#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 vdelecroix):
Hi Peter,
Either I badly explained something or there is something contradictory in
your argument. First of all you said
> The main use for it [the equality] is in deciding whether
> to allow coercion from one `AlgebraicClosureFiniteField`
> to another.
Fine. But that was my point, equality is broken as we currently have with
your branch applied
{{{
sage: p = next_prime(100000)
sage: K = GF(p)
sage: F1 = K.algebraic_closure()
sage: F2 = K.algebraic_closure()
sage: F1 == F2
True
sage: _ = F1.gen(3) # force computation in PCL 1
sage: F1 == F2
False
sage: _ = F2.gen(3) # same computation in PCL 2
sage: F1 == F2
True
}}}
So depending in which stage of the computation you are, there will or will
not be a coercion between your fields! Do you agree that there is a
problem here?
> we do definitely want to check "only" equality, not identity [of PCL].
Here it depends on what you mean by "equality". If it is equality as
mathematical object I do agree if it is equality as Python comparison I
strongly disagree. The Python equality of PCL currently is: "two PCL are
equal if they agree on their already made computations". And, as Jean-
Pierre mentioned, it is not the purpose of that ticket to improve that.
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:69>
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