#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):
Replying to [comment:11 niles]:
> Replying to [comment:10 pernici]:
> > 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.
>
> I see -- maybe -- can this patch be written to use PARI directly by
default then? In the cases where it isn't as fast, the computation time
should be small anyway, right?
It depends on the use cases; a user may need to do usually a lot of
computations with low precision series; then it is important that they are
done fast; in the rare case in which he needs a high precision
computation, maybe he does not care that it takes 3x longer. Another user
may care only for long computations.
Another observation: I suspect that total degree multivariate power series
implemented with PARI would require changes in the implementation in
ticket #1956, not only in this patch; the background power series ring
would not be `PowerSeriesRing(self.__poly_ring, T)`, but a PARI power
series. For certain rings probably one cannot use PARI (e.g. symbolic
rings?), then the current implementation should be used instead.
Maybe it would be better to make a specialized multivariate power series
class using PARI; this would be the argument of another ticket, if someone
is interested in working on it; ticket #1956 and this patch would deal
with the generic implementation.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10532#comment:12>
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