Bill Page wrote:
>
>
> 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?
1) My feeling is that given one factorization it should be easier
to produce other. But that requires some theoretical work.
In particular all examples of non-uniqueness I saw are very
special -- I do not know if there is a general principle or
I just did not saw more tricky examples.
2) ATM 'dc_fact1' produces just one factorization of given degree,
but by using all results from solve that are in base field
we would get all factorizations with given highest degree part.
Currently 'dc_fact' tries low degree left factor first and
do not try higher degree left factors. By calling 'dc_fact1'
with all possible splittings of highest degree part one would
get all possible factorizations into two factors. Recursively
one could get from this all possible factorizations.
--
Waldek Hebisch
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