#12880: Inconsistent domain, codomain and parent in EllipticCurveIsogeny
-----------------------------------+------------------------
Reporter: nthiery | Owner: cremona
Type: defect | Status: new
Priority: minor | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #11474 | Stopgaps:
-----------------------------------+------------------------
Changes (by pbruin):
* priority: major => minor
* dependencies: => #11474
Old description:
> In the following example, the domain and codomain of phi does not match
> with that of its parent::
>
> {{{
> sage: sage: E = EllipticCurve(j=GF(7)(0))
> sage: phi = EllipticCurveIsogeny(E, [E(0), E((0,1)), E((0,-1))])
> sage: phi.parent()
> Set of Morphisms from Abelian group of points on Elliptic Curve
> defined by y^2 = x^3 + 1 over Finite Field of size 7 to Abelian group of
> points on Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of
> size 7 in Category of hom sets in Category of Schemes
> sage: phi.parent().domain()
> Abelian group of points on Elliptic Curve defined by y^2 = x^3 + 1
> over Finite Field of size 7
> sage: phi.domain()
> Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 7
> sage: phi.parent().codomain()
> Abelian group of points on Elliptic Curve defined by y^2 = x^3 + 1
> over Finite Field of size 7
> sage: phi.codomain()
> Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 7
> }}}
New description:
In the following example, the domain and codomain of phi do not match
those of its parent::
{{{
sage: E = EllipticCurve(j=GF(7)(0))
sage: phi = EllipticCurveIsogeny(E, [E(0), E((0,1)), E((0,-1))])
sage: phi.parent()
Set of Morphisms from Abelian group of points on Elliptic Curve defined by
y^2 = x^3 + 1 over Finite Field of size 7 to Abelian group of points on
Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 7 in
Category of hom sets in Category of Schemes
sage: phi.parent().domain()
Abelian group of points on Elliptic Curve defined by y^2 = x^3 + 1 over
Finite Field of size 7
sage: phi.domain()
Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 7
sage: phi.parent().codomain()
Abelian group of points on Elliptic Curve defined by y^2 = x^3 + 1 over
Finite Field of size 7
sage: phi.codomain()
Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 7
}}}
--
Comment:
It should be very easy to fix in principle:
{{{
#!diff
diff --git a/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
b/src/sage/schemes/e
index 5cdbbdf..a729d3a 100644
--- a/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
+++ b/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
@@ -1322,12 +1322,9 @@ class EllipticCurveIsogeny(Morphism):
self._codomain = self.__E2
# sets up the parent
- parent = homset.Hom(self.__E1(0).parent(), self.__E2(0).parent())
+ parent = homset.Hom(self.__E1, self.__E2)
Morphism.__init__(self, parent)
- return
-
-
# initializes the base field
def __init_algebraic_structs(self, E):
r"""
}}}
The only problem is that this breaks testing for equality of isogenies,
due to #11474. Suppose `E -> E1` is an isogeny and `E2` is an elliptic
curve that is equal but not ''identical'' to `E1`. Then `Hom(E, E1)` and
`Hom(E, E2)` will also be equal but not identical; since the coercion
model assumes uniqueness of parents, it will never regard corresponding
elements of `Hom(E, E1)` and `Hom(E, E2)` as equal.
For some reason the Hom sets between the groups of points, on the other
hand, ''are'' identical, which explains why equality testing currently is
not broken.
--
Ticket URL: <http://trac.sagemath.org/ticket/12880#comment:6>
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