#8335: Finite Field lattices for (pseudo-)Conway polynomials
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Reporter: roed | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: algebra | Resolution:
Keywords: days49 | Work issues:
Report Upstream: N/A | Reviewers: Jean-Pierre
Flori, Luca De Feo
Authors: David Roe, Jean-Pierre Flori | Merged in:
Dependencies: #13894 | Stopgaps:
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Comment (by pbruin):
Continuing the discussion from #13214; in the context of my remark
>> there should probably be two categories into which a finite field can
be put:
>> - the category of all finite fields. In this category, between any two
objects there are either several morphisms or none at all, but no
canonical one.
>> - the category of finite subfields of a given algebraic closure of Fp.
In this category there is at most one morphism beteen any two objects,
namely the inclusion qua subfields of the given algebraic closure.
Jean-Pierre Flori wrote (referring to the second option)
> #8335 provides such an imlementation, though it not really practical for
large fields and there is no proper categorical framework as you suggest.
> This framework could be implemented in an independent ticket (and should
if we want to be able to merge some tickets in a finite amount of time).
Certainly; both this ticket and #13214 are already large enough. The
question is whether (a draft of) a categorical framework (i.e. algebraic
closure of '''F''',,''p'',,) should be made first, or whether the new code
from this ticket should be inserted into the current framework (which
implements the first of the two categories) and be moved to a new
framework as soon as we have it.
I would personally prefer the first option to keep things better packaged;
this patch seems to make (pseudo-)Conway polynomials pop up in many
different places, and moving them all to one place would require another
intrusive Trac ticket later.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8335#comment:81>
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