field-theory motivated computer algebra system

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