#11271: there is a serious bug in the documentation or code for is_surjective
for
Galois representations attached to elliptic curves
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Reporter: was | Owner: cremona
Type: defect | Status: new
Priority: critical | Milestone: sage-4.7.1
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by was):
That was pretty illegible. Let me try again:
"Professor Stein,
In relation to your recently-opened ticket about Sage's elliptic curve
galois representation code
(http://trac.sagemath.org/sage_trac/ticket/11271): not only is
is_surjective's docstring wrong, but non_surjective()'s docstring is also
wrong. It says the function can be inconclusive at 2, but in fact it calls
is_surjective(), which is always right at 2 and 3 since it determines the
size of the Galois group of the p-division polynomial. Probably someone
wrote that before the special cases for 2 and 3 in is_surjective() had
been implemented.
I don't yet have a trac account to report this, or I would've just opened
a ticket. (I've requested an account.) But since you opened the ticket, I
thought you might like to know of this bug as well.
Also, regarding the other ticket (implementing the algorithm in Zywina's
paper): I've already written code that takes care of some (easy) cases in
the paper, and is pretty fast compared to the existing is_surjective.
(Specifically, just checking for surjectivity mod 8, 9 by first checking
mod 2, 4, 3 in appropriate cases with a view to determining whether a
curve is a Serre curve.) If you haven't already written it, I can clean it
up and send it to you. I'm also willing to help further.
-David Pathakjee
"
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11271#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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