On Thu, 31 Aug 2023 at 15:00, John Cremona <[email protected]> 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.


>
> I will raise an issue and (probably) fix it right away.
>
> John
>
> On Thu, 31 Aug 2023 at 08:06, Ralf Hemmecke <[email protected]> wrote:
>
>> 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
>>
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>

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