ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 26 Oct 2011 15:03:17 +0200Factorization of non-commutative Laurent polynomialshttps://ask.sagemath.org/question/8417/factorization-of-non-commutative-laurent-polynomials/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!Wed, 26 Oct 2011 02:37:53 +0200https://ask.sagemath.org/question/8417/factorization-of-non-commutative-laurent-polynomials/Answer by Mike Hansen for <p>Hi, can Sage factorize non-commutative Laurent polynomials in several variables?</p>
<p>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.</p>
<p>(The case with Z/2- instead of Z-coefficients would also be interesting.)</p>
<p>Thank you!</p>
https://ask.sagemath.org/question/8417/factorization-of-non-commutative-laurent-polynomials/?answer=12819#post-id-12819Sage 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.Wed, 26 Oct 2011 15:03:17 +0200https://ask.sagemath.org/question/8417/factorization-of-non-commutative-laurent-polynomials/?answer=12819#post-id-12819