#8327: Implement the universal cyclotomic field, using Zumbroich basis
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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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Comment (by robertwb):
Lots of good code here!
Some comments:
* Why is get_parent_of_embedding in the pyx file when it's only used in
the py file?
* No need to lazily import universal_cyclotomic_field_c, it's already
behind another lazy import.
* CyclotomicField._coerce_map_from_ # TODO: use the embedding of other
properly: you could use the method introduced in #13765, but if you don't
want to do that then at least check it has the "standard" embedding
sending the generator to the primitive root of unity CC or return None
rather than silently producing wrong answers.
* Shouldn't _coerce_map_from_ accept QQ?
* Does "endowed with the Zumbroich basis" need to be part of the printed
name? Also, what about a nice _latex_ representation?
* Using {{{<>}}} for != is deprecated, and I think goes away in python 3.
* Any reason not to inherit from Field?
* The {{{if bracket == ...}}} list might be better done with a dictionary
mapping left to right, with a good exception on KeyError. Even better,
IMHO, is to accept any even-character string (so one would pass "" or "[]"
or "<<>>" or whatever one wanted).
* {{{_gap_init = _repr_}}} Not now that we've allowed different printing
options.
* {{{__hash__}}} will fail on a 32-bit machine. Instead, test making a
dict with UCF items then retrieving one.
* is ZumbroichBasisIndices really a Parent?
* I agree with nbruin, there's a lot of caching going on that never gets
freed. I would suggest having capped size caches, if you determine that
you really need them. (Also, for CyclotomicFieldCached, better to fix this
to make CyclotomicField faster, possibly using a weakref cache or one of
the unique parent factories.)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8327#comment:151>
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