Re: [Axiom-developer] Bug in GeneralizedMultivariateFactorize?

[Stephen Wilson]

Waldek Hebisch <address@hidden> writes:
> Practically, when working with polynomils we may want to ignore
> problems due to coefficient ring, that is consider degree 0 factors
> as trivial.  But it is still not clear if we can do square free
> decomposition (without for example extending coefficient ring to a
> field).   However, assuming that we can compute such a decomposition
> it would be a different operation than the normal square free
> decomposition, so I feel that it deserves different name.


Please forgive that this question may be elementary, uninformed, etc
(I am no mathematician).

Is it common enough to encounter integral domains which are not UFD's
yet admit a computable extension to a field?

If so, then can we not use both squarefree factorization and
Berlekamps algorithm to obtain a complete factorization, apply Hensel
lifting, and do (in the most general case) an exponential algorithm to
recombine the factors?

If this is nonsense, just say "thats nonsense".  Im not asking you
to spend your time explaining why my question is uninformed.


Take care,
Steve