I am looking for tensor manipulation software that would allow me:
- declare indices
- declare results of contraction (or simplification rules)
- allow algebraic simplifications and expansion
- index renaming
So far I have found Maxima to satisfy my requirement more or less, http://maxima.sourceforge.net/docs/manual/en/maxima_27.html
one last thing I also want, (but not necessarily require), is interface with python. In principle I could use sage to interface with maxima.
Is there some other Cas that has package with similar tensor manipulation properties?
from links given below, I also found this, http://cadabra.phi-sci.com/, which looks geared specifically for tensor manipulations.