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. Both a
command-line and a graphical interface are available.

* Designed for field-theory problems, with handling of anti-commuting
  and non-commuting objects without special notations for their
  products, gamma matrix algebra, Fierz identities, Dirac conjugation,
  vielbeine, flat and curved, covariant and contravariant indices,
  implicit dependence of tensors on coordinates, partial and covariant
  derivatives...

* Powerful tensor simplification algorithms, not just for mono-term
  symmetries but also for multi-terms symmetries like the Bianchi
  identity, or dimensionally-dependent symmetries like the Schouten
  identity.

* Allows for both abstract and component computations.

* A standalone graphical notebook interface which can also be used as a
  front-end for SymPy.

* Input and output using a subset of LaTeX notation.

* Programmable using Python.

Mathematica (not on SBo) is an optional dependency, it will be
autodetected at build time.