> > Thanks, that was fast!  If I may ask, what was the problem?  Must've
> > been something not particularly exciting...
>
> Robert Miller implemented root finding for RDF polynomials right
> before SAGE-2.8.3, and he messed up.  Basically SAGE represents
> polynomials as list with one "endian-ness", and numpy uses
> the other.  So I just reverse the list before passing it into numpy.

Actually, I just moved already-broken code:
http://www.sagemath.org/hg/sage-main/diff/7085de591817/sage/rings/polynomial/polynomial_element.pyx
(at the bottom...). What I implemented was factoring of RDF
polynomials.

> > Double precision is more than sufficient for my purposes--even floats
> > (!) are fine, I just need fast and reasonably accurate.

Using numpy, reasonably accurate means up to only a few places, not
the full double precision. This leads to badness when you try to
factor anything. If it finds that 1.0000112451357 is a root of
(x-1)^3, you will likely get a quadratic irreducible as a factor...

> What polynomials are you evaluating?  If they are double precision,
> I wonder if making a special GSL-based polynomial class will help
> a lot?

The root finding is much much more accurate, and no doubt faster too.



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