Ticket #8998 (closed defect: fixed)
galois_action on cusps has a bug
|Reported by:||was||Owned by:||craigcitro|
|Report Upstream:||N/A||Reviewers:||John Cremona|
|Authors:||William Stein||Merged in:||sage-4.7.alpha5|
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.
- Status changed from needs_review to positive_review
- Reviewers set to John Cremona
- Authors set to William Stein
- Status changed from positive_review to closed
- Resolution set to fixed
- Merged in set to sage-4.7.alpha5