On Saturday, September 17, 2016 at 11:13:46 AM UTC-7, William stein wrote:
>
>
>
> On Sat, Sep 17, 2016 at 10:39 AM, Jonathan Bober <jwb...@gmail.com
> <javascript:>> wrote:
>
>> Ok, so I figured out what is going on here, at least.
>>
>> When S = CuspForms(N, k), a call to S.hecke_polynomial() passes through a
>> bunch of abstract layers and then eventually arrives at
>> S._compute_hecke_matrix_prime(self, p, prec=None),
>> in sage/modular/modform/space.py. To compute the hecke matrix, this
>> function computes a basis of cusp forms, explicitly computes the action of
>> the Hecke operator on this basis, and then does linear algebra to find the
>> matrix of this operator on this basis. Which is all rather roundabout,
>> since it ends up using modular symbols to compute hecke matrices to compute
>> a basis. I understand why this might take 5 hours.
>>
>> Maybe there is some sense to this very generic functionality, if, e.g., I
>> can use it to more efficiently compute the same thing for a small
>> dimensional subspace.
>>
>
> You should implement a more optimized approach in the case of just
> computing the Hecke polynomial. There's a million things in Sage (or any
> math software) where the most optimal strategy isn't implemented, so the
> system falls back to something generic that works.
>
> -- William
>
>

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+1. I just created ticket #21546 for this issue.
Kiran
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