Cadabra is a symbolic computer algebra system (CAS) designed
specifically for the solution of problems encountered in field
theory. It has extensive functionality for tensor computer algebra,
tensor polynomial simplification including multi-term symmetries,
fermions and anti-commuting variables, Clifford algebras and Fierz
transformations, component computations, implicit coordinate
dependence, multiple index types and many more. The input format
is a subset of TeX.

WWW: http://cadabra.science/