Pytearcat: PYthon TEnsor AlgebRa calCulATor - A python package for general relativity and tensor calculus

Pytearcat is an open-source Python package created to work with general tensor operations, either in the field of General Relativity (GR) or others that need to use tensor calculus. It provides the basic GR tensors built in the package and uses a standard syntax for the Einstein notation.

Installation

As a Python package, Pytearcat can be installed through pip using

pip install pytearcat

To use the Giacpy core in Pytearcat, the user must explicitly indicate during the package installation that the installer must include the Giacpy module in the process. This is done through

pip install pytearcat[giapy]

File structure summary

Inside the Pytearcat package, there are two sub-packages named gr and tensor. Inside the first one, there are six modules related to GR expressions. These libraries allow calculating quantities that are very common in GR, such as the Christoffel symbols (first and the second kind, christoffel.py), the Ricci tensor and the Ricci scalar (ricci.py), the Riemann tensor (riemann.py) and the Einstein tensor (einstein.py). Also, there is a module to define the metric (metric.py) and another to calculate the geodesics (geodesic.py). The second sub-package named tensor contains modules that allow to define tensors and operate with them. The misc.py module contains functions that allow defining symbolic functions, variables, and constants. It also contains other functions to work with series expansions and to simplify expressions. The kdelta.py and lcivita.py modules contain the data classes which define the Kronecker Delta symbol and the Levi-Civita symbol, respectively. The tensor.py module contains the code related with the class tensor and many functions that are useful to define a tensor, operate tensors, recognise the contravariant and covariant indices, lower and raise indices and expand a tensor like a series up to a specific order. Inside this sub-package, there is another one named core which contains essential information that the program needs to operate tensors. All the functions required by the user are located at the top level of the package.

Usage

Pytearcat works using Jupyter Notebooks to give the outputs in mathematical form. To use the package the user should import Pytearcat within a Jypyter Notebook

import pytearcat as pt

Later, it is possible to access the functions and methods of the package within the notebook. Different usage examples can be found in the Examples directory of the GitHub repository.

How to cite this work

To cite this work, please refer to Pytearcat's release paper San Martin & Sureda (2021) (also available on arXiv) and use the following Bibtex citation:

@article{pytearcat2022,
	abstract = {This paper introduces the first release of Pytearcat, a Python package developed to compute tensor algebra operations in the context of theoretical physics, for instance, in general relativity. Given that working with tensors can become a complex task, people often rely on computational tools to perform tensor calculations. We aim to build a tensor calculator based on Python, which benefits from being free and easy to use. Pytearcat syntax resembles the usual physics notation for tensor calculus, such as the Einstein notation for index contraction. This version allows the user to perform many tensor operations, including derivatives and series expansions, along with routines to obtain the typical General Relativity tensors. A particular concern was put in the execution times, leading to incorporate an alternative core for the symbolic calculations, enabling to reach much faster execution times. The syntax and the versatility of Pytearcat are the most important features of this package, where the latter can be used to extend Pytearcat to other areas of theoretical physics.},
	author = {M. San Mart\'in and J. Sureda},
	doi = {https://doi.org/10.1016/j.ascom.2022.100572},
	issn = {2213-1337},
	journal = {Astronomy and Computing},
	keywords = {Software, Public release, General relativity, Tensor algebra, Computer algebra system},
	pages = {100572},
	title = {Pytearcat: PYthon TEnsor AlgebRa calCulATor A python package for general relativity and tensor calculus},
	url = {https://www.sciencedirect.com/science/article/pii/S221313372200018X},
	year = {2022},
	Bdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S221313372200018X},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.ascom.2022.100572}}