Publications

[2005b] van Hoeij, Mark; Weil, Jacques-Arthur Solving second order differential equations with Klein’s theorem Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation (Beijing), ACM, New York, 2005.

[2005a] Cluzeau, Thomas; Barkatou, Moulay ; Weil, Jacques-Arthur Factoring Partial Differential Systems in Positive Characteristic Differential Equations with Symbolic Computation (D. Wang, Ed), Birkhauser, Basel Boston, 2005. 

[2004b] Maciejewski, Andrzej J.; Przybylska, Maria; Weil, Jacques-Arthur Non-integrability of the generalized spring-pendulum problem. J. Phys. A 37 (2004), no. 7, 2579--2597. 

[2004a] Compoint, É.; Weil, Jacques-Arthur Absolute reducibility of differential operators and Galois groups. J. Algebra 275 (2004), no. 1, 77--105

[2003] Boucher, Delphine; Weil, Jacques-Arthur Application of J.-J. Morales and J.-P. Ramis' theorem to test the non-complete integrability of the planar three-body problem. From combinatorics to dynamical systems, 163--177, IRMA Lect. Math. Theor. Phys., 3, de Gruyter, Berlin, 2003. 
An earlier, different, version of this paper was not published : A non-integrability criterion for Hamiltonian systems illustrated on the planar 3-body problem (2001)

[1999] van Hoeij, Mark; Ragot, Jean-François; Ulmer, Felix; Weil, Jacques-Arthur Liouvillian solutions of linear differential equations of order three and higher. Differential algebra and differential equations. J. Symbolic Comput. 28 (1999), no. 4-5, 589--609.

[1997b] Bronstein, Manuel; Mulders, Thom; Weil, Jacques-Arthur On symmetric powers of differential operators. Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), 156—163, ACM, New York, 1997.

[1997a] van Hoeij, Mark; Weil, Jacques-Arthur An algorithm for computing invariants of differential Galois groups. Algorithms for algebra (Eindhoven, 1996). J. Pure Appl. Algebra 117/118 (1997), 353--379.

[1996] Ulmer, Felix; Weil, Jacques-Arthur Note on Kovacic's algorithm. J. Symbolic Comput. 22 (1996), no. 2, 179—200.

[1995] Weil, Jacques-Arthur First integrals and Darboux polynomials of homogeneous linear differential systems. Applied algebra, algebraic algorithms and error-correcting codes (Paris, 1995), 469--484, Lecture Notes in Comput. Sci., 948, Springer, Berlin, 1995.

[1994] Weil, Jacques-Arthur The Use of the Special Semi-group for Solving Differential Equations. Proceedings of the 1994 International Symposium on Symbolic and Algebraic Computation (Oxford), ACM, New York, 1994.

Surveys, lectures, etc

• Jacques-Arthur Weil, Ariane Germa-Peladan, Francois Ollivier, et J-Albert Shih, Quelques approches algébriques effectives des phénomènes différentiels ``Images des mathématiques 1995'' (Eds: J-L Colliot-Thelene & F. Murat), éditions du CNRS.

• Calcul formel et équations différentielles linéaires (Notes d'exposés dans le cadre des conférences X-UPS 97)

• Felix Ulmer , J.A. Weil:Résolution d'équations differentielles linéaires par les fonctions usuelles
• Introduction to differential algebra and differential galois theory (Notes de cours pour une école du CIMPA à Hanoï,Vietnam, en décembre 2001)

Notes from talks

Equations differentielles lineaires et solutions Liouvilliennes (F. Ulmer, summary by J.A Weil)

Special polynomials of ordinary differential equations (J.A Weil, summary by B. salvy)

Absolute factorization of differential operators (E. Compoint & J.A Weil, summary by F. Chyzak)

Concrete resolution of differential problems using Tannakian categories (J.A Weil, summary by F. Chyzak)

Recent algorithms for solving second order differential equations (M. Berkenbosch, M. van Hoeij, J.A Weil, summary by M. Loday-Richaud)

Implementations

Implementations are realised in Maple. Please contact me for details.

PhD:
Constantes et polynômes de Darboux en algèbre différentielle : applications aux systèmes différentiels linéaires. (supervision: Jean Moulin Ollagnier). Slides