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0 pointswbhart10y ago0 comments

Just out of curiosity I tried adding a couple of lines of code to Nemo to force it to use its mul_ks for the first benchmark. This was actually way slower. I didn't look into why.

That first benchmark is pretty dense, so it's not at all unreasonable to use KS.

On the other hand, if we force it to use KS for Z[x][y][z][t] down to Z[x][y], then classical down to Z[x], then Flint for Z[x] itself, it gets marginally faster, with 40.6s.

Clearly neither of these approaches is an optimal strategy, as the Maple timings show.

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2 comments · 1 top-level

rp21a10y ago· 1 in thread

The first benchmark is dense up to the total degree and the staircase structure is bad for Kronecker substitution. The fastest method is probably sparse polynomial interpolation.

wbhartOP10y ago

It can certainly be done much faster, even on that CPU. We'll eventually get around to that.

We have a lot of generic matrix stuff missing at present though, so that's the priority for now.

There's also things like Puiseux series and capped absolute power series and a few things like that which we can't do without.

It would be a hell of a lot of fun to optimise the hell out of both those polynomial benchmarks, but we have to be realistic and go for breadth first, rather than depth, I think.

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