Also Rob, the real name for the field is M._NumberField_relative__gens
(or similar).

John

On Sat, Aug 20, 2011 at 8:32 PM, William Stein <wst...@gmail.com> wrote:
> 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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