#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 vdelecroix):
Hi Peter,
I still think that the equality of algebraic closures is broken for
several reasons. I think (please correct me if you do not agree) that
- we do not want that the equality between unmutable objects changes: if
two unmutable objects are equal at a given time they still should be equal
a minute later (this is true for parents and elements)
- comparisons with == and != may never raise an error.
This is why the example I gave you before is a bug (see the other one
below if you are not convinced). I am in favour of a '''more'''
restrictive equality for fields based on identity of the pseudo conway
lattice. It will allow less coercion but at least it will be consistent
with the two things above.
Within your branch
{{{
sage: p = next_prime(100000)
sage: K = GF(p).algebraic_closure()
sage: x = K.gen(2)
sage: y = loads(dumps(x))
sage: x == y # sanity check
True
sage: _ = K.gen(5) # force computation
sage: x.parent() == y.parent()
False
sage: x == y
Traceback (most recent call last):
...
RuntimeError: BUG in map ...
}}}
In principle we could hope for a False above but the coercion system has a
cache. This is the reason for the `RuntimeError`.
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:74>
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