Tensor calculus with open-source software: the SageManifolds project

TL;DR

The SageManifolds project enhances SageMath with open-source tools for differential geometry and tensor calculus, enabling accessible and extendable mathematical computations in Python.

Contribution

It introduces a new open-source module for SageMath that specifically supports tensor calculus and differential geometry, expanding Sage's capabilities.

Findings

Implementation based on Sage's parent/element framework

Provides a concrete example of differential geometry computations

Extends SageMath with tensor calculus functionalities

Abstract

The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. Like Sage, SageManifolds is free, open-source and is based on the Python programming language. We discuss here some details of the implementation, which relies on Sage's parent/element framework, and present a concrete example of use.