> I see. So what could be done to speed up the factorization?
>
> > I've lost my hope on the univariate integer polynomial factorization
> > already, that's why i stopped implementing the other corresponding
> > algorithms.
>
> Could you please ellaborate? I don't understand what is the problem
> with integer polynomial factorization.
>

At the end of the Summer of Code, I thought that the polynomial
algorithms were so slow, because they carry (complicated) SymPy
objects as coefficients. That's why I played around with a more light-
weight univariate Polynomial class. First, with the finite fields
coefficients, I was quite satisfied, also with factorization. But when
I tried to lift the results to (Python) integer coefficients, it got
incredibly slow. I took the algorithms 'out of the book', so I'm sure
that improvement is possible. I think that this improvement would help
asymptotically, rather, and the algorithms already take very long with
small example polynomials. Initially I'd planned to do another
(multivariate) gcd and factorization as well, but I didn't try,
because the simpler univariate factorization was just disappointing.

The book "Modern Computer Algebra" is a great reference for all of
this, you rarely need anything else for this.
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