Computer Algebra   Writing Symmetry Paper     

Jacques-Arthur Weil : Publications

Preprints (2015)

• Guy Casale and Jacques-Arthur Weil. Galoisian Methods for Testing Irreducibility of Order Two Nonlinear Differential Equations. April 2015. Submitted. ArXiv:1504.08134

Research Papers

Note : ISSAC (international symposium on Symbolic and algebraic computation) is the main international conference in Computer Algebra.
Papers are refereed and competitively selected : a publication at this conference is considered as a journal publication.

   2016
• Ainhoa Aparicio, Thomas Dreyfus and Jacques-Arthur Weil. Liouville Integrability: an Effective Morales-Ramis-Sim\'o Theorem.  Journal of Symbolic Computation, Volume 74, May–June 2016, Pages 537–560. ArXiv:1505.02808
 
   2015
• A. Bostan, S. Boukraa, J-M. Maillard, J-A. Weil. Diagonals of rational functions and selected differential Galois groupsarXiv:1507.03227 Journal of Physics A: Mathematical and Theoretical, 48(50):504001, 2015.

• David Bl\'azquez-Sanz, Juan Jos\'e Morales-Ruiz, Jacques-Arthur Weil. Differential Galois theory and Lie symmetries. SIGMA 11 (2015), 092, 17 pages. ArXiv:1503.09023

• Alin Bostan, Guillaume Chèze, Thomas Cluzeau, and Jacques-Arthur Weil. Efficient Algorithms for Computing Rational First Integrals and Darboux Polynomials of Planar Polynomial Vector Fields. Math of Comp. 2015.
http://dx.doi.org/10.1090/mcom/3007
http://dx.doi.org/10.1090/mcom/3007
http://dx.doi.org/10.1090/mcom/3007.
http://dx.doi.org/10.1090/mcom/3007    (Preprint, Oct. 2013: arXiv:1310.2778 )

• S. Boukraa, S. Hassani, J.-M. Maillard, and J.-A. Weil. Canonical decomposition of irreducible linear di fferential operators with symplectic or orthogonal di fferential Galois groups. Journal of Physics A: Mathematical and Theoretical, 48(10):105202, 2015 arXiv:1407.5541

    2014
• S. Boukraa, S. Hassani, J.-M. Maillard, and J.-A. Weil. Differential algebra on lattice green and calabi-yau operators. J. Phys. A: Math. Theor., 47(9):095203, March 2014.  arXiv:1311.2470v2
  
     2013
• Ainhoa Aparicio Monforte, Élie Compoint, and Jacques-Arthur Weil. A characterization of reduced forms of linear differential systems.  Journal of Pure and Applied Algebra, 217(8):1504–1516, March 2013. ArXiv:1206.6661

     2012
• Ainhoa Aparicio-Monforte and Jacques-Arthur Weil. A reduced form for linear differential systems and its application to integrability of hamiltonian systems. Journal of Symbolic Computation, 47(2):192 – 213, 2012. doi:10.1016/j.jsc.2011.09.011

• Moulay A. Barkatou, Thomas Cluzeau, Carole El Bacha, and Jacques-Arthur Weil. Computing closed form solutions of integrable connections. In Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '12, New York, NY, USA, 2012. ACM.

     2011
• Ainhoa Aparicio-Monforte and Jacques-Arthur Weil. A reduction method for higher order variational equations of hamiltonian systems. In Symmetries and Related Topics in Differential and Difference Equations, volume 549 of Contemporary Mathematics, pages 1-15. Amer. Math. Soc., Providence, RI, September 2011
• Ainhoa Aparicio-Monforte, Moulay A. Barkatou, Sergi Simon, and Jacques-Arthur Weil. Formal first integrals along solutions of differential systems i. In Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pages 19-26, New York, NY, USA, 2011. ACM.
• Primitivo B. Acosta-Humanez, Juan J. Morales-Ruiz, and Jacques-Arthur Weil. Galoisian approach to integrability of schrödinger equation.Reports on Mathematical Physics, 67(3):305 - 374, 2011.

• A. Bostan, S. Boukraa, S. Hassani, M. van Hoeij, J.-M. Maillard, J.-A. Weil, and N. Zenine. The Ising model: from elliptic curves to modular forms and Calabi-Yau equations. J. Phys. A, 44(4):045204, 44, 2011.
   
         2010
• Elie Compoint, Marius van der Put, and Jacques-Arthur Weil. Effective descent for differential operators. J. Algebra, 324(1):146-158, 2010.
• O. Pujol, J. P. Pérez, J. P. Ramis, C. Simó, S. Simon, and J. A. Weil. Swinging atwood machine: experimental and numerical results, and a theoretical study. Physica D: Nonlinear Phenomena, 239(12):1067-1081, 2010.
• A. Bostan, S. Boukraa, S. Hassani, J.-M. Maillard, J.-A. Weil, N. Zenine, and N. Abarenkova. Renormalization, isogenies, and rational symmetries of differential equations. Adv. Math. Phys., pages Art. ID 941560, 44p, 2010.

