#8335: Finite Field lattices for (pseudo-)Conway polynomials
------------------------------------------------+---------------------------
Reporter: roed | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: algebra | Resolution:
Keywords: days49 | Work issues:
Report Upstream: N/A | Reviewers: Jean-Pierre
Flori, Luca De Feo
Authors: David Roe, Jean-Pierre Flori | Merged in:
Dependencies: #13894 | Stopgaps:
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Comment (by jpflori):
Ok, the last tests I added:
{{{
sage: old_exists_cp =
sage.rings.finite_rings.constructor.exists_conway_polynomial
sage: sage.rings.finite_rings.constructor.exists_conway_polynomial
= lambda p, n: False
sage: k = GF(3**10)
sage: l = GF(3**20)
sage: k.modulus() == conway_polynomial(3, 10)
False
sage: l(k.gen()**10) == l(k.gen())**10
True
sage: del k, l
sage: import gc
sage: gc.collect();
sage: sage.rings.finite_rings.constructor.exists_conway_polynomial
= old_exists_cp
}}}
introduced some failures in the test:
{{{
sage: GF.other_keys(key, K)
[(9, ('a',), x^2 + 2*x + 2, None, '{}', 3, 2, True),
(9, ('a',), x^2 + 2*x + 2, 'givaro', '{}', 3, 2, True)]
}}}
Indeed, although I explicitely asked to delete k and l and restored a
proper exists_... function, the field GF(3**20) stay cached and so the
pseudo-Conway, but not Conway, modulus used to build GF(3**2).
The reason for that is that we performed arithmetic on elements of k and l
which triggered creation of an embedding of k into l which prevents the
collection of k and l.
This is bad and is surely the same problem as in #14711.
So I just removed the hack forcing the use of pseudo-Conway polynomials.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8335#comment:69>
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