#13214: Frobenius endomorphism over finite fields
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Reporter: caruso | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: basic arithmetic | Resolution:
Keywords: frobenius finite fields | Work issues: does not build
Report Upstream: N/A | Reviewers: Paul Zimmermann
Authors: Xavier Caruso | Merged in:
Dependencies: #13184 | Stopgaps:
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Comment (by jpflori):
Replying to [comment:26 pbruin]:
> As for the differing purposes of the two approaches, 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.
Which is basically what we currently have and also what this ticket does.
>
> - the category of finite subfields of a given algebraic closure of
'''F''',,''p'',,. In this category there is at most one morphism beteen
any two objects, namely the inclusion qua subfields of the given algebraic
closure.
I would like this to be the default at some point, just like in Magma, not
because I want to replicate Magma but for usual computations it seems a
more practical choice.
#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).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13214#comment:27>
Sage <http://www.sagemath.org>
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