Indexed tensor manipulation CAS hello.
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.
 A: I think that everything in your list (except the Python interface) can be found in Kasper Peeters' Cadabra.  
As for a Python interface, there are two directions:


*

*It is planned to add an interface layer to Cadabra to either Maxima or SymPy - in the latter case you'd probably get access to Python.

*There is talk of adding a Cadabra interface to sage using the standard sage.interfaces.expect class.


As an aside some of the index algorithms come from José Martin-Garcia's xPerm, a Mathematica package. xPerm seems to be more suited to GR while Cadabra is focused on QFT.
FORM (the successor of Schoonschip) is also very powerful and used in a lot of high energy physics computing.
A: I think your best bet is a physics oriented package which I think is just called R or maybe Reduce. Meanwhile, here is the msri page of documentation for most packages currently available there.
http://www.msri.org/about/computing/mathdocs
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http://en.wikipedia.org/wiki/FORM_(symbolic_manipulation_system)
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http://en.wikipedia.org/wiki/List_of_computer_algebra_systems
