#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 defeo):
Replying to [comment:83 pbruin]:
This discussion looks like the dear old dichotomy between quick feature
integration and long specification design.
Having some kind of support for lattices of finite fields has been a long
standing request. I agree with pbruin that a better interface between
generic finite fields and their actual implementation would be beneficial.
But this ticket is ready for review, while pbruin's is not. Would it be
that hard to adapt pbruin's or any other interface if this ticket is
merged? I'm willing to give positive review to this ticket, if it stands
some more testing, and it doesn't mess too much with #12142.
I'm not convinced that the interface can be decided independently of the
actual algorithms. Magma's interface is engineered around the fact that
constructing fields is fast, but constructing the embeddings is slow
(hence the Embed function, which must explicitly be called by the user).
If Sage ends up having a different construction (e.g., De Smit-Lenstra
lattices... although I've looked into it, and I don't think it is viable
in general), I think the interface could be different.
There are many solutions to the compatibly embedded finite fields problem,
no one being ideal. I'm more in favor of seeing them emerge in parallel,
being developed in different tickets under different namespaces and APIs,
rather than fixing the API now, and than realizing that it needs to be
amended. Once a construction clearly stands out, then we can thrash it
upon the user as the default ``GF(p^n^)`` construction (ok, this ticket is
already thrashing, but it has the merit of being the first one!).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8335#comment:84>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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