Commutative Algebra

Differential Algebra

12H05, 13Nxx

  1. Alin Bostan, Frédéric Chyzak, and Nicolas Le Roux, Products of ordinary differential operators by evaluation and interpolation, in ISSAC '08: International Symposium on Symbolic and Algebraic Computation, ACM, New York, NY, USA, 2008, pp. 23–30.[doi/arXiv]
  2. Alin Bostan, Frédéric Chyzak, Bruno Salvy, Grégoire Lecerf, and Éric Schost, Differential equations for algebraic functions, ISSAC 2007, ACM, New York, 2007, pp. 25–32.[MR/arXiv]
  3. Alin Bostan, Thomas Cluzeau, and Bruno Salvy, Fast algorithms for polynomial solutions of linear differential equations, ISSAC'05: Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2005, pp. 45–52 (electronic).[MR]
  4. Olivier Cormier, On Liouvillian solutions of linear differential equations of order 4 and 5, in ISSAC '01: Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2001, pp. 93–100 (electronic).[MR]
  5. Olivier Cormier, Michael F. Singer, and Felix Ulmer, Computing the Galois group of a polynomial using linear differential equations, in Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews), ACM, New York, 2000, pp. 78–85 (electronic).[MR]
  6. Boris Feigin and Boris Shoikhet, On [A,A]/[A, [A,A]] and on a Wn-action on the consecutive commutators of free associative algebra, Math. Res. Lett. 14 (2007), no. 5, 781–795.[MR/arXiv]
  7. Julia Hartmann, Invariants and differential Galois groups in degree four, Differential Galois Theory, Banach Center Publ., vol. 58, Polish Acad. Sci., Warsaw, 2002, pp. 79–87.[MR]
  8. Sabrina A. Hessinger, Computing the Galois group of a linear differential equation of order four, Appl. Algebra Engrg. Comm. Comput. 11 (2001), no. 6, 489–536.[MR]
  9. V. A. Krasikov and T. M. Sadykov, Linear differential operators for generic algebraic curves, preprint (2010).[arXiv]
  10. Ariane Péladan-Germa, Testing equality in differential ring extensions defined by PDE's and limit conditions, Appl. Algebra Engrg. Comm. Comput. 13 (2002), no. 4, 257–288.[MR]
  11. Kira Samol and Duco van Straten, Frobenius polynomials for Calabi-Yau equations, Commun. Number Theory Phys. 2 (2008), no. 3, 537–561.[MR/arXiv]
  12. Michael F. Singer, Testing reducibility of linear differential operators: A group-theoretic perspective, Appl. Algebra Engrg. Comm. Comput. 7 (1996), no. 2, 77–104.[MR]
  13. Michael F. Singer and Felix Ulmer, Galois groups of second and third order linear differential equations, J. Symbolic Comput. 16 (1993), no. 1, 9–36.[MR]
  14. Michael F. Singer and Felix Ulmer, Liouvillian and algebraic solutions of second and third order linear differential equations, J. Symbolic Comput. 16 (1993), no. 1, 37–73.[MR]
  15. Michael F. Singer and Felix Ulmer, On a third order differential equation whose differential Galois group is the simple group of 168 elements, Applied algebra, algebraic algorithms and error-correcting codes (San Juan, PR, 1993), Lecture Notes in Comput. Sci., vol. 673, Springer, Berlin, 1993, pp. 316–324.[MR]
  16. Michael F. Singer and Felix Ulmer, Necessary conditions for Liouvillian solutions of (third order) linear differential equations, Appl. Algebra Engrg. Comm. Comput. 6 (1995), no. 1, 1–22.[MR]
  17. Felix Ulmer, On algebraic solutions of linear differential equations with primitive unimodular Galois group, Applied Algebra, Algebraic Algorithms and Error-correcting Codes (New Orleans, LA, 1991), Lecture Notes in Comput. Sci., vol. 539, Springer, Berlin, 1991, pp. 446–455.[MR]
  18. Felix Ulmer, On Liouvillian solutions of linear differential equations, Appl. Algebra Engrg. Comm. Comput. 2 (1992), no. 3, 171–193.[MR]
  19. Felix Ulmer, Liouvillian solutions of third order differential equations, J. Symbolic Comput. 36 (2003), no. 6, 855–889.[MR]