#6018: Confusing behaviour with Dirichlet characters
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Reporter: davidloeffler | Owner: craigcitro
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-6.4
Component: modular forms | Resolution:
Keywords: Dirichlet | Merged in:
characters | Reviewers:
Authors: David Loeffler, | Work issues:
Peter Bruin | Commit:
Report Upstream: N/A | d0bb0e4bc7c13e5b6b8a4c6d188b65b6d501eb2c
Branch: | Stopgaps:
u/pbruin/6018-DirichletGroup_zeta |
Dependencies: #18540 |
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Comment (by pbruin):
Replying to [comment:24 jdemeyer]:
> Replying to [comment:18 pbruin]:
> > Besides solving the problems in the ticket description, this ticket
greatly speeds up constructing Dirichlet groups over number fields.
>
> I assume that this is the main motivation for making `zeta` optional,
right? I am not really convinced though that this extra complexity is
needed...
This is not really true; it also makes more sense conceptually if one does
not have to make a choice of root of unity. I think the problems related
to base extension do deserve to be solved and are at least as important as
the speed-up.
> It is true that `zeta()` for number fields is slow, but that can easily
be improved (#18917).
It would be great if it could, but when making a speed improvement to
`zeta()` in #15486, I found out that it was necessary to avoid calling
PARI's `nfinit()`, because it was too slow for the number fields involved.
This unfortunately precludes using PARI's `nfrootsof1()`...
--
Ticket URL: <http://trac.sagemath.org/ticket/6018#comment:25>
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