#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 | f9162dbae92551a67aea7a489d96591141fdebc8
Dependencies: #14958, #13214 | Stopgaps:
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Comment (by pbruin):
This is not an easy problem. First of all, I have to say I don't
understand precisely what it means for an object to be immutable. Roughly
speaking it is supposed to mean that "its value cannot change", but that
doesn't seem to be a completely well-defined notion either.
It seems to me that in the case of
`AlgebraicClosureFiniteField_pseudo_conway`, the indeterminacy of pseudo-
Conway lattices forces us to say that (1) the "value" of an instance has
to include the set of subfields that have been computed, and (2) the only
way to guarantee immutability is to define equality using identity of the
lattices.
If this reasoning is correct, ''and'' we accept that parents should be
immutable (which does sound like a reasonable condition, although I'm not
immediately convinced that it should hold in this situation), then we have
to accept Vincent's opinion that for two instances to compare equal it is
a necessary condition that the lattices be identical. In that case I
guess we may as well go all the way back to comparing by identity of the
fields themselves.
It is a bit annoying, and I do not see how to easily avoid breaking the
sanity check `loads(dumps(x)) == x` if we take this approach. Maybe we
should just capitulate on this point and disable this check in the
`TestSuite`, or explicitly give the error as the expected result of the
`TestSuite`.
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:75>
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