#18942: Weird bug in roots of a polynomial in relative number field extension
------------------------------------------------+------------------------
Reporter: robharron | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: number fields | Resolution:
Keywords: Relative number field, roots | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
------------------------------------------------+------------------------
Comment (by kedlaya):
Replying to [comment:2 pbruin]:
> In fact, in the above example we have
> {{{
> sage: K == L
> True
> }}}
> which causes a cache lookup in `PolynomialRing` to return `K['x']` when
given `L` as input.
>
> We should probably make number fields satisfy `K == L` if and only if `K
is L`, i.e. make them inherit from `WithEqualityById`. Doing this in the
most naive way unfortunately leads to a number of doctest failures.
In this example, we also have:
{{{
sage: hash(K) == hash(L)
True
}}}
which is presumably why `PolynomialRing` is fooled. Digging into
`src/sage/rings/number_field/number_field.py`:
{{{
def __hash__(self):
r"""
Compute the hash value of this number field.
TESTS:
Since there is a custom implementation of :meth:`__cmp`, we need a
custom ``__hash__``. The number fields ``K`` and ``L`` in the
following
example used to have different hashes prior to :trac:`11670`::
sage: R.<x> = QQ[]
sage: R.<y> = QQ[]
sage: K.<a> = NumberField(x^2+1)
sage: L.<a> = NumberField(y^2+1)
sage: K == L
True
sage: hash(K) == hash(L)
True
"""
return hash((self.variable_name(), self.base_field(),
tuple(self.__polynomial)))
}}}
It appears that `self.__polynomial` is the absolute defining polynomial,
not the relative one. I'm guessing this was done on purpose to fix some
other problem, judging from this byline:
{{{
- Julian Rueth (2014-04-03): absolute number fields are unique parents
}}}
It might be worth trying to replace `self.__polynomial` with something
like `self.relative_polynomial()` to see how much doctest breakage
results.
--
Ticket URL: <http://trac.sagemath.org/ticket/18942#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
