#10532: Faster multiplication for multivariate power series
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Reporter: niles | Owner: malb
Type: enhancement | Status: needs_info
Priority: major | Milestone:
Component: commutative algebra | Keywords: multivariate power series
multiplication Karatsuba
Author: pernici | Upstream: N/A
Reviewer: Niles Johnson | Merged:
Work_issues: |
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Comment(by pernici):
niles wrote:
>This looks *really good* -- but I'm a little confused by the comparison
with `gp` . . . If that's always faster, should we just always do the
multiplication there? There must be more subtleties involved, but I
don't
know *anything* about them :(
Well, I don't know either, I just looked at it today.
I think that if one would like to use PARI, one should avoid `gp`
as much as possible and call directly the PARI C library functions;
in fact `gp` has a big overhead
{{{
sage: g = gp('1 + (x+y)*t + O(t^6)')
sage: %timeit g^2
25 loops, best of 3: 16 ms per loop
sage: R.<x,y> = QQ[[]]
sage: p = 1 + x + y + R.O(6)
sage: %timeit p^2
625 loops, best of 3: 56.5 µs per loop
}}}
so that it starts to be convenient to use it when the computation is long
enough.
For this reason
in the benchmark in the previous mail `gp` is slower for small precision
{{{
N prec n (0) (2) (3)
2 10 1 0.02 0.01 0.02
2 20 1 0.23 0.03 0.03
}}}
In the above benchmarks `gp` is at most 2.5x faster;
in those cases the overhead is negligible, so I guess that using directly
the PARI library the speedup would be the same.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10532#comment:10>
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