#8998: galois_action on cusps has a bug
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Reporter: was | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone: sage-4.4.3
Component: modular forms | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Ticket #5822 implemented the action of Galois on cusps. I think the
algorithm was only designed to work for Gamma_0(N). However, the code
runs for other groups, and doesn't raise an error. Unfortunately, it
gives completely wrong results in some cases, e.g.,
{{{
sage: G = Gamma1(19)
sage: rational_cusps = [c for c in G.cusps() if
c.galois_action(2,19).is_gamma1_equiv(c,19)]
sage: rational_cusps
[0, 2/19, 1/9, 1/8, 1/7, 3/19, 1/6, 1/5, 4/19, 1/4, 5/19, 6/19, 1/3,
7/19, 8/19, 9/19, 1/2, Infinity]
}}}
However, exactly half the cusps are rational (see, e.g., my paper
http://wstein.org/papers/j1p/ or the work of Kubert-Lang).
This came up in research that Michael Stoll and I were doing, and it was
temporarily very confusing.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8998>
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