Hi,
For more correct context, I'm taking the quotient of the ring of integers
in my worksheet.
f = QQ['t']({16:1, 0:262})
K.<s> = NumberField(f)
R = K.ring_of_integers()
QuotientRing(R, Ideal(263,s+1))
I forgot to include that when simplifying the example.
On Monday, June 5, 2017 at 1:26:18 PM UTC-6, William wrote:
>
> On Mon, Jun 5, 2017 at 12:17 PM, Vincent Delecroix
> <20100.d...@gmail.com <javascript:>> wrote:
> > On 05/06/2017 22:15, William Stein wrote:
> >>
> >> On Mon, Jun 5, 2017 at 11:48 AM, Joel Ornstein
> >> <joel.o...@colorado.edu <javascript:>> wrote:
> >>>
> >>> Hi all,
> >>>
> >>> I'm trying to work with several quotient rings and occasionally
> creating
> >>> the
> >>> quotient ring takes an extremely long time:
> >>>
> >>> f = QQ['t']({16:1, 0:262})
> >>> K.<s> = NumberField(f)
> >>> QuotientRing(K, Ideal(263,s+1))
> >>
> >>
> >> Question: What are you really trying to do exactly? The quotient of a
> >> number field by absolutely any nonzero ideal is just 0.
> >
> >
> > That's a good point. However, it would still be useful if Sage had the
> same
> > answer straight! Don't you think?
> >
> > I believe the OP was interested in the ring of integers of such number
> field
>
> Probably. Even then it would be very relevant to know what the OP
> actually wants to do with this quotient ring... Just arithmetic?
> Something harder?
>
> Here's a little worksheet working with the quotient as a module, which
> shows the quotient is cyclic of order 263:
>
>
> https://cocalc.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/quotient-ring.ipynb?fullscreen
>
>
> It would be easy to build on that to do arithmetic quickly at least
> (without ever worrying about is_principal).
>
> William
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