Waldek, On Sat, Nov 10, 2018 at 12:02 PM you wrote: > > One update to what I wrote before. In > > J. P. Bell, A. Heinle, and V. Levandovskyy, > On Noncommutative Finite Factorization Domains, > Trans. Amer. Math. Soc. 369 (2017), 2675-2695 > > there is proof of finite number of factorizations. > > I have now implemented the lift part of Davenport-Caruso method. > ...
Since the number of factorizations of a non-commutative polynomial over a unique factorization domain is finite but not unique there may be some applications where it maybe interesting to know more than one or even all possible factorizations. Your current implementation produces just one factorization. Do you see any opportunity to extend the Davenport-Caruso method to produce multiple factorizations or a complete enumeration of factorizations? I did some experiments with the xdpolyf1 factorizer to produce such multiple factorizations. This was relatively easy since the solution algorithm (with the "pruning" heuristic) naturally produces factorizations in which either the left factor or right factor at each step has a minimum number of terms. By alternately choosing to minimize first the right factor and then the left factor it is possible to explore alternate factorizations. I did not get so far as to attempt to prove completeness. -- 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 fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
