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Welcome to PySymmetry

A SageMath-based Python library for applying group representation theory to problems with symmetry.

About the Project

PySymmetry is a powerful tool designed to simplify complex computational problems by leveraging their underlying symmetries. Many problems in physics, engineering, and mathematics involve systems that are symmetric under certain transformations (like rotations or reflections).

The core feature of this library is the block diagonalization of equivariant operators. By finding a symmetry-adapted basis, PySymmetry can transform a large, complex matrix into a set of smaller, independent block matrices. This decomposition significantly simplifies subsequent calculations, such as finding eigenvalues, and leads to substantial performance improvements.

Where to Go Next?

  • New to PySymmetry? Start with our step-by-step Installation Guide.

  • Want to see it in action? Follow the Tutorial to solve a real-world physics problem.

  • Looking for specific functions or classes? Check out the detailed API Reference.