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Factorization of non-commutative Laurent polynomials

asked 2011-10-25 19:37:53 -0600

bm gravatar image

Hi, can Sage factorize non-commutative Laurent polynomials in several variables?

By those polynomials I mean elements in the group algebra Z[F(n)], where Z is the integers and F(n) is the free group on n letters.

(The case with Z/2- instead of Z-coefficients would also be interesting.)

Thank you!

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answered 2011-10-26 08:03:17 -0600

Mike Hansen gravatar image

Sage does not have algorithms to do such a factorization. The notion of unique factorization for noncommutative rings needs a bit more thought than in the commutative case. Work by P.M. Cohn showed that free associative algebra is a (noncommutative) UFD, but I don't know of any algorithm implementing this.

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Asked: 2011-10-25 19:37:53 -0600

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Last updated: Oct 26 '11