OrthoBase

A Python library for constructing multiplet projectors in the decomposition of the product of adjoint representations in the $\mathrm{SU}(N_c)$ group. The library also provides numerous methods to work with Young tableaux. The software achieves high efficiency through a combination of the Z3 satisfiability modulo theories solver and the symbolic manipulation program FORM.

Key features:

• Construct multiplet projectors for the decomposition of adjoint representation products in $\mathrm{SU}(N_c)$ groups
• Efficient algorithms implemented using the Z3 solver and FORM symbolic manipulation
• Comprehensive set of methods for working with Young tableaux
• Easy-to-use Python interface for seamless integration into your projects
• Well-documented code and extensive online documentation for quick start and reference

The library's toolset provides researchers working in fields involving $\mathrm{SU}(N_c)$ groups and Young tableaux with a powerful and efficient means to streamline their work in these domains.

Installation

OrthoBase requires Python version 3.10 or newer and can be installed on any Unix-like operating system.

The latest release can be installed from PyPI using pip:

$ python3 -m pip install --user --upgrade OrthoBase

This will install the library with all its python dependencies. There are additional dependencies described below. They should be installed manually or using the package manager of your operating system.

Additional dependencies

These dependencies are not automatically installed via pip. Therefore, users must manually install them and ensure that the relevant files are included in the $PATH and $LD_LIBRARY_PATH environment variables:

• FORM (http://www.nikhef.nl/~form/)
• An implementation of MPI (Message Passing Interface) should be installed. Some popular implementations include:
  • Open MPI
  • MPICH
  • Intel MPI
  • Microsoft MPI

Usage

Refer to the online documentation of our package.

You can run the example calculation as follows:

$ ./demo.py

Current limitations

• The automatic calculation of normalization factors is currently disabled. This feature will be implemented in an upcoming release.
• The parallelization feature using MPI is a work in progress. For stable results, it is recommended to set Projectors.parallel_evaluation = False. However, you can still freely select the value of Projectors.FORM_np.