Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

• 1A. Bostan, S. Boukraa, J.-M. Maillard, J.-A. Weil.
  
  Diagonals of rational functions and selected differential Galois groups, in: Journal of Physics A: Mathematical and Theoretical, December 2015, vol. 48, n^o 50, pp. 504001–504030. [ DOI : 10.1088/1751-8113/48/50/504001 ]
  
  https://hal.archives-ouvertes.fr/hal-01242668
• 2A. Bostan, M. Bousquet-Mélou, M. Kauers, S. Melczer.
  
  On 3-dimensional lattice walks confined to the positive octant, in: Annals of Combinatorics, March 2015, 36 p, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-01063886
• 3A. Bostan, I. Kurkova, K. Raschel.
  
  A human proof of Gessel's lattice path conjecture, in: Transactions of the American Mathematical Society, October 2015, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-00858083
• 4P. Lairez.
  
  Computing periods of rational integrals, in: Mathematics of Computation, 2015, 34 p, forthcoming.
  
  https://hal.inria.fr/hal-00981114

International Conferences with Proceedings

• 5B. Barras, C. Tankink, E. Tassi.
  
  Asynchronous processing of Coq documents: from the kernel up to the user interface, in: Proceedings of ITP, Nanjing, China, August 2015.
  
  https://hal.inria.fr/hal-01135919
• 6A. Bostan, X. Caruso, É. Schost.
  
  A Fast Algorithm for Computing the p-Curvature, in: ISSAC 2015, Bath, United Kingdom, ACM Press, July 2015, pp. 69–76. [ DOI : 10.1145/2755996.2756674 ]
  
  https://hal.archives-ouvertes.fr/hal-01164471
• 7A. 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 ]
  
  https://hal.archives-ouvertes.fr/hal-01240729
• 8D. Rouhling, M. Farooque, S. Graham-Lengrand, J.-M. Notin, A. Mahboubi.
  
  Axiomatic constraint systems for proof search modulo theories, in: 10th International Symposium on Frontiers of Combining Systems (FroCoS'15), Wroclaw, Poland, C. Lutz, S. Ranise (editors), LNAI, Springer, September 2015, vol. 9322. [ DOI : 10.1007/978-3-319-24246-0_14 ]
  
  https://hal.inria.fr/hal-01107944

Scientific Books (or Scientific Book chapters)

• 9P. Nicodeme (editor)
  
  Nablus2014 CIMPA Summer School, Proceedings of the Nablus2014 CIMPA Summer School, Pierre Nicodeme and Naji Qatanani, Nablus, Palestinian Territories, December 2015, 138 p.
  
  https://hal.archives-ouvertes.fr/hal-01214113

Internal Reports

• 10G. Gonthier, A. Mahboubi, E. Tassi.
  
  A Small Scale Reflection Extension for the Coq system, Inria Saclay Ile de France, 2015, n^o RR-6455.
  
  https://hal.inria.fr/inria-00258384

Scientific Popularization

• 11A. Bostan, K. Raschel.
  
  Compter les excursions sur un échiquier, in: Pour la science, March 2015, n^o 449, pp. 40–46.
  
  https://hal.archives-ouvertes.fr/hal-01246339

Other Publications

• 12A. Bostan.
  
  Computer Algebra for Lattice Path Combinatorics, March 2015, Lecture.
  
  https://hal.archives-ouvertes.fr/cel-01242698
• 13A. Bostan, L. Dumont, B. Salvy.
  
  Algebraic Diagonals and Walks: Algorithms, Bounds, Complexity, October 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01244914
• 14A. Bostan, P. Lairez, B. Salvy.
  
  Multiple binomial sums, October 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01220573

References in notes

• 15M. 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.
• 16Computer Algebra Errors, Article in mathematics blog MathOverflow.
  
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• 17F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark (editors)
  
  NIST Handbook of mathematical functions, Cambridge University Press, 2010.
• 18M. 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.
• 19B. Beckermann, G. Labahn.
  
  A uniform approach for the fast computation of matrix-type Padé approximants, in: SIAM J. Matrix Anal. Appl., 1994, vol. 15, n^o 3, pp. 804–823.
• 20A. 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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• 21M. Boespflug, M. Dénès, B. Grégoire.
  
