Edit detail for Jet Bundles revision 2 of 5

On February 7, 2006 10:24 AM C Y wrote:

Subject: [Axiom-developer]? JET source code up in the Axiom portal

Werner M. Seiler's JET - An AXIOM Environment for Geometric Computations with Differential Equations - is now available under Modified BSD. Code only, but the an abstract of the paper can be read online:

http://iaks-www.ira.uka.de/iaks-calmet/werner/Abstracts/IMACS95.ps.gz

Other links are also available in the axiom portal:

http://axiom-portal.newsynthesis.org/search?SearchableText=JET

The code can be downloaded from here:

http://axiom-portal.newsynthesis.org/Members/starseeker/Jet-June1995.tar.gz

I wish to thank Werner Seiler for digging up this code and granting permission to use it, and apologize for not announcing this sooner - it was actually online back in late December.

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Basic data structures and procedures for jet bundles.

Copyright (c) 1993, Joachim Schue, Werner M. Seiler

All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
• Neither the name of the Karlsruhe University nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

(C) Version 1 1993 Joachim Schue, Werner M. Seiler

(C) Version 2 1993 Werner M. Seiler

SPAD

• [Jet BaseFunctionCategory]?
• [Jet CartanKuranishi]?
• [Jet Differential]?
• [Jet DifferentialEquation]?
• JetBundle?
• JetBundleCategory?
• JetBundleExpression?
• JetBundleFunctionCategory?
• IndexedJetBundle?
• [Jet LUDecomposition]?
• [Jet SparseEchelonMatrix]?
• [Jet VectorField]?

Aldor

• [Aldor JetBundle]?
• [Aldor Jet Sparse]?

Applying AXIOM to Partial Differential Equations

by W.M. Seiler, 1997.

Examples from the paper:

[Jet Figure 4]?

In- and output for the Janet example

[Jet Figure 5]?

In- and output for the Euler Equation

[SandBox Jet Figure 6]?

Output for the contrained system

[SandBox Jet Figure 7]?

Determining system for the Heat Equation

[SandBox Jet Figure 8]?

Cole-Hopf transformation of the Burgers Equation