jets

(2000-2010)

Authors:	Mohamed Barakat (2000-active) and Gehrt Hartjen (2000-2002)
Coauthors:	Pieter Eendebak (2003) and Arne Lorenz (2005-2009)

The Maple package jets was developed by Mohamed Barakat and Gehrt Hartjen. Originally it was an extension of the package desolv, adding to it the facility of computing generalized symmetries. At the current stage it is an independent package going beyond symmetries to handle different aspects I. M. Gel'fand, in his 1970 address to the International Congress in Nice, called "formal differential geometry". Important parts of the variational bicomplex, as playing a crucial role in the formal theory of PDEs, are implemented in jets. Recently, the formalism of jet-groupoids found its way into jets.
If you find a bug please feel free to send me an email.

Talks referring to jets

Mohamed Barakat, Geometric objects on fibered manifolds and integrable systems. Aachen, May 2010.
Arne Lorenz, Laplace Invariants via Vessiot Equivalence Method, RISC Linz, February 2009.
Arne Lorenz, Vessiot's Equivalence Method Applied to Linear Partial Differential Operators, RISC Linz, May 2008.
Arne Lorenz, Integrabilitätsbedingungen in der Geometrie, Aachen, December 2007.

Publications using jets

Arne Lorenz, Jet Groupoids, Natural Bundles and the Vessiot Equivalence Method. Ph.D. thesis, Department of Mathematics, RWTH-Aachen, March 2009, (published electronically)
Arne Lorenz, On local integrability conditions of jet groupoids. (arXiv:math.DG/0708.1419)
Pieter Eendebak, Contact Structures of Partial Differential Equations, Ph.D. thesis, Department of Mathematics, Utrecht University, January 2007, (published electronically)
Daniel Robertz, Formal Computational Methods for Control Theory, Ph.D. thesis, Department of Mathematics, RWTH-Aachen, June 2006, (published electronically)
Y.A. Blinkov and C.F. Cid and V.P. Gerdt and W. Plesken and D. Robertz, The MAPLE Package <Janet: II. Linear Partial Differential Equations, Proc. 6th Int. Workshop on Computer Algebra in Scientific Computing, 2003, Passau, Germany. (pdf)
Mohamed Barakat, Functional spaces. A direct approach, Ph.D. thesis, Department of Mathematics, RWTH-Aachen, January 2002, (pdf)
Gehrt Hartjen, Variational Calculus and Conservation Laws with MAPLE, Master thesis, December 2001, unpublished. (pdf)
Mohamed Barakat, jets. A MAPLE-package for formal differential geometry, Computer algera in scientific computing (Konstanz, 2001), Springer, Berlin, 2001, pp. 1-12. MR MR1942047 (2003j:53001) (pdf)