#10448: Side-effect of EllipticCurve.torsion_group: Destroying uniqueness of
parents
-------------------------------+--------------------------------------------
Reporter: SimonKing | Owner: cremona
Type: defect | Status: new
Priority: critical | Milestone: sage-4.6.1
Component: elliptic curves | Keywords: torsion_group, uniqueness of
parents, coerce map
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-------------------------------+--------------------------------------------
We have
{{{
sage: K.<i>=NumberField(x^2 + 1)
sage: R = ZZ.extension(x**2+1,'i')
sage: f1 = K.coerce_map_from(R)
sage: f1.domain() is R
True
sage: E = EllipticCurve(K,[0,0,0,1,0])
sage: E.torsion_subgroup()
Torsion Subgroup isomorphic to Z/2 + Z/2 associated to the Elliptic Curve
defined by y^2 = x^3 + x over Number Field in i with defining polynomial
x^2 + 1
sage: R = ZZ.extension(x**2+1,'i')
sage: f2 = K.coerce_map_from(R)
sage: f2.domain() is R
False
sage: f2.domain() == R
True
}}}
Hence, on the one hand, computing the torsion group destroys uniqueness of
parents, and moreover, it makes the coerce map from an order to its
ambient field have a domain that is not the same that is requested.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10448>
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 post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
