Perhaps this describes what you are looking for: https://arxiv.org/abs/1002.3180
Factorization of Non-Commutative Polynomials Fabrizio Caruso (Submitted on 16 Feb 2010) We describe an algorithm for the factorization of non-commutative polynomials over a field. The first sketch of this algorithm appeared in an unpublished manuscript (literally hand written notes) by James H. Davenport more than 20 years ago. This version of the algorithm contains some improvements with respect to the original sketch. An improved version of the algorithm has been fully implemented in the Axiom computer algebra system. -- There is reference to some code that apparently was contributed to Axiom but after a quick look I was not able to find it. Perhaps you could contact the author? Bill Page. On Sun, May 27, 2018 at 1:59 PM, Marduk <[email protected]> wrote: > Dear all, > > given a multivariate monomial defined with: > > poly := MPOLY([x,y], Integer) > > p : poly := 3*x*y > > one can obtain the factors of the monomial with factors(p). > > However, given a multivariate monomial with noncommutative variables defined > with: > > ops := OVAR[A,B] > > ncomm := XDPOLY(ops, Integer) > > q : ncomm := 3*B::ops*A::ops > > factors(q) fails. > > I did some research and learned that: > > - factors ultimately retrieves an entry from a record corresponding to the > representation of an object in the Factored domain > > - multivariate polynomials are domains in the PolynomialCategory, which in > its > definition contains the line > > import from Factored(%) > > - in the noncommutative case the corresponding category is XPolynomialsCat, > which > is more modest than PolynomialCategory, i.e. it is missing a lot of stuff > > It is not clear to me whether the above import statement is the reason why > one can > obtain the factors in the commutative case. What I would like to know is, > how should I > modify XPolynomialsCat in order to have factors available. > > Thanks in advance. > > Marduk > > -- > You received this message because you are subscribed to the Google Groups > "FriCAS - computer algebra system" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/fricas-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
