#9400: modify the NumberField constructor to pass in optional integer B such
that
all the internal pari routines will replace the discriminant by its gcd
with B, making some things massively faster.
-----------------------------+----------------------------------------------
Reporter: was | Owner: davidloeffler
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.5.3
Component: number fields | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by was):
Replying to [comment:7 jdemeyer]:
> Replying to [comment:6 was]:
> > I saw that. I think the best solution is exactly what I implemented
in the attached patch. Hash based on gens (trivial, as a hash should be).
>
> Why not hash based on the HNF representation, as I propsed in #9666?
> I think this is more canonical than gens() and it is the native PARI
format.
CONS:
I think number fields will frequently be relative extensions, and we'll
also consider ideals both in the maximal order and in suborders. Pari
will likely have almost nothing to do with our general relative extensions
(it's only currently used for relative extensions as a miserable crutch),
and HNF doesn't apply for ideals in orders.
PROS:
When it works, hashing based on the HNF has the property that if I==J then
hash(I) == hash(J). That's a very good property to have. With hashing
of gens that fails.
Thus taken together, I'm OK with your proposal with the caveat that at
some future time it has to be revisited for *relative* extensions.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9400#comment:9>
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