G. Almkvist, The art of finding Calabi-Yau differential equations In: Gems in experimental mathematics, Contemp. Math. Providence, RI: Amer. Math. Soc, vol.517, pp.1-18, 2010.

G. Almkvist, C. Van-enckevort, D. Van-straten, and W. Zudilin, Tables of Calabi?Yau equations. arXiv:math/0507430, 2010.

M. Apagodu and D. Zeilberger, Multi-variable Zeilberger and Almkvist???Zeilberger algorithms and the sharpening of Wilf???Zeilberger theory, Advances in Applied Mathematics, vol.37, issue.2, pp.139-152, 2006.
DOI : 10.1016/j.aam.2005.09.003

V. Batyrev and M. Kreuzer, Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions, Advances in Theoretical and Mathematical Physics, vol.14, issue.3, pp.879-898, 2010.
DOI : 10.4310/ATMP.2010.v14.n3.a3

V. Batyrev and D. Van-straten, Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties, Communications in Mathematical Physics, vol.1, issue.2, pp.493-533, 1995.
DOI : 10.1007/BF02101841

W. Bosma, J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Computational algebra and number theory, pp.3-4, 1993.
DOI : 10.1006/jsco.1996.0125

A. Bostan, S. Chen, F. Chyzak, and Z. Li, Complexity of creative telescoping for bivariate rational functions, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, pp.203-210, 2010.
DOI : 10.1145/1837934.1837975
URL : https://hal.archives-ouvertes.fr/hal-00780066

A. Bostan, P. Lairez, and B. Salvy, Creative telescoping for rational functions using the Griffiths?Dwork method, Proceedings of the 38 th international symposium on symbolic and algebraic computation. ISSAC '13, pp.93-100, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00777675

N. Bourbaki, Algèbres tensorielles, algèbres extérieures, algèbres symétriques, Algèbre. Éléments de mathématiques. Hermann, 1961.

M. Bousquet-mélou and M. Mishna, Walks with small steps in the quarter plane, In: Algorithmic probability and combinatorics. Contemp. Math. Providence, RI: Amer. Math. Soc, vol.520, pp.1-39, 2010.
DOI : 10.1090/conm/520/10252

S. Chen, M. Kauers, and M. F. Singer, Telescopers for rational and algebraic functions via residues, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.130-137
DOI : 10.1145/2442829.2442851

F. Chyzak, An extension of Zeilberger's fast algorithm to general holonomic functions Formal power series and algebraic combinatorics, In: Discrete Math, vol.217, pp.1-3, 1997.

F. Chyzak, The ABC of Creative Telescoping: Algorithms, Bounds, Complexity. Mémoire d'habilitation à diriger les recherches, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01069831

A. David, S. Cox, and . Katz, Mirror symmetry and algebraic geometry . Mathematical Surveys and Monographs 68, 1999.

D. A. Cox, J. Little, and D. O. Shea, Using algebraic geometry. GTM, 1998.
DOI : 10.1007/978-1-4757-6911-1

P. Deligne, Lettre à Bernard Malgrange, 1991.

A. Dimca, On the de Rham cohomology of a hypersurface complement, In: Amer. J. Math, vol.1134, pp.763-771, 1991.

A. Dimca, On the Milnor fibrations of weighted homogeneous polynomials, In: Compositio Math, vol.761, issue.2, pp.19-47, 1990.
DOI : 10.1007/978-94-009-0685-3_3

A. Dimca, Singularities and topology of hypersurfaces, p.263, 1992.
DOI : 10.1007/978-1-4612-4404-2

A. Dimca and M. Saito, A generalization of Griffiths's theorem on rational integrals, Duke Mathematical Journal, vol.135, issue.2, pp.303-326, 2006.
DOI : 10.1215/S0012-7094-06-13523-8

B. Dwork, On the zeta function of a hypersurface, Publications math??matiques de l'IH??S, vol.23, issue.1, pp.5-68, 1962.
DOI : 10.1007/BF02684275

B. Dwork, On the zeta function of a hypersurface, Publications math??matiques de l'IH??S, vol.23, issue.1, pp.227-299, 1964.
DOI : 10.1007/BF02684275

