On Tue, Dec 31, 2019 at 12:13:21AM +0100, Ralf Hemmecke wrote:
> Does someone by chance know whether there is a function in FriCAS that
> computes just ONE irreducible factor of a polynomial over K where K is a
> finite field?
>
> All I have found so far is ddfact.spad. But that does a full factorization.
AFAIK there is no such function. It would be easy to add function
that computes lowest degree factors. OTOH all reasonably efficient
methods will give you simultaneously all factors of given degree.
ANd spent at least some work on computing higher degree factors
(the trick to efficiency is to amortize work over sevaral
degrees).
Most efficient should be 'ffact.spad', but part of its efficiency
is use of efficient coefficient arithemtic and currently this
is implemented only for Z_p with p small enough that all
intermediate calculations can be done in machine arithmetic.
Method used in 'ffact.spad' (due to Kaltofen and Shoup) is
essentialy generic (general finite step need additonal trace
style step not present in current code), but one would need
create versions for other coeffienct (say using macros so that
each version could get needed optimizations) and provide a
bunch of needed subroutines.
If you do not care about efficiency, you can just throw out
unneded factors.
--
Waldek Hebisch
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