#331: compiled implementation of dense univariate polynomial arithmetic
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Reporter: dmharvey | Owner: somebody
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.1.3
Component: basic arithmetic | Resolution:
Keywords: |
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Comment (by dmharvey):
For multiplication, Karatubsa has complexity n^1.58^ in the degree; there
exist algorithms with complexity n log(n) log(log(n)) over arbitrary
(associative unital) rings. I think it's worth implementing this at some
point.
Yes, we need division too. And we need a framework to deal with the very
nasty bug you mentioned above. Basically Karatsuba should be disallowed by
default for such rings, I don't see any other way around it. Perhaps the
user should be able to call some interface for multiplication which uses
karatsuba/etc on polynomials when the user knows in advance that the data
is "uniform" enough to make the asymptotically fast algorithm accurate
enough.
I totally can't work on this right now.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/331#comment:8>
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