Computer Programs for Research in Gravitation and Differential Geometry

Abstract

This report contains a description of all current functions and features (with many examples) of the programs CTENSR and ITENSR which are available with MACSYMA. CTENSR is a standard Component TENSoR manipulation system which means that geometrical tensor objects are represented as arrays or matrices. Tensor operations such as contraction or covariant differentiation are carried out by actually summing over repeated (dummy) indices with DO statements. ITENSR, is a unique Indicial TENSoR manipulation system which is implemented by representing rensors as functions of their covariant, contravariant and derivative indicies. Tensor operations such as contraction or covariant differentiation are performed by manipulating the indices themselves rather than the components to which they correspond. The programs are connected in the sense that one can obtain an expression in ITENSR and have the corresponding expression generated in the CTENSR format automatically.