#11683: ell_curve_isogeny initialization
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Reporter: saraedum | Owner: cremona
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-4.8
Component: elliptic curves | Keywords: startup,
initialization, sd32, sd35
Work_issues: | Upstream: N/A
Reviewer: Julian Rueth, Frithjof Schulze | Author: Julian Rueth,
John Cremona
Merged: | Dependencies:
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Changes (by cremona):
* status: needs_info => needs_review
Comment:
Replying to [comment:17 saraedum]:
> [the docstring said "10" hours of course]
>
> We fixed a few typos. Looking at the changes to
{{{isogenies_prime_degree_genus_0()}}} we're wondering if this actually
adds any new functionality/fixes a problem? If so, shouldn't there be a
doctest for it?
The algorithm has been slightly simplified in the following ways: it
works with the Fricke polynomials which are ZZ[t] rather than the actual
Fricke modules (which are rational functions with denominator t), thus
avoiding the creation of rational functions. Secondly, it uses a
different model for the universal elliptic curve defined over Q(t), which
is integral over Z[t] and has good reduction at as many places as
possible. This makes the generic kernel polynomials lie in Z[t][x] rather
than Q(t)[x], and also makes them simpler.
The previous version was not incorrect at all, but this seemed to be the
right time to replace the older models with new ones, since the code was
being refactored anyway.
Thanks for fixing the typos; I have set the ticket back to "needs
review".
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11683#comment:19>
Sage <http://www.sagemath.org>
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