  Full reduction at full throttle, in: First International Conference on Certified Programs and Proofs, Taiwan, December 7–9, Lecture Notes in Computer Science, Springer, 2011.
• 22S. 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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• 23S. 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.
• 24A. 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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• 25A. 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.
  
  http://dx.doi.org/10.1088/1751-8113/42/12/125206
• 26A. 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
• 27A. 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
• 28A. 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
• 29A. Bostan, G. Chèze, T. Cluzeau, J.-A. Weil.
  
  Efficient Algorithms for Computing Rational First Integrals and Darboux Polynomials of Planar Polynomial Vector Fields, in: Mathematics of Computation, December 2014, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-00871663
• 30A. 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.
• 31A. Bostan, P. Lairez, B. Salvy.
  
  Creative telescoping for rational functions using the Griffiths-Dwork method, in: ISSAC'13 - 38th International Symposium on Symbolic and Algebraic Computation, Boston, United States, Northeastern University, Boston, Massachusetts, USA, 2013, pp. 93-100. [ DOI : 10.1145/2465506.2465935 ]
  
  http://hal.inria.fr/hal-00777675
• 32F. 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).
• 33F. 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.
  
  http://dx.doi.org/10.1145/1576702.1576720
• 34F. Chyzak, B. Salvy.
  
  Non-commutative elimination in Ore algebras proves multivariate identities, in: J. Symbolic Comput., 1998, vol. 26, n^o 2, pp. 187–227.
• 35T. Coquand, G. P. Huet.
  
  The Calculus of Constructions, in: Inf. Comput., 1988, vol. 76, n^o 2/3, pp. 95-120.
  
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• 36T. Coquand, C. Paulin-Mohring.
  
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• 37D. 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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• 38F. 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.
• 39J. von zur. Gathen, J. Gerhard.
  
  Modern computer algebra, 2nd, Cambridge University Press, New York, 2003, xiv+785 p.
• 40G. Gonthier.
  
  Formal proofs—the four-colour theorem, in: Notices of the AMS, 2008, vol. 55, n^o 11, pp. 1382-1393.
• 41G. 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.
• 42G. 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
• 43G. Gonthier, E. Tassi.
  
  A language of patterns for subterm selection, in: ITP, LNCS, 2012, vol. 7406, pp. 361–376.
• 44B. 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.
• 45T. Hales.
  
  Formal proof, in: Notices of the AMS, 2008, vol. 55, n^o 11, pp. 1370-1380.
• 46J. 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.
• 47J. 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.
• 48J. Harrison.
  
  Theorem proving with the real numbers, CPHC/BCS distinguished dissertations, Springer, 1998, I p.
• 49J. 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.
• 50J. 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.
  
  http://dx.doi.org/10.1023/A:1006023127567
• 51F. Johansson.
  
  Another Mathematica bug, Article on personal blog.
  
  http://fredrik-j.blogspot.fr/2009/07/another-mathematica-bug.html
• 52C. Koutschan.
  
  A fast approach to creative telescoping, in: Math. Comput. Sci., 2010, vol. 4, n^o 2-3, pp. 259–266.
  
  http://dx.doi.org/10.1007/s11786-010-0055-0
• 53P. Lairez.
  
  Periods of rational integrals : algorithms and applications, École polytechnique, November 2014.
  
  https://pastel.archives-ouvertes.fr/tel-01089130
• 54A. 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.
• 55R. Matuszewski, P. Rudnicki.
  
  Mizar: the first 30 years, in: Mechanized Mathematics and Its Applications, 2005, vol. 4.
• 56M. Mayero.
  
  Problèmes critiques et preuves formelles, Université Paris 13, novembre 2012, Habilitation à Diriger des Recherches.
• 57M. 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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• 58P. Paule, M. Schorn.
  
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• 59B. Petersen.
  
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• 61B. Salvy, P. Zimmermann.
  
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• 62N. J. A. Sloane, S. Plouffe.
  
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• 63The Coq Development Team.
  
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  A Formalization of the Odd Order Theorem using the Coq proof assistant, September 2012.
  
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• 65L. Théry.
  
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• 66K. Wegschaider.
  
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