Maple package Brackets

PDE systems formal integrability study tool

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

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


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


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Installation guide

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

Linux-based OS
sudo cp ~/Downloads/brackets.mla /opt/maple2019/lib/

Open the Terminal application. Then type

sudo cp ~/Downloads/brackets.mla /Library/Frameworks/Maple.framework/Versions/2019/lib/

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


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


The source code is available under terms of the 0BSD license.

Source code


Known issues

No issues found. You can help us to discover them.


  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