Factorization

[Richard B. Kreckel]

On Mon, 9 Jul 2001, Wolfgang Abele wrote:
> This is the standard Trager algorithm. Like you're saying, you need to have a 
> gcd over extensions and resultant as subroutines. If Richy provides that 
> adaptor stuff, I'll try and implement Trager. If anybody's interested in the 
> more difficult multivariate factorization I could provide him or her with a 
> step-by-step guide to start with.

Err,...  the problem is that we never bothered with univariate polynomials
in GiNaC.  You can of course declare them using the sparse general
representation provided by classes `add' and `mul'.  Then you need a
conversion routine from NTL's data type to this one and vice-versa.  Is
that what you are looking for?  (It seems like Stefan has written this
already; I'll look into it this weekend.)  However, nothing prevents
people from poking multivariate polynomials into such a factorizer.  
Hence, the general mutivariate stuff would be what is really suited for
GiNaC.  But if you think that doing univariate first is the right thing to
do in order to get started with factorization, then please go ahead!

Two remarks: there is currently no class that represents algebraic
extensions.  Representation is another no-brainer, as far as I can see,
since it should just hold one expression which represents the zero.  Also,
our GCD routines are not prepared for extensions.  Is that needed?  Is it
difficult???

Regards
     -richy.
-- 
Richard Kreckel
<Richard.Kreckel at Uni-Mainz.DE>
<http://wwwthep.physik.uni-mainz.de/~kreckel/>