Maple package Brackets

PDE systems formal integrability study tool

Brackets package provides means to study formal integrability conditions of overdetermined PDE systems. Package exports two main functions KLMbracket, KLmultibracket for calculating Mayer bracket [1] and Kruglikov-Lychagin multi-bracket [2] respectively. On comparison of this method with differential Gröbner basis see [3].

Package is created on the base of DifferentialGeometry package by Ian Anderson and intended to be used alongside with it.

Downloads

You can get Brackets package here. Also an example is available. Both files zipped.

Documentation

A documentation is not ready yet.

Installation guide

The most convinient way to install Brackets package is to copy file ‘brackets.mla’ to the subdirectory ‘lib’ of your Maple installation directory. You can obtain path to this directory by running Maple command

kernelopts(mapledir);
Linux
sudo cp ~/Downloads/brackets.mla /opt/maple2016/lib/
Mac OS X

Run your favourive terminal emulator like built-in Terminal app or iTerm. Then

sudo cd ~/Downloads/brackets.mla /Library/Frameworks/Maple.framework/Versions/2016/lib/

You may need to change Maple installation path according to your actual Maple version.

Windows

Using Explorer copy file ‘brackets.mla’ to your Maple installation directory, e.g. ‘C’.

Licence

You may freely use Brackets package for educational, personal and commercial purposes. But you may not decompile package or perform any reverse engineering of it.

Source code

Will be available soon.

Known issues

  1. Functions Brackets package provides work correctly with “JetNotation2” setting only, hence the following line
    DifferentialGeometry:-Preferences( "JetNotation", "JetNotation2" ):

    must be put in your Maple program.

References

  1. Kruglikov, B. & Lychagin, V. Mayer brackets and solvability of PDEs—I, Differential Geometry and its Applications, Elsevier BV, 2002, 17, 251–272.
  2. Kruglikov, B. & Lychagin, V. Compatibility, Multi-brackets and Integrability of Systems of PDEs Acta Applicandae Mathematicae, Springer, 2010, 109, 151.
  3. Kruglikov B., Note on two compatibility criteria: Jacobi–Mayer bracket vs. differential Gröbner basis, Lobachevskii J. Math., 23, 2006, 57–70

Contact

Suggestions, questions, comments etc are welcome at brackets@d-omega.org.