Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

1J. P. Bell, F. Chyzak, M. Coons, P. Dumas.

Becker's conjecture on Mahler functions, in: Transactions of the American Mathematical Society, 2018, 17 p, In press.

https://hal.inria.fr/hal-01885598
2P. Bürgisser, F. Cucker, P. Lairez.

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time, in: Journal of the ACM (JACM), December 2018, vol. 66, n^o 1, pp. 1-30. [ DOI : 10.1145/3275242 ]

https://hal.archives-ouvertes.fr/hal-01545657
3F. Chyzak, T. Dreyfus, P. Dumas, M. Mezzarobba.

Computing solutions of linear Mahler equations, in: Mathematics of Computation, July 2018, vol. 87, pp. 2977-3021. [ DOI : 10.1090/mcom/3359 ]

https://hal.inria.fr/hal-01418653
4A. Mahboubi, G. Melquiond, T. Sibut-Pinote.

Formally Verified Approximations of Definite Integrals, in: Journal of Automated Reasoning, March 2018, pp. 1-20. [ DOI : 10.1007/s10817-018-9463-7 ]

https://hal.inria.fr/hal-01630143

International Conferences with Proceedings

5A. Bostan, X. Caruso, G. Christol, P. Dumas.

Fast Coefficient Computation for Algebraic Power Series in Positive Characteristic, in: Thirteenth Algorithmic Number Theory Symposium ANTS-XIII, Madison, United States, Algorithmic Number Theory, July 2018, https://arxiv.org/abs/1806.06543.

https://hal.archives-ouvertes.fr/hal-01816375
6A. Bostan, F. Chyzak, P. Lairez, B. Salvy.

Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions, in: ISSAC 2018 - International Symposium on Symbolic and Algebraic Computation, New York, United States, July 2018, pp. 1-8. [ DOI : 10.1145/3208976.3208992 ]

https://hal.inria.fr/hal-01788619

Other Publications

7A. Bostan, M. Bousquet-Mélou, S. Melczer.

Counting walks with large steps in an orthant, May 2018, https://arxiv.org/abs/1806.00968 - working paper or preprint.

https://hal.archives-ouvertes.fr/hal-01802706
8A. Bostan, T. Krick, A. Szanto, M. Valdettaro.

Subresultants of ${(x - α)}^{m}$ and ${(x - β)}^{n}$ , Jacobi polynomials and complexity, December 2018, working paper or preprint.

https://hal.archives-ouvertes.fr/hal-01966640
9F. Chyzak, K. Yeats.

Bijections between Łukasiewicz walks and generalized tandem walks, October 2018, working paper or preprint.

https://hal.inria.fr/hal-01891792
10P. Lairez, E. Can Sertöz.

A numerical transcendental method in algebraic geometry, November 2018, working paper or preprint.

https://hal.archives-ouvertes.fr/hal-01932147

References in notes

11M. 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.
12Computer Algebra Errors, Article in mathematics blog MathOverflow.

http://mathoverflow.net/questions/11517/computer-algebra-errors
13F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark (editors)

NIST Handbook of mathematical functions, Cambridge University Press, 2010.
14M. 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.
15B. 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.
16A. 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.

http://dx.doi.org/10.1007/978-3-642-15582-6_7
17M. 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.
18S. 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.

http://dx.doi.org/10.1007/978-3-642-35308-6_22
19S. 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.
20A. 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.

http://ccirm.cedram.org:80/ccirm-bin/fitem?id=CCIRM_2010__1_2_75_0
21A. 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
22A. 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
23A. 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
24A. 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
25A. 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.
26F. 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).
27F. 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
28F. 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.
29T. Coquand, G. P. Huet.

The Calculus of Constructions, in: Inf. Comput., 1988, vol. 76, n^o 2/3, pp. 95-120.

http://dx.doi.org/10.1016/0890-5401(88)90005-3
30T. Coquand, C. Paulin-Mohring.

