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The diffalg package


Presentation

The diffalg package is a collection of routines to handle systems of polynomial differential equations and inequations. The functionalities include differential elimination, expansion of the solutions into formal power series and analysis of singular solutions. The underlying theory and terminology belongs to differential algebra.

An illustrated overview of the package functionnalities is given in the overview help page.

Basic concepts in constructive differential algebra and their representation in the diffalg package are presented in a more substantial way in the help page diffalg[differential_algebra] of diffalg(00).

Availability

If you use the diffalg package for your research, either centrally or as an exploratory or verification tool, please acknowledge it by refering to this web page ( http://www-sop.inria.fr/members/Evelyne.Hubert/diffalg) and the related publications (see bibliography below).
diffalg(04): diffalg04.zip

  • non commuting derivations [H05]
    Check ?diffalg , ?differential_ring
  • dynamic parameters
diffalg(01): diffalg01.zip

  • supports the convention for derivatives of the Vessiot package.
  • New options available for characteristic decomposition.
diffalg(00): diffalg00.tar.gz available in Maple 7,8,9...
  • New help pages
  • Couple of bugs fixed compared to diffalg(99) in Maple6.
diffalg(99): Available in Maple 6
  • Improvement following the theoretical advances of [H00]
diffalg(98): Available in Maple V.5.1
  • Tools for the analysis of singular solutions [H99]
  • Improvement of performances
diffalg(96): Available in Maple V.5


Please send comments and bug reports to E. Hubert.

diffalg in action

If you are a diffalg user, please feel welcome to send some additionnal worksheets of examples to be included here.

Bibliographic references

[BLOP95] Boulier, F., Lazard, D., Ollivier, F., Petitot, M. Computing Representations for Radicals of Finitely Generated Differential Ideals. Proceedings of ISSAC'95, ACM Press.
[BLOP97] Boulier, F., Lazard, D., Ollivier, F., Petitot, M. Computing Representations for Radicals of Finitely Generated Differential Ideals. Technical Report IT-306, LIFL. 1997.
[BLMM01] Boulier, F., Lemaire, F. and Moreno-Maza, M. PARDI! Proceedings of ISSAC 2001, ACM Press.
[H99] Hubert, E. Essential Components of Algebraic Differential Equations. Journal of Symbolic Computations (1999) volume 28 number 4-5 pages 657-680.
[H00] Hubert, E. Factorization Free Decomposition Algorithms in Differential Algebra. Journal of Symbolic Computations (2000) volume 29 number 4-5 pages 641-662.
[H03p] Hubert, E. Notes on triangular sets and triangulation-decomposition algorithms I: Polynomial systems. Chapter of Symbolic and Numerical Scientific Computations Edited by U. Langer and F. Winkler. LNCS (2003), volume 2630, Springer-Verlag Heidelberg.
[H03d] Hubert, E. Notes on triangular sets and triangulation-decomposition algorithms II: Differential Systems. Chapter of Symbolic and Numerical Scientific Computations Edited by U. Langer and F. Winkler. LNCS, volume 2630, Springer-Verlag Heidelberg.
[H04] Hubert, E. Improvements to a triangulation-decomposition algorithm for ordinary differential systems in higher degree cases, Proceedings of ISSAC'04, ACM Press.
[H05] Hubert, E. Differential Algebra for Derivations with Nontrivial Commutation Rules, Journal of Pure and Applied Algebra (2005), Volume 200, Issues 1-2.


E. Hubert