#8723: Change to return type of E.multiplication_by_m(m,True)
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Reporter: cremona | Owner: cremona
Type: defect | Status: closed
Priority: minor | Milestone: sage-6.1
Component: elliptic curves | Resolution: fixed
Keywords: | Merged in:
Authors: Frédéric Chapoton | Reviewers: John Cremona
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/cremona/ticket/8723 | b8268eaa6c967c22fe13f08a13017f4e82ce8476
Dependencies: | Stopgaps:
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Comment (by saraedum):
I just stumbled upon this while working on #16129.
Replying to [comment:20 cremona]:
> New commits:
>
||[[http://git.sagemath.org/sage.git/commit/?id=1fec983|1fec983]]||reviewer's
patch, makes sure that the parents are correct even with caching||
If I understand correctly, this is to make sure that the returned elements
live in the correct rings. Does this really work the way it is meant to?
The `x` in a univariate/bivariate ring can not be distinguished in the
cache:
{{{
sage: R.<x,y> = QQ[]
sage: S.<x> = QQ[]
sage: R(x) == S(x)
True
sage: hash(R(x))==hash(S(x))
True
}}}
So what actually makes the patch work is this explicit conversion back to
the right ring:
{{{
- mx = self._multiple_x_numerator(m.abs(), x) /
self._multiple_x_denominator(m.abs(), x)
+ mx = (x.parent()(self._multiple_x_numerator(m.abs(), x))
+ / x.parent()(self._multiple_x_denominator(m.abs(), x)))
}}}
In other words, `_multiple_x_numerator/denominator` still return elements
in the wrong ring. This is probably acceptable since they are marked as
internal methods anyway:
{{{
sage: E = EllipticCurve([0,0,0,0,1])
sage: R.<x,y> = QQ[]
sage: E._multiple_x_numerator(2, x).parent()
Univariate Polynomial Ring in x, y over Rational Field
sage: E._multiple_x_numerator(2).parent()
Univariate Polynomial Ring in x, y over Rational Field
}}}
Should I fix this in #16129?
What causes actual trouble for me is that `x` has been added to the cache
key in `division_polynomial_0`. Why is it necessary there? Is
`division_polynomial_0` ever called with a different `x` but the same
`cache`?
--
Ticket URL: <http://trac.sagemath.org/ticket/8723#comment:33>
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