#11276: bug in documentation for non_surjective for Galois representations
attached
to elliptic curves
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Reporter: dpathakjee
| Owner: cremona
Type: defect
| Status: new
Priority: minor
| Milestone: sage-5.10
Component: elliptic curves
| Resolution:
Keywords: galois representation, elliptic curves, non_surjective,
documentation | Work issues:
Report Upstream: N/A
| Reviewers:
Authors:
| Merged in:
Dependencies:
| Stopgaps:
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Description changed by chapoton:
Old description:
> non_surjective() docstring incorrectly states that it's inconclusive and
> often wrong for p=2. The function it calls, is_surjective, is correct for
> p=2.
>
> The docstring states that "[the] list of primes p such that the mod-p
> representation *might* not be surjective... usually contains 2, because
> of shortcomings of the algorithm..." However, non_surjective calls
> is_surjective, which should always be correct for p=2,3 because it
> computes the Galois group of the 2-division polynomial. (More precisely,
> its helper, _is_surjective, does this.) I suspect this caveat may have
> been written before the special cases for p=2,3 in _is_surjective had
> been written.
>
> All that really needs to be done is to remove the phrase "(this list
> usually contains 2, because of shortcomings of the algorithm)" from the
> docstring.
>
> See also [http://trac.sagemath.org/sage_trac/ticket/11271 11271],
> [http://trac.sagemath.org/sage_trac/ticket/11270 11270]
New description:
non_surjective() docstring incorrectly states that it's inconclusive and
often wrong for p=2. The function it calls, is_surjective, is correct for
p=2.
The docstring states that "[the] list of primes p such that the mod-p
representation *might* not be surjective... usually contains 2, because of
shortcomings of the algorithm..." However, non_surjective calls
is_surjective, which should always be correct for p=2,3 because it
computes the Galois group of the 2-division polynomial. (More precisely,
its helper, _is_surjective, does this.) I suspect this caveat may have
been written before the special cases for p=2,3 in _is_surjective had been
written.
All that really needs to be done is to remove the phrase "(this list
usually contains 2, because of shortcomings of the algorithm)" from the
docstring.
See also #11271, #11270
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11276#comment:1>
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