SymboLie
A Mathematica program
for determining optimal systems of families of Lie subalgebras
SymboLie is a package written in the Wolfram Language designed to automatically determine optimal systems of families of Lie subalgebras of a finite-dimensional Lie algebra.
Papers related to SymboLie:
- L. Amata, F. Oliveri. Automatic determination of optimal systems of Lie subalgebras: the package SymboLie. Contemporary Mathematics, 789, 1-17, 2023. Paper
- L. Amata, F. Oliveri, E. Sgroi. Optimal Systems of Families of Lie Subalgebras: A Computational Approach. Preprint, 2024.
- L. Amata, F. Oliveri, E. Sgroi. Symbolic computation of optimal systems of subalgebras of three and four--dimensional real Lie algebras. Preprint, 2024.
Below you may download some Mathematica Notebooks where SymboLie is used.
- Algebra of traceless 2x2 matrices: Mathematica Notebook; PDF.
- Algebra of Lie symmetries of KdV equation: Mathematica Notebook; PDF.
- Algebra of Lie symmetries of Burgers' equation: Mathematica Notebook; PDF.
- Algebra of Lie symmetries of 2D stable viscous gas equations: Mathematica Notebook; PDF.
- Algebra of Lie symmetries of linear Heat equation: Mathematica Notebook; PDF.
- 6D Algebra (Ovsiannikov): Mathematica Notebook; PDF.
- 3D Real Lie Algebras: Mathematica Notebook; PDF.
- 4D Real Lie Algebras: Mathematica Notebook; PDF.