L. Euler, Specimen de constructione aequationum differentialium sine indeterminatarum separatione " . In: Commentarii academiae scientiarum Petropolitanae 6 (1733). (Opera omnia, 1 e série, pp.168-174

M. C. Fasenmyer, Some generalized hypergeometric polynomials, Bulletin of the American Mathematical Society, vol.53, issue.8, pp.806-812, 1947.
DOI : 10.1090/S0002-9904-1947-08893-5

J. Von, Z. Gathen, and J. Gerhard, Modern computer algebra, p.753, 1999.

A. Phillip and . Griffiths, On the periods of certain rational integrals, Ann. of Math, vol.90, pp.460-541, 1969.

A. Grothendieck, On the de rham cohomology of algebraic varieties, Publications math??matiques de l'IH??S, vol.VI, issue.1, pp.95-103, 1966.
DOI : 10.1007/BF02684807

C. Hermite, Sur l'int??gration des fractions rationnelles, Annales scientifiques de l'??cole normale sup??rieure, vol.1, pp.215-218, 1872.
DOI : 10.24033/asens.82

. Mark-van-hoeij, Factorization of Differential Operators with Rational Functions Coefficients, Journal of Symbolic Computation, vol.24, issue.5, pp.537-561, 1997.
DOI : 10.1006/jsco.1997.0151

M. Nicholas and . Katz, Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin, In: Inst. Hautes Études Sci. Publ. Math, vol.39, pp.175-232, 1970.

M. Kauers and D. Zeilberger, The computational challenge of enumerating high-dimensional rook walks, Advances in Applied Mathematics, vol.47, issue.4, pp.813-819, 2011.
DOI : 10.1016/j.aam.2011.03.004

C. Koutschan, A Fast Approach to Creative Telescoping, Mathematics in Computer Science, vol.32, issue.3, pp.2-3, 2010.
DOI : 10.1007/s11786-010-0055-0

B. Malgrange, Lettre à Pierre Deligne, 1991.

H. Matsumura, Commutative algebra Mathematics Lecture Note Series, p.313, 1980.

P. Metelitsyn, How to compute the constant term of a power of a Laurent polynomial efficiently, 2012.

P. Monsky, Finiteness of De Rham Cohomology, American Journal of Mathematics, vol.94, issue.1, pp.237-245, 1972.
DOI : 10.2307/2373603

R. David and . Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces " . In: Essays on mirror manifolds, pp.241-264, 1992.

R. David, J. Morrison, and . Walcher, D-branes and normal functions, In: Adv. Theor. Math. Phys, vol.13, issue.2, pp.553-598, 2009.

T. Oaku and N. Takayama, An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation Effective methods in algebraic geometry, In: J. Pure Appl. Algebra, vol.139, pp.1-3, 1998.

É. Picard, Sur les intégrales doubles de fonctions rationnelles dont tous les résidus sont nuls, Bulletin des sciences mathématiques, p.26, 1902.

É. Picard and G. Simart, Théorie des fonctions algébriques de deux variables indépendantes, I. Gauthier-Villars et fils, 1897.

É. Picard and G. Simart, Théorie des fonctions algébriques de deux variables indépendantes, II. Gauthier-Villars et fils, 1906.

. Duco-van-straten, Calabi-Yau Operators Database

P. Verbaeten, The automatic construction of pure recurrence relations, ACM SIGSAM Bulletin, vol.8, issue.3, pp.96-98, 1974.
DOI : 10.1145/1086837.1086854

S. Herbert, D. Wilf, and . Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and " q " ) multisum/integral identities, In: Invent. Math, vol.1083, pp.575-633, 1992.

D. Zeilberger, The method of creative telescoping, Journal of Symbolic Computation, vol.11, issue.3, pp.195-204, 1991.
DOI : 10.1016/S0747-7171(08)80044-2

I. Saclay and . Équipe-specfun, France Current address: Pierre Lairez ? Fäk. II, Sekr. 3-2 ? Technische Universität zu Berlin ? Straße des 17