         2009
• A. Bostan, S. Boukraa, S. Hassani, J.-M. Maillard, J.-A. Weil, and N. Zenine. Globally nilpotent differential operators and the square Ising model. J. Phys. A, 42(12):125206, 50, 2009.
• Delphine Boucher and Jacques-Arthur Weil. About the non-integrability in the friedmann-robertson-walker cosmological model. Braz. J. Phys., 37(2a):398-405, 2007.
• S. Boukraa, S. Hassani, J.-M. Maillard, B. M. McCoy, J.-A. Weil, and N. Zenine. Fuchs versus Painlevé. J. Phys. A, 40(42):12589-12605, 2007.

• S. Boukraa, S. Hassani, J.-M. Maillard, B. M. McCoy, J.-A. Weil, and N. Zenine. Painlevé versus Fuchs. J. Phys. A, 39(39):12245-12263, 2006.

• Mark van Hoeij and Jacques-Arthur Weil. Solving second order differential equations with klein's theorem. In ISSAC 2005 (Beijing). ACM, New York, 2005.
        Elaborated after joint work with Maint Berkenbosch on his PhD.

• Moulay A. Barkatou, Thomas Cluzeau, and Jacques-Arthur Weil. Factoring partial differential systems in positive characteristic (With an appendix by Marius van der Put). sIn Differential equations with symbolic computation, Trends Math., pages 213-238. Birkhäuser, Basel, 2005.

• Elie Compoint and Jacques-Arthur Weil. Absolute reducibility of differential operators and Galois groups. J. Algebra, 275(1):77-105, 2004.
• Andrzej J. Maciejewski, Maria Przybylska, and Jacques-Arthur Weil. Non-integrability of the generalized spring-pendulum problem. J. Phys. A, 37(7):2579-2597, 2004.
• Delphine Boucher and Jacques-Arthur Weil. Application of J.-J. Morales and J.-P. Ramis' theorem to test the non-complete integrability of the planar three-body problem. In From combinatorics to dynamical systems, volume 3 of IRMA Lect. Math. Theor. Phys., pages 163-177. 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)
• Mark van Hoeij, Jean-François Ragot, Felix Ulmer, and Jacques-Arthur Weil. Liouvillian solutions of linear differential equations of order three and higher. J. Symbolic Comput., 28(4-5):589-609, 1999.

• Manuel Bronstein, Thom Mulders, and Jacques-Arthur Weil. On symmetric powers of differential operators. In Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), pages 156-163 (electronic), New York, 1997. ACM.

• Mark van Hoeij and Jacques-Arthur Weil. An algorithm for computing invariants of differential Galois groups. J. Pure Appl. Algebra, 117/118:353-379, 1997.

• Felix Ulmer and Jacques-Arthur Weil. Note on Kovacic's algorithm. J. Symbolic Comput., 22(2):179-200, 1996.
• Jacques-Arthur Weil. First integrals and Darboux polynomials of homogeneous linear differential systems. In Applied algebra, algebraic algorithms and error-correcting codes (Paris, 1995), volume 948 of Lecture Notes in Comput. Sci., pages 469-484. Springer, Berlin, 1995.
• Jacques-Arthur Weil. The use of the special semi-groups for solving differential equations. In Proceedings of the international symposium on Symbolic and algebraic computation, ISSAC '94, pages 341-347, New York, NY, USA, 1994. ACM.
• Jacques-Arthur Weil. Constantes et polynômes de Darboux en algèbre différentielle : applications aux systèmes différentiels linéaires. PhD thesis, École polytechnique, 1995. Slides of the defense.

Textbooks

• Jacques-Arthur Weil et Alain Yger. Mathématiques L3 - Mathématiques appliquées (Cours complet avec 500 tests et exercices corrigés, 890p et Dvd). Pearson, 2009.
• Jean-Pierre Marco, Philippe Thieullen, and Jacques-Arthur Weil. Mathématiques L2 (Cours complet avec 700 tests et exercices corrigés, 838p). Pearson, 2007.

Surveys, Research Lectures

• Felix Ulmer and Jacques-Arthur Weil. Some methods to solve linear differential equations in closed form. In Algebraic theory of differential equations, volume 357 of London Math. Soc. Lecture Note Ser., pages 83-110. Cambridge Univ. Press, Cambridge, 2009.
• Delphine Boucher and Jacques-Arthur Weil. Cours "Linear Differential Equations, Differential Galois Groups, First Integrals of Differential Systems.". In Journées Nationales de Calcul Formel, page 50, Novembre 2007. Slides of the first set of lectures and of the second set of lectures.
• Jacques-Arthur Weil. Cours "Introduction to differential algebra and differential galois theory". In École CIMPA "Théorie du contrôle et systèmes intégrables" (Hanoi), 26 Novembre - 7 décembre, 2001.
• Jacques-Arthur Weil. Calcul formel pour les équations différentielles linéaires. In C. Sabbah, editor, Journées X-UPS 97. École Polytechnique, 1997.
• Felix Ulmer and Jacques-Arthur Weil. On Kovacic's algorithm. Sigsam Bulletin, 29(2), April 1995.
• Jacques-Arthur Weil, Ariane Germa-Péladan, François Ollivier, and Shih Jirung-Albert. Quelques approches algébriques effectives des phénomènes différentiels. In F. Murat & J.L Colliot-Thélène, editor, Images des Mathématiques 95. Éditions du CNRS, 1995.



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