Dear Joel,
On Oct 9, 7:28 pm, "Joel B. Mohler" <[EMAIL PROTECTED]> wrote:
<snip>
> Hmm, that's a pretty big improvement over the SAGE time above. I suspect that
> we will have to work a lot harder than either of our optimizations have so
> far.
After slightly improving my MeatAxe extension type for Sage, i had a
closer look of what happens.
In the following table, r_n denotes the ratio
(computation time with Sage)/(computation time with MTX)
for nxn matrices over GF(p).
The table provides r_1 and r_100, and a matrix size c so that r_c is
close to 1.
p | r_1 | c | r_100
----------------------------
2 | 39.0 | 70 | 0.67
3 | 38.0 | -- | 1.35
5 | 38.5 | 37 | 0.68
29 | 38.3 | 18 | 0.21
97 | 38.5 | 18 | 0.19
I think this indicates that simply the multiplication of field
elements is faster in MTX.
As far as i understand, MeatAxe (at least in the 1995 version) uses
multiplication tables read from a file, at least for fields of order
<256.
So, if i'm right, it doesn't do an actual computation, which may
explain why it is faster for small matrices.
Cheers
Simon
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