CARTAN: A Mathematica package for tensor computations

TL;DR

CARTAN is a user-friendly Mathematica package that facilitates symbolic tensor computations in various geometric spaces, supporting tensors like Riemann, Ricci, Einstein, and Weyl, with applications in curvature and torsion analysis.

Contribution

It introduces a comprehensive, easy-to-use tensor computation package for Mathematica that handles spaces with curvature and torsion across any dimensions and signatures.

Findings

Supports tensor calculations in spaces with curvature and torsion

Provides predefined functions for key tensors like Riemann, Ricci, Einstein, Weyl

Works in any number of dimensions and signatures

Abstract

CARTAN is an easy-to-use symbolic, tensor component package based on the popular Mathematica program. CARTAN makes use of the powerful formalism of rigid frames, and can return results both in this frame and in the coordinate basis. CARTAN has predefined functions for computation of tensors such as Riemann, Ricci, Einstein, Weyl, as well as other tensors and invariants. CARTAN works for spaces with curvature and/or torsion with any constant signature and for any number of dimensions. A free copy of CARTAN 1.01 for Unix with the installation program is contained in the file CARTAN.FILES.uu. The documentation is found in CARTAN.DOC.uu. The program has built-in Help functions.