PS:

On 18 Jul., 18:22, Simon King <simon.k...@uni-jena.de> wrote:
> ...
> 3rd test: Multiplication of two 2000x2000 matrices over GF(125).
> Default multiplication takes ages.
> New Strassen implementation, cutoff=20: 427 seconds using 6.9% of my
> computer's memory.
> Old Strassen implementation, cutoff=20: 431 seconds using 9.3% of my
> computer's memory.
>
> I don't know if it is worth it. Shall I open a ticket and post my
> patch?

Concerning "worth it": Even without Strassen multiplication, MeatAxe
only needs about 12 seconds for that example.

So, one could argue that it is not worth it: One easily gets a better
speed in a different way.

Or one could argue that it is worth it: If one uses
sage.matrix.strassen on top of MeatAxe then the speed might be even
better (perhaps close to Magma speed). By the way, the MeatAxe version
I started with is 2.2.4 -- it was a special release under GPL 2+
(otherwise identical to 2.2.3, which is GPL2 only). So, the licence
problem might be solvable.

Or one could argue that it is not worth it: LinBox already has
Strassen. So, it might be better if Burcin and Martin revived the
LinBox wrapper (so that we have full speed over finite prime fields)
and then use the tricks discussed earlier in this thread to extend it
to non-prime fields (which would be quite a lot of work).

Anyway, I think Strassen multiplication should become the default for
Matrix_modn_dense.

What do people think?
Cheers,
Simon

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