#14990: Implement algebraic closures of finite fields
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_work
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 pbruin):
I agree with Jean-Pierre's analysis. Let me just add that one shouldn't
read too much mathematical meaning into equality (`==`) of parents. The
main use for it is in deciding whether to allow coercion from one
`AlgebraicClosureFiniteField` to another. For that, the only thing that
make sense is to check if the PCPL's are the same. Here we do definitely
want to check "only" equality, not identity. If we did anything less than
checking equality, say only checking if one lattice is equal to a
sublattice of the other, then we would be asking for trouble. For
example, if we had an element ''x'' in the subfield of degree ''n'' in one
of the two, then we would have no guarantee that the subfield of degree
''n'' that would have to be constructed in the other instance (where we
want to coerce ''x'') would be the same.
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Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:68>
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