#14990: Implement algebraic closures of finite fields
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Reporter: pbruin | Owner:
Type: enhancement | Status:
Priority: major | needs_review
Component: algebra | Milestone: sage-5.13
Keywords: finite field algebraic | Resolution:
closure | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #14958, #13214 | Stopgaps:
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Changes (by defeo):
* cc: defeo (added)
Comment:
Nice work. I agree this is the way to go for Fp-bar. Here's some thoughts.
1. It'd be nice to implement a `_latex_` method in the elements.
2. There's a quote problem in the first paragraph of the docstring:
{{{
'[\Bold{F}_n:\Bold{F}]=1`
}}}
3. I'm perplexed about the `_cmp_` function in `conway_polynomials.py`:
{{{
sage: PCL3 = PseudoConwayLattice(3, use_database=False)
sage: PCL5 = PseudoConwayLattice(5, use_database=False)
sage: PCL3 == PCL5
True
}}}
Is this the intended result?
4. `F.inclusion(1, a).section()` is `None` for any `a`, this makes
`_change_level` fail.
5. I wonder: wouldn't it be more efficient if `_coerce_2` had a shortcut
for when `x` and `y` are in the same level? (I really don't know, just
wondering)
6. This patch lacks some obvious coercions, for example,
`F._subfield(2)(F.gen(2))`. Should this wait for another ticket, or should
this ticket do it?
I'd like to play around with different implementations of Fp-bar. This
would help understand if the abstract class
`AlgebraicClosureFiniteField_generic` is abstract enough, or if we need to
think more carefully about its interface.
I don't know what's best: make this ticket enter 5.13, then start
experimenting? Or, rather, keep experimenting and wait the different
implementations to have settled before giving positive review?
If you want to go for the first, I'd be happy to give positive review as
soon as the minor problems mentioned above are solved. If you prefer the
second option, would you mind switching to git, so to ease collaboration?
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:7>
Sage <http://www.sagemath.org>
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