This C++ headers only library provides tools for manipulating elements of algebras; the tensor algebra, free lie algebra etc. Early versions can be found in sourceforge. It is capable of calculations over many rings including the arbitrary precision rationals from gmp/mpir . The associated library libalgebra_tests has many examples of how to use the code. the pypy package wraps a version of it - with a simple interface (and vastly reduced functionality)
Lot's of incremental improvements to the tensor multiplication.
On my laptop, I've got the times down to just above 200ms for 4,13,3 (down from ~500ms on what currently is there). Lots of other improvements.