I'm not surprised. These fields should be written to use NTL as a  
backend directly (and probably using the same ideas as polynomial  
template, and there's enough finite fields that they should probably  
be put into their own directory while all the re-factoring is going  
on...) but no one's found the time or need to do it yet.

- Robert


On Jul 30, 2009, at 3:19 PM, VictorMiller wrote:

> Thanks, I found that it even gets much worse with a bigger finite
> field.
>
> For example if p = next_prime(1000000)
>
> and I try the same experiment in GF(p^2), Magma is over 100 times
> faster!
>
> Victor
>
> On Jul 30, 6:07 pm, Robert Bradshaw <[email protected]>
> wrote:
>> On Jul 30, 2009, at 2:50 PM, VictorMiller wrote:
>>
>>> I just did a test of SAGE versus Magma on the same computer.
>>
>>> I had a finite field GF(19991^2), and timed generating a random
>>> element in SAGE and in Magma.
>>> I found, much to my surprise, that Magma was a factor of 7 times
>>> faster.  Does anyone know what
>>> method they use?
>>
>> No, but for this size field we're using a wrapper around pari, so I'm
>> sure there's lots of needless overhead converting and copying in our
>> implementation.
>>
>> - Robert
> >


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