@incollection{XUPS_1997____31_0, author = {Jacques-Arthur Weil}, title = {Calcul formel pour les~\'equations~diff\'erentielles~lin\'eaires}, booktitle = {Calcul formel}, series = {Journ\'ees math\'ematiques X-UPS}, pages = {31--53}, publisher = {Les \'Editions de l{\textquoteright}\'Ecole polytechnique}, year = {1997}, doi = {10.5802/xups.1997-02}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/xups.1997-02/} }
TY - JOUR AU - Jacques-Arthur Weil TI - Calcul formel pour les équations différentielles linéaires JO - Journées mathématiques X-UPS PY - 1997 SP - 31 EP - 53 PB - Les Éditions de l’École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/xups.1997-02/ DO - 10.5802/xups.1997-02 LA - fr ID - XUPS_1997____31_0 ER -
%0 Journal Article %A Jacques-Arthur Weil %T Calcul formel pour les équations différentielles linéaires %J Journées mathématiques X-UPS %D 1997 %P 31-53 %I Les Éditions de l’École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/xups.1997-02/ %R 10.5802/xups.1997-02 %G fr %F XUPS_1997____31_0
Jacques-Arthur Weil. Calcul formel pour les équations différentielles linéaires. Journées mathématiques X-UPS (1997), pp. 31-53. doi : 10.5802/xups.1997-02. https://proceedings.centre-mersenne.org/articles/10.5802/xups.1997-02/
[1] S. A. Abramov; K. Yu. Kvansenko Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients, ISSAC ’91. Proceedings of the 1991 international symposium on symbolic and algebraic computation (Bonn, 1991), ACM Press, New York, NY, 1991, pp. 267-270 | DOI | Zbl
[2] Sergei A. Abramov; Manuel Bronstein; Marko Petkovšek On polynomial solutions of linear operator equations, ISSAC ’95. Proceedings of the 1995 international symposium on symbolic and algebraic computation, Association for Computing Machinery, New York, NY, 1995, p. 290–296 | DOI | Zbl
[3] Frits Beukers Differential Galois theory, From number theory to physics (Les Houches, 1989), Springer, Berlin, 1992, pp. 413-439 | DOI | MR | Zbl
[4] Manuel Bronstein On solutions of linear ordinary differential equations in their coefficient field, J. Symb. Comput., Volume 13 (1992) no. 4, pp. 413-439 | DOI | MR | Zbl
[5] Manuel Bronstein Symbolic integration. I. Transcendental Functions, Algorithms and Computation in Math., 1, Springer-Verlag, Berlin, 2005
[6] Manuel Bronstein; Thom Mulders; Jacques-Arthur Weil On symmetric powers of differential operators, Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), ACM, New York, 1997, pp. 156-163 | DOI | Zbl
[7] Winfried Fakler On second order homogeneous linear differential equations with Liouvillian solutions, Theoret. Comput. Sci., Volume 187 (1997) no. 1-2, pp. 27-48 Computer algebra (Saint-Louis, 1996) | DOI | MR | Zbl
[8] K. O. Geddes; S. R. Czapor; G. Labahn Algorithms for computer algebra, Kluwer Academic Publishers, Boston, MA, 1992 | DOI
[9] Peter A. Hendriks; Marius van der Put Galois action on solutions of a differential equation, J. Symb. Comput., Volume 19 (1995) no. 6, pp. 559-576 | DOI | MR | Zbl
[10] Irving Kaplansky An introduction to differential algebra., Hermann, Paris, 1996
[11] E. R. Kolchin Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. (2), Volume 49 (1948), pp. 1-42 | DOI | MR | Zbl
[12] Ellis Kolchin Direct and inverse problems in differential Galois theory, Selected works of Ellis Kolchin with commentary, American Mathematical Society, Providence, RI, 1999 | Zbl
[13] Jerald J. Kovacic An algorithm for solving second order linear homogeneous differential equations, J. Symbolic Comput., Volume 2 (1986) no. 1, pp. 3-43 | DOI | MR | Zbl
[14] F. Marotte Les équations différentielles linéaires et la théorie des groupes., Ann. Fac. Sci. Toulouse Math. (1), Volume 12 (1898), p. h1-h92 | DOI | Numdam | MR | Zbl
[15] Marius van der Put Symbolic analysis of differential equations, Some tapas of computer algebra, Springer, Berlin, 1999, pp. 208-236 | DOI | Zbl
[16] Maxwell Rosenlicht Integration in finite terms, Amer. Math. Monthly, Volume 79 (1972), pp. 963-972 | DOI | MR | Zbl
[17] Michael F. Singer Liouvillian solutions of th order homogeneous linear differential equations, Amer. J. Math., Volume 103 (1981) no. 4, pp. 661-682 | DOI | Zbl
[18] Michael F. Singer An outline of differential Galois theory, Computer algebra and differential equations (Comput. Math. Appl.), Academic Press, London, 1990, pp. 3-57 | MR
[19] Michael F. Singer; Felix Ulmer Galois groups of second and third order linear differential equations, J. Symbolic Comput., Volume 16 (1993) no. 1, pp. 9-36 | DOI | MR | Zbl
[20] Michael F. Singer; Felix Ulmer Liouvillian and algebraic solutions of second and third order linear differential equations, J. Symbolic Comput., Volume 16 (1993) no. 1, pp. 37-73 | DOI | MR | Zbl
[21] Michael F. Singer; Felix Ulmer Linear differential equations and products of linear forms, J. Pure Appl. Algebra, Volume 117/118 (1997), pp. 549-563 Algorithms for algebra (Eindhoven, 1996) | DOI | MR | Zbl
[22] Felix Ulmer; Jacques-Arthur Weil Note on Kovacic’s algorithm, J. Symbolic Comput., Volume 22 (1996) no. 2, pp. 179-200 | DOI | MR | Zbl
[23] J.-A. Weil; A. Germa-Péladan; F. Ollivier; J.A. Shih Quelques approches algébriques effectives des phénomènes différentiels, Images des Mathématiques (F. Murat; J.-L. Colliot-Thélène, eds.), Éditions du CNRS, 1995
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