Hi!

Working at #11589, I revisited the almost-forgotten ticket #8096 (no
activity since 16 months), which aims at speeding up matrix
multiplication.

#10763 (already merged) and #11589 (positive review) provide some
improvement. However, using the defaults in Sage, the multiplication
of two random dense 2000x2000 matrices over GF(3) still takes 8.34
seconds (it used to be 12 seconds).
That does not compare nicely with my tuned (i.e. unpublished) version
of C-MeatAxe, which completes the same task in 1.72 seconds.

So, obviously it makes sense to try and improve Sage's matrix
multiplication. That may actually be rather easy, because linbox can
do the above multiplication in 1.65 seconds (using _multiply_linbox).

Is there a compelling reason why linbox multiplication is not the
default for dense matrices over finite fields?

Best regards,
Simon

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