B. Adamczewski and J. Bell, Diagonalization and rationalization of algebraic Laurent series, Annales scientifiques de l'??cole normale sup??rieure, vol.46, issue.6, pp.963-1004, 2013.
DOI : 10.24033/asens.2207
URL : https://hal.archives-ouvertes.fr/hal-00698706

M. E. Alonso, F. J. Castro-jiménez, and H. Hauser, Encoding algebraic power series, pp.1403-4104

M. E. Alonso, T. Mora, and M. Raimondo, On the complexity of algebraic power series, Lecture Notes in Compt. Sci, vol.508, pp.197-207, 1990.
DOI : 10.1007/3-540-54195-0_51

M. Artin, Etale Coverings of Schemes Over Hensel Rings, American Journal of Mathematics, vol.88, issue.4, pp.915-934, 1966.
DOI : 10.2307/2373088

M. Artin, Algebraic approximation of structures over complete local rings, Publications math??matiques de l'IH??S, vol.35, issue.1, pp.23-58, 1969.
DOI : 10.1007/BF02684596

M. Aschenbrenner, An effective Weierstrass Division Theorem

J. Ax, On Schanuel's Conjectures, The Annals of Mathematics, vol.93, issue.2, pp.93-252, 1971.
DOI : 10.2307/1970774

D. Bertrand and F. Beukers, ??quations diff??rentielles lin??aires et majorations de multiplicit??s, Annales scientifiques de l'??cole normale sup??rieure, vol.18, issue.1, pp.181-192, 1985.
DOI : 10.24033/asens.1488

R. Cluckers and L. Lipshitz, Strictly convergent analytic structures, Journal of the European Mathematical Society, vol.19, issue.1, pp.1312-5932
DOI : 10.4171/JEMS/662

A. Galligo, Th??or??me de division et stabilit?? en g??om??trie analytique locale, Annales de l???institut Fourier, vol.29, issue.2, pp.107-184, 1979.
DOI : 10.5802/aif.745

H. Grauert, ???ber die deformation isolierter singularit???ten analytischer mengen, Inventiones Mathematicae, vol.3, issue.Number 5, pp.171-198, 1972.
DOI : 10.1007/BF01404124

H. Hauser and C. Koutschan, Multivariate linear recurrences and power series division, Discrete Math, pp.312-3553, 2012.

G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Mathematische Annalen, vol.95, issue.1, pp.736-788, 1926.
DOI : 10.1007/BF01206635

H. Hironaka, Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II, The Annals of Mathematics, vol.79, issue.2, pp.79-109, 1964.
DOI : 10.2307/1970547

H. Hironaka, Idealistic exponents of singularity, Algebraic Geometry, The John Hopkins Centennial Lectures, 1977.

C. Huneke and I. Swanson, Integral closure of ideals, rings, and modules, 2006.

]. S. Iz92a and . Izumi, Increase, convergence and vanishing of functions along a Moishezon space, J. Math. Kyoto Univ, vol.32, pp.245-258, 1992.

]. S. Iz92b and . Izumi, A criterion for algebraicity of analytic set germs, Proc. Japan Acad, pp.307-309, 1992.

]. S. Iz98 and . Izumi, Transcendence measures for subsets of local algebras, Real analytic and algebraic singularities, Pitman Res. Notes Math. Ser, vol.381, pp.189-206, 1996.

I. Kurkova and K. , On the functions counting walks with small steps in the quarter plane, Publications math??matiques de l'IH??S, vol.14, issue.1, pp.69-114, 2012.
DOI : 10.1007/s10240-012-0045-7
URL : https://hal.archives-ouvertes.fr/hal-00628424

L. Lipshitz, D-finite power series, Journal of Algebra, vol.122, issue.2, pp.353-373, 1989.
DOI : 10.1016/0021-8693(89)90222-6

L. Lipshitz and L. , A Gap Theorem for Power Series Solutions of Algebraic Differential Equations, American Journal of Mathematics, vol.108, issue.5, pp.1193-1213, 1986.
DOI : 10.2307/2374602

E. Mayr and A. Meyer, The complexity of the word problems for commutative semigroups and polynomial ideals, Advances in Mathematics, vol.46, issue.3, pp.305-329, 1982.
DOI : 10.1016/0001-8708(82)90048-2

Y. V. Nesterenko, Measures of algebraic independence of numbers and functions, Astérisque, pp.147-148, 1985.

K. Nishioka, On an estimate for the orders of zeros of Mahler type functions, Acta Arith, pp.249-256, 1990.

T. Mora, An algorithm to compute the equations of tangent cones, Lecture Notes in Comput. Sci, vol.144, pp.158-165, 1982.
DOI : 10.1007/3-540-11607-9_18

R. Ramanakoraisina, Complexit?? des fonctions de nash, Complexité des fonctions de Nash, pp.1395-1406, 1989.
DOI : 10.1090/S0002-9947-1986-0814925-3

P. Samuel, Algébricité de certains points singuliers algébroïdes, J. Math. Pures Appl, vol.35, pp.1-6, 1956.

A. Seidenberg, Constructions in algebra, Transactions of the American Mathematical Society, vol.197, pp.273-313, 1974.
DOI : 10.1090/S0002-9947-1974-0349648-2

A. Shidlovskii, On a criterion for the algebraic independence of the values of a class of entire functions, Izv. Akad. Nauk. S.S.S.R, vol.23, pp.35-66, 1959.

R. Stanley, Differentiably Finite Power Series, European Journal of Combinatorics, vol.1, issue.2, pp.175-188, 1980.
DOI : 10.1016/S0195-6698(80)80051-5