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Does anyone if there exists a math program that can work with free associative algebras ? By work with associative algebras, I mean

  • It can define any ideal $I$, being it left-,right- or twosided.
  • It can define quotientrings $R/I$ and I can do summation and multiplication in it. (if it can work only with ideals generated by homogeneous elements, it's ok).
  • It can calculate elements of the center of an associatieve algebra(= a quotient of a free algebra) of a certain degree (I don't need to find the complete center, just the elements of a certain degree).

Additionally, it would be nice if it were free (opensource or something like that) and it works on Windows.

Thanks in advance.

Forgot to mention: if it can be done in Sage, is there any good documentation on how to do those things ?

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You can use Sagemath : there is a documentation about how to manipulate free algebras. But unfortunately, sagemath is linux native and isn't optimized for Windows...

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Does it do all those things ? The only examples I find give finite dimensional algebras and $R/I$ only works in the case $I$ is a power ideal (if I copy the code from rings). – KevinDL Oct 29 '12 at 8:38

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