MathTensor

Gives Elementary and Advanced Tensor Analysis Functionality

MathTensor is the largest Mathematica package yet developed outside of Wolfram Research. It adds over 250 new functions and objects to Mathematica to give you both elementary and advanced tensor analysis functionality. MathTensor is a general tool for handling both indicial and concrete tensor indices.

Standard objects like Riemann tensor, Ricci tensor, metric tensor, and others are built into the system along with common functions like the covariant derivative, index commutation, raising and lowering of indices, and various differential forms operations.