Mathematica package TensoriaCalc, which tackles (semi-)Riemannian tensor calculus problems encountered in general relativity, cosmology, and field theory. Currently, it calculates geometric objects - Christoffel symbols, the Riemann curvature tensor, Ricci tensor and scalar, etc. - given a metric and the relevant coordinates; and performs basic operations such as covariant derivatives of tensors. Development is ongoing, and is expected to continue for the foreseeable future. TensoriaCalc was the outgrowth of tensorial calculations I performed during my own theoretical physics research. It also parallels a closely related effort to develop an abstract tensor manipulation package similar to xAct, but also allowing for concrete computations such as the ones peformed by TensoriaCalc.

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  1. Craps, Ben; Evnin, Oleg; Nguyen, Kévin: Matrix thermalization (2017)