Gamma(N)

[Ralf Hemmecke]

The following contradicts the specification of reduce_cusp for Gamma(7).

https://doc.sagemath.org/html/en/reference/arithgroup/sage/modular/arithgroup/congroup_gamma.html

sage: Gamma(7).are_equivalent(Cusp(6,7),Cusp(1,0))
True
sage: Gamma(7).reduce_cusp(Cusp(1,0))
Infinity
sage: Gamma(7).reduce_cusp(Cusp(6,7))
6/7

Ralf

[John Cremona]

Thanks for the report, you are correct and there is a bug in the code.  When reducing the cusp 6/7 it first reduced 6 and 7 mod the level 7 to get 6 and 0, then calls an internal function _lift_pair() which assumes that the new pair of integers is coprime.

I will raise an issue and (probably) fix it right away.

John

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[John Cremona]

On Thu, 31 Aug 2023 at 15:00, John Cremona <john.c...@gmail.com> wrote:

Thanks for the report, you are correct and there is a bug in the code.  When reducing the cusp 6/7 it first reduced 6 and 7 mod the level 7 to get 6 and 0, then calls an internal function _lift_pair() which assumes that the new pair of integers is coprime.

In fact the bug was slightly different:  after reducing u and v mod N (for the cusp u/v) when v=0 it was only returning Infinity (1/0) when u=1, not also when u=N-1.  I'll make a PR for this soon.