#14264: Fix negation of Jacobian morphisms
-------------------------------------+--------------------------------------
Reporter: SimonKing | Owner: AlexGhitza
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: algebra | Resolution:
Keywords: Jacobian morphism | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Simon King | Merged in:
Dependencies: | Stopgaps:
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Description changed by SimonKing:
Old description:
> The following fails with a coercion error:
> {{{
>
> sage: P.<x> = QQ[]
> sage: f = x^5 - x + 1; h = x
> sage: C = HyperellipticCurve(f,h,'u,v')
> sage: J = C.jacobian()
> sage: K.<t> = NumberField(x^2-2)
> sage: R.<x> = K[]
> sage: Q = J(K)([x^2-t,R(1)])
> sage: Q
> (u^2 - t, v - 1)
> sage: -Q
> (u^2 - t, v + u + 1)
> }}}
>
> The reason is that in the `__neg__` method, the remainder of a polynomial
> h over the rationals is computed modulo a non-constant polynomial over a
> number field. The involved `__mod__` method of FLINT polynomials would
> try to coerce the modulus into the parent of h, which fails here for
> obvious reasons.
>
> I see two possible solutions:
>
> 1. Make sure in `JacobianMorphism_divisor_class_field.__neg__` that h and
> the modulus live in the same ring, e.g., by adding the modulus to h
> before computing the remainder (which won't change the result).
> 2. In the `__mod__` method of FLINT polynomials, invoke
> coercion_model.canonical_coercion on h and the modulus, rather than
> trying to coerce the modulus into the parent of h.
>
> With the second approach, the output of `__mod__` would potentially live
> in a different ring (which should not be the case!) and since it would
> imply a general slowdown of the `__mod__` method. Therefore I prefer the
> first approach.
New description:
The following fails with a coercion error:
{{{
sage: P.<x> = QQ[]
sage: f = x^5 - x + 1; h = x
sage: C = HyperellipticCurve(f,h,'u,v')
sage: J = C.jacobian()
sage: K.<t> = NumberField(x^2-2)
sage: R.<x> = K[]
sage: Q = J(K)([x^2-t,R(1)])
sage: Q
(u^2 - t, v - 1)
sage: -Q
(u^2 - t, v + u + 1)
}}}
The reason is that in the `__neg__` method, the remainder of a polynomial
h over the rationals is computed modulo a non-constant polynomial over a
number field. The involved `__mod__` method of FLINT polynomials would try
to coerce the modulus into the parent of h, which fails here for obvious
reasons.
I see two possible solutions:
1. Make sure in `JacobianMorphism_divisor_class_field.__neg__` that h and
the modulus live in the same ring, e.g., by adding the modulus to h before
computing the remainder (which won't change the result).
2. In the `__mod__` method of FLINT polynomials, invoke
coercion_model.canonical_coercion on h and the modulus, rather than trying
to coerce the modulus into the parent of h.
With the second approach, the output of `__mod__` would potentially live
in a different ring (which should not be the case!) and it would imply a
general slowdown of the `__mod__` method. Therefore I prefer the first
approach.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14264#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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