On Sat, Aug 20, 2011 at 10:58 AM, Rob Beezer <goo...@beezer.cotse.net> wrote:
> Thanks for the sleuthing and ideas, John. Yes, I should have used a
> monic polynomial in my example since the original problem I have is
> with factors of a characteristic polynomial (and get similar
> behavior).
>
> I also get
>
> sage: M._gens is None
> True
>
> The eigenspace code (and probably eigenvalues, too) assume the root
> field has just one generator, so there is more to do there perhaps.
>
> Is that indicative of anything? I'll dig deeper and see if I can get
> to the bottom of this. Maybe at Bug Days 32. ;-)
Number fields defined by polynomials that are not monic *and* integral
are not supported by PARI.
Trying to define them in Sage right now should just give a big error
on creation, but currently doesn't.
It would probably be a 2-3 day project for somebody to make Sage fully
support fields defined by arbitrary
polynomials though, by secretely using the function
sage.schemes.elliptic_curves.heegner.make_monic
This project would save people from a lot of headaches, and *has* to
happen. It just a matter of time until somebody does it.
-- William
>
> Rob
>
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--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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