#14832: Unified construction of irreducible polynomials over finite fields
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Reporter: pbruin | Owner: cpernet
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.12
Component: finite rings | Resolution:
Keywords: polynomials | Work issues: double colons, check for
finite fields
Report Upstream: N/A | Reviewers: Jean-Pierre Flori
Authors: Peter Bruin | Merged in:
Dependencies: #14817 | Stopgaps:
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Comment (by jpflori):
Replying to [comment:8 pbruin]:
> I did not introduce this way of checking for finite fields; I just moved
it to a more specific `__init__` method. Having said that, I wouldn't
agree that using the category framework here is a good thing.
>
> First, a finite field might be in different categories (e.g.
`FiniteFields` or the future category of subfields of an algebraic closure
of '''F''',,''p'',, that we were discussing at #8335); probably the
polynomial ring constructor shouldn't have to care about that.
>
I'd say that a subfield of an algebraic closure would be in the category
of finite fields and the new one, just as it is as well in that of
integral domains.
> Second, one reason to have different implementations of `PolynomialRing`
''is'' so that we can take advantage of implementation details of
(subclasses of) `FiniteField`. There already is an implementation for
polynomials over NTL finite fields; similarly, for PARI finite fields it
would be desirable to have an implementation for polynomials over those
fields. (I have some code that is much slower than necessary because it
uses PARI finite field elements but NTL polynomials over the same finite
fields.)
I agree, but I don't think the test performed by is_FiniteField is to
ensure implementations details, but really the fact that the robject
represents a finite field.
Anyway, as you pointed out you just moved the test so let's keep this for
later.
If you fix the doc, I'll happily positive review that.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14832#comment:9>
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