#14990: Implement algebraic closures of finite fields
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: algebra | Resolution:
Keywords: finite field | Merged in:
algebraic closure | Reviewers:
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: u/pbruin/14990 | fdd883792076e8cdb2b1ae7a15cfe28b36d653ca
Dependencies: #14958, #13214 | Stopgaps:
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Comment (by pbruin):
Hi Vincent,
> 1) I found that your explanation is rather vague: it is not clear if you
speak about mathematics or the Sage implementation.
Both: mathematically speaking, algebraic closures are not unique up to
unique isomorphism unless you fix some standard model, and therefore we
necessarily have a similar non-uniqueness in Sage reflecting this
mathematical fact. I tried to make clear how the mathematical fact
influences the Sage implementation, but let me know if you have a concrete
idea for improving this paragraph.
> Moreover, this weirdness only concerns pseudo-Conway implementation
(which is right now the only one).
Certainly, that is why the new paragraph starts with "In the current
implementation".
> In a future, we might implement Jean-Pierre idea: deal with Conway
polynomial or have a certified- non-random version of pseudo-Conway.
Of course, but we are still in the present... 8-)
(Actually, I'm sceptical about the possibility of defining "certified-non-
random version of pseudo-Conway" in a way that would improve on the
original Conway polynomials. Besides, I would say that the "idea" of
using Conway polynomials should be attributed to Conway!)
> 2) It must absolutely be clear in the documentation of
`.algebraic_closure` that the pickling is broken! This is the main entry
point for users.
OK, I'll add some explanation there too. But I am against phrasing it as
"pickling is broken"; we should really say that this is an inherent
"feature" of the non-unicity of algebraic closures, at least until we
support any standard model.
> 3) Do you agree to add to the documentation the different weirdnesses I
described in my comments ? (possibly in a TODO section)
I don't see quickly which "weirdnesses" are still remaining, could you
give me a list?
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:83>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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