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
KLmultibracket for calculating the Mayer bracket  and Kruglikov-Lychagin multi-bracket , respectively. On comparison of this method with the differential Gröbner basis, see .
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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:
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:\Program Files\Maple 2019\lib’.
The source code is available under terms of the 0BSD license.
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- Kruglikov, B. & Lychagin, V. Mayer brackets and solvability of PDEs—I, Differential Geometry and its Applications, Elsevier BV, 2002, 17, 251–272.
- Kruglikov, B. & Lychagin, V. Compatibility, Multi-brackets and Integrability of Systems of PDEs Acta Applicandae Mathematicae, Springer, 2010, 109, 151.
- Kruglikov B., Note on two compatibility criteria: Jacobi–Mayer bracket vs. differential Gröbner basis, Lobachevskii J. Math., 23, 2006, 57–70