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
>  
>

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

Kiran

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