The newest release of the Ortocartan set of programs for algebraic calculations in relativity

TL;DR

The paper introduces the latest version of Ortocartan, a computer algebra system for relativity, now compatible with Windows 98 and Linux, with new features for tensor calculations, LaTeX output, and differential equations.

Contribution

It presents new functionalities and improvements in Ortocartan, including support for multiple operating systems and advanced tensor and differential equation calculations.

Findings

Enhanced compatibility with Windows 98 and Linux

New subprograms for curvature and kinematic tensor calculations

Ability to generate LaTeX and Ortocartan input code

Abstract

The program Ortocartan for algebraic calculations in relativity has just been implemented in the Codemist Standard Lisp and can now be used under the Windows 98 and Linux operating systems. The paper describes the new facilities and subprograms that have been implemented since the previous release in 1992. These are: the possibility to write the output as Latex input code and as Ortocartan's input code, the calculation of the Ellis evolution equations for the kinematic tensors of flow, the calculation of the curvature tensors from given (torsion-free) connection coefficients in a manifold of arbitrary dimension, the calculation of the lagrangian from a given metric by the Landau-Lifshitz method, the calculation of the Euler-Lagrange equations from a given lagrangian (only for sets of ordinary differential equations) and the calculation of first integrals of sets of ordinary differential equations of second order (the first integrals are assumed to be polynomials of second degree in the first derivatives of the functions).