#14990: Implement algebraic closures of finite fields
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
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 | 33f982f1acbf61cf08897e6a46ee23bb14e78e1e
Dependencies: #14958, #13214 | Stopgaps:
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Comment (by defeo):
Hi,
> As far as I understand, a pseudo Conway polynomial is not uniquely
defined. But nevertheless, the implementation of
`PseudoConwayLattice.polynomial` is, no? The only thing that today
prevents the uniqueness is the use of the database
I think there are some random choices of roots in the pseudo-Conway
algorithm. Am I wrong? And even then, in practice a pseudo-Conway lattice
can never be computed completely, and when you are given a partial pseudo-
Conway lattice, there are many different ways of completing it.
Anyway, I agree with Peter. This ticket is not only about pseudo-Conway
polynomials. There's plenty of algorithmic ways of constructing the
algebraic closure of GF(p), each with its pros and cons. None of them is
canonical: even the famous "canonically embedded lattices" of Lenstra and
De Smit, use an arbitrary lexicographic order at some point to make things
canonical. So my opinion is that even for those "canonical" constructions,
it is arguable whether they should be unique representations.
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:64>
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