
  
  Formal Solutions of Singularly Perturbed Linear Differential Systems, January 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01417265

References in notes

• 21M. Abramowitz, I. A. Stegun (editors)
  
  Handbook of mathematical functions with formulas, graphs, and mathematical tables, Dover, New York, 1992, xiv+1046 p, Reprint of the 1972 edition.
• 22Computer Algebra Errors, Article in mathematics blog MathOverflow.
  
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• 23F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark (editors)
  
  NIST Handbook of mathematical functions, Cambridge University Press, 2010.
• 24M. Armand, B. Grégoire, A. Spiwack, L. Théry.
  
  Extending Coq with Imperative Features and its Application to SAT Verication, in: Interactive Theorem Proving, international Conference, ITP 2010, Edinburgh, Scotland, July 11–14, 2010, Proceedings, Lecture Notes in Computer Science, Springer, 2010.
• 25B. Beckermann, G. Labahn.
  
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• 26A. Benoit, F. Chyzak, A. Darrasse, S. Gerhold, M. Mezzarobba, B. Salvy.
  
  The Dynamic Dictionary of Mathematical Functions (DDMF), in: The Third International Congress on Mathematical Software (ICMS 2010), K. Fukuda, J. van der Hoeven, M. Joswig, N. Takayama (editors), Lecture Notes in Computer Science, 2010, vol. 6327, pp. 35–41.
  
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• 27M. Boespflug, M. Dénès, B. Grégoire.
  
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• 28S. Boldo, C. Lelay, G. Melquiond.
  
  Improving Real Analysis in Coq: A User-Friendly Approach to Integrals and Derivatives, in: Certified Programs and Proofs, C. Hawblitzel, D. Miller (editors), Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2012, vol. 7679, pp. 289-304.
  
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• 29S. Boldo, G. Melquiond.
  
  Flocq: A Unified Library for Proving Floating-point Algorithms in Coq, in: Proceedings of the 20th IEEE Symposium on Computer Arithmetic, Tübingen, Germany, July 2011, pp. 243–252.
• 30A. Bostan.
  
  Algorithmes rapides pour les polynômes, séries formelles et matrices, in: Actes des Journées Nationales de Calcul Formel, Luminy, France, 2010, pp. 75–262, Les cours du CIRM, tome 1, numéro 2.
  
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• 31A. Bostan, S. Boukraa, S. Hassani, J.-M. Maillard, J.-A. Weil, N. Zenine.
  
  Globally nilpotent differential operators and the square Ising model, in: J. Phys. A: Math. Theor., 2009, vol. 42, n^o 12, 50 p.
  
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• 32A. Bostan, S. Chen, F. Chyzak, Z. Li.
  
  Complexity of creative telescoping for bivariate rational functions, in: ISSAC'10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, New York, NY, USA, ACM, 2010, pp. 203–210.
  
  http://doi.acm.org/10.1145/1837934.1837975
• 33A. Bostan, F. Chyzak, G. Lecerf, B. Salvy, É. Schost.
  
  Differential equations for algebraic functions, in: ISSAC'07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation, C. W. Brown (editor), ACM Press, 2007, pp. 25–32.
  
  http://dx.doi.org/10.1145/1277548.1277553
• 34A. Bostan, F. Chyzak, M. van Hoeij, L. Pech.
  
  Explicit formula for the generating series of diagonal 3D rook paths, in: Sém. Loth. Comb., 2011, vol. B66a, 27 p.
  
  http://www.emis.de/journals/SLC/wpapers/s66bochhope.html
• 35A. Bostan, L. Dumont, B. Salvy.
  
  Algebraic Diagonals and Walks, in: ISSAC'15 International Symposium on Symbolic and Algebraic Computation, Bath, United Kingdom, ACM Press, July 2015, pp. 77–84. [ DOI : 10.1145/2755996.2756663 ]
  
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• 36A. Bostan, M. Kauers.
  
  The complete generating function for Gessel walks is algebraic, in: Proceedings of the American Mathematical Society, September 2010, vol. 138, n^o 9, pp. 3063–3078, With an appendix by Mark van Hoeij.
• 37F. Chyzak.
  
  An extension of Zeilberger's fast algorithm to general holonomic functions, in: Discrete Math., 2000, vol. 217, n^o 1-3, pp. 115–134, Formal power series and algebraic combinatorics (Vienna, 1997).
• 38F. Chyzak, M. Kauers, 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, J. May (editor), 2009, pp. 111–118.
  
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• 39F. Chyzak, B. Salvy.
  
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• 40T. Coquand, G. P. Huet.
  
