Dear David,
On Fri, Mar 13, 2009 at 05:00:55PM -0700, David Kohel wrote:
>
> Hi,
>
> I am finding problems, holes, or missing features in power series
> rings
> and Laurent series rings.
>
> sage: K.<u> = LaurentSeriesRing(QQ)
> sage: R.<t> = PowerSeriesRing(QQ)
...
+1 for making all of those, and also LazyPowerSeriesRing, consistent.
> P.S. A first start with log -- is there a more efficient algorithm
> already implemented somewhere