On Wednesday, October 29, 2014 1:25:08 PM UTC+1, parisse wrote:
>
> Just curious: what is the algorithm used by sage here? 
> I have tried Bareiss, modular and p-adic with giac, and Bareiss seems the 
> fastest: 0.02s on my Mac, vs about 1s for (proven) modular/p-adic. 
> sage 6.3 returns the answer in 0.12s on my computer, while Maxima takes 
> 15s.
>

Sage uses different algorithms based on difficulty.
http://git.sagemath.org/sage.git/tree/src/sage/matrix/matrix_integer_dense.pyx#n3252

I'm guessing in this case it's this branch:
http://git.sagemath.org/sage.git/tree/src/sage/matrix/matrix_integer_dense_hnf.py#n184

-- harald
 

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