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• 41T. Coquand, C. Paulin-Mohring.
  
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• 42D. Delahaye, M. Mayero.
  
  Dealing with algebraic expressions over a field in Coq using Maple, in: J. Symbolic Comput., 2005, vol. 39, n^o 5, pp. 569–592, Special issue on the integration of automated reasoning and computer algebra systems.
  
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• 43F. Garillot, G. Gonthier, A. Mahboubi, L. Rideau.
  
  Packaging Mathematical Structures, in: Theorem Proving in Higher-Order Logics, S. Berghofer, T. Nipkow, C. Urban, M. Wenzel (editors), Lecture Notes in Computer Science, Springer, 2009, vol. 5674, pp. 327–342.
• 44J. von zur. Gathen, J. Gerhard.
  
  Modern computer algebra, 2nd, Cambridge University Press, New York, 2003, xiv+785 p.
• 45G. Gonthier.
  
  Formal proofs—the four-colour theorem, in: Notices of the AMS, 2008, vol. 55, n^o 11, pp. 1382-1393.
• 46G. Gonthier, A. Mahboubi.
  
  An introduction to small scale reflection in Coq, in: Journal of Formalized Reasoning, 2010, vol. 3, n^o 2, pp. 95–152.
• 47G. Gonthier, A. Mahboubi, E. Tassi.
  
  A Small Scale Reflection Extension for the Coq system, Inria, 2008, n^o RR-6455.
  
  http://hal.inria.fr/inria-00258384
• 48G. Gonthier, E. Tassi.
  
  A language of patterns for subterm selection, in: ITP, LNCS, 2012, vol. 7406, pp. 361–376.
• 49B. Grégoire, A. Mahboubi.
  
  Proving Equalities in a Commutative Ring Done Right in Coq, in: Theorem Proving in Higher Order Logics, 18th International Conference, TPHOLs 2005, Oxford, UK, August 22-25, 2005, Proceedings, Lecture Notes in Computer Science, Springer, 2005, vol. 3603, pp. 98–113.
• 50T. Hales.
  
  Formal proof, in: Notices of the AMS, 2008, vol. 55, n^o 11, pp. 1370-1380.
• 51J. Harrison.
  
  A HOL Theory of Euclidean space, in: Theorem Proving in Higher Order Logics, 18th International Conference, TPHOLs 2005, Oxford, UK, J. Hurd, T. Melham (editors), Lecture Notes in Computer Science, Springer-Verlag, 2005, vol. 3603.
• 52J. Harrison.
  
  Formalizing an analytic proof of the prime number theorem, in: Journal of Automated Reasoning, 2009, vol. 43, pp. 243–261, Dedicated to Mike Gordon on the occasion of his 60th birthday.
• 53J. Harrison.
  
  Theorem proving with the real numbers, CPHC/BCS distinguished dissertations, Springer, 1998.
• 54J. Harrison.
  
  A Machine-Checked Theory of Floating Point Arithmetic, in: Theorem Proving in Higher Order Logics: 12th International Conference, TPHOLs'99, Nice, France, Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin, L. Théry (editors), Lecture Notes in Computer Science, Springer-Verlag, 1999, vol. 1690, pp. 113–130.
• 55J. Harrison, L. Théry.
  
  A Skeptic's Approach to Combining HOL and Maple, in: J. Autom. Reason., December 1998, vol. 21, n^o 3, pp. 279–294.
  
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• 56F. Johansson.
  
  Another Mathematica bug, Article on personal blog.
  
  http://fredrik-j.blogspot.fr/2009/07/another-mathematica-bug.html
• 57C. Koutschan.
  
  A fast approach to creative telescoping, in: Math. Comput. Sci., 2010, vol. 4, n^o 2-3, pp. 259–266.
  
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• 58P. Lairez, T. Vaccon.
  
  On $p$-adic differential equations with separation of variables, in: ISSAC 2016, Waterloo, Canada, Proceedings ISSAC'16, pp. 127–134, ACM Press, 2016., July 2016, 8 p.
  
  http://dx.doi.org/10.1145/2930889.2930907
• 59A. Mahboubi.
  
  Implementing the cylindrical algebraic decomposition within the Coq system, in: Mathematical Structures in Computer Science, 2007, vol. 17, n^o 1, pp. 99–127.
• 60R. Matuszewski, P. Rudnicki.
  
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• 61M. Mayero.
  
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• 62M. Mezzarobba.
  
  NumGfun: a package for numerical and analytic computation and D-finite functions, in: ISSAC 2010—Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, New York, ACM, 2010, pp. 139–146.
  
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• 63P. Paule, M. Schorn.
  
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