#14990: Implement algebraic closures of finite fields
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.13
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 | 4265b4fe176d32b3bc7cbc616f8f0964e273ecdb
Dependencies: #14958, #13214 | Stopgaps:
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Comment (by pbruin):
Something else: I would prefer if the implementation of `nth_root()` could
be improved before getting this ticket merged. The basic difficulty is
figuring out in which subfield we have to look. Rather than trying
extensions of degrees dividing ''n'' (is it true/clear that the degree has
to divide ''n''?), I think we should either factor ''x^n^'' - ''a'' (where
''a'' is the element whose ''n''-th root we want) and look at the smallest
degree of a factor, or we should compute the multiplicative order of
''a''. Also, before doing anything else, we should take all factors ''p''
out of ''n'' and use `pth_root()`.
I hope to have an update soon, at least for the remaining things mentioned
in the previous comment.
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:50>
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