Inductively defined types, in: Proceedings of Colog'88, P. Martin-Löf, G. Mints (editors), Lecture Notes in Computer Science, Springer-Verlag, 1990, vol. 417.
31D. 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.

http://dx.doi.org/10.1016/j.jsc.2004.12.004
32F. 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.
33J. von zur. Gathen, J. Gerhard.

Modern computer algebra, 2nd, Cambridge University Press, New York, 2003, xiv+785 p.
34G. Gonthier.

Formal proofs—the four-colour theorem, in: Notices of the AMS, 2008, vol. 55, n^o 11, pp. 1382-1393.
35G. 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.
36G. 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
37G. Gonthier, E. Tassi.

A language of patterns for subterm selection, in: ITP, LNCS, 2012, vol. 7406, pp. 361–376.
38B. 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.
39T. Hales.

Formal proof, in: Notices of the AMS, 2008, vol. 55, n^o 11, pp. 1370-1380.
40J. 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.
41J. 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.
42J. Harrison.

Theorem proving with the real numbers, CPHC/BCS distinguished dissertations, Springer, 1998.
43J. 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.
44J. 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
45F. Johansson.

Another Mathematica bug, 2009, Article on personal blog.

http://fredrik-j.blogspot.fr/2009/07/another-mathematica-bug.html
46C. 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
47A. 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.
48R. Matuszewski, P. Rudnicki.

Mizar: the first 30 years, in: Mechanized Mathematics and Its Applications, 2005, vol. 4.
49M. Mayero.

Problèmes critiques et preuves formelles, Université Paris 13, novembre 2012, Habilitation à Diriger des Recherches.
50M. 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.

http://dx.doi.org/10.1145/1837934.1837965
51P. Paule, M. Schorn.

A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities, in: J. Symbolic Comput., 1995, vol. 20, n^o 5-6, pp. 673–698, Symbolic computation in combinatorics $Δ_{1}$ (Ithaca, NY, 1993).

http://dx.doi.org/10.1006/jsco.1995.1071
52B. Petersen.

Maple, Personal web site.
53P. Rudnicki, A. Trybulec.

On the Integrity of a Repository of Formalized Mathematics, in: Proceedings of the Second International Conference on Mathematical Knowledge Management, London, UK, MKM '03, Springer-Verlag, 2003, pp. 162–174.

http://dl.acm.org/citation.cfm?id=648071.748518
54B. Salvy, P. Zimmermann.

Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable, in: ACM Trans. Math. Software, 1994, vol. 20, n^o 2, pp. 163–177.
55N. J. A. Sloane, S. Plouffe.

The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995.
56The Coq Development Team.

The Coq Proof Assistant: Reference Manual.

http://coq.inria.fr/doc/
57The Mathematical Component Team.

A Formalization of the Odd Order Theorem using the Coq proof assistant, September 2012.

http://www.msr-inria.fr/projects/mathematical-components/
58L. Théry.

A Machine-Checked Implementation of Buchberger's Algorithm, in: J. Autom. Reasoning, 2001, vol. 26, n^o 2, pp. 107-137.

http://dx.doi.org/10.1023/A:1026518331905
59K. Wegschaider.

Computer generated proofs of binomial multi-sum identities, RISC, J. Kepler University, May 1997, 99 p.
60S. Wolfram.

Mathematica: A system for doing mathematics by computer (2nd ed.), Addison-Wesley, 1992.
61D. Zeilberger.

Opinion 94: The Human Obsession With “Formal Proofs” is a Waste of the Computer's Time, and, Even More Regretfully, of Humans' Time, 2009.

http://www.math.rutgers.edu/~zeilberg/Opinion94.html
62D. Zeilberger.

A holonomic systems approach to special functions identities, in: J. Comput. Appl. Math., 1990, vol. 32, n^o 3, pp. 321–368.
63D. Zeilberger.

The method of creative telescoping, in: J. Symbolic Comput., 1991, vol. 11, n^o 3, pp. 195–204.

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