#8327: Implement the universal cyclotomic field, using Zumbroich basis
-----------------------------------------------------+----------------------
Reporter: nthiery | Owner:
Type: enhancement | Status:
needs_review
Priority: major | Milestone: sage-5.6
Component: number fields | Resolution:
Keywords: Cyclotomic field, Zumbroich basis | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Christian Stump, Simon King | Merged in:
Dependencies: #13727, #13728 | Stopgaps:
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Changes (by stumpc5):
* dependencies: #13727, #13728, #13734, #13735 => #13727, #13728
Comment:
Replying to [comment:115 chapoton]:
Thanks for your first look!
- I deleted the two later dependencies, since they are not really
necessary (I only needed them at some point to work with the universal
cyclotomics).
- I took your remarks into account:
> - why are we changing the import of hecke_modules in this patch ?
because the import of hecke_modules and of universal_cyclotomic_field
causes an import loop. Since we want to use {{{UCF}}}, it was easier and
cleaner to lazily import hecke_modules.
> - is_unit should be removed, as already implemented in the class of
Field elements
the inherited {{{is_unit}}} method is not capturing the situation. It's
implementation is
{{{
def is_unit(self):
if self == 1 or self == -1:
return True
raise NotImplementedError
}}}
> - it would be worth adding some of the methods of QQbar elements :
minpoly and abs maybe
not yet done!
> - maybe consider a coercion of real elements to the field AA ?
This is impossible, isn't it? Here is a quote from the documentation:
"Another consequence of the consistency condition is that coercions can
only go from exact rings (e.g., the rationals QQ) to inexact rings (e.g.,
real numbers with a fixed precision RR), but not the other way around."
Or am I misunderstanding something?
> 1 the field UCF is contained in the complex field
This coercion is going through QQbar, so I only documented the later.
Best, Christian
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8327#comment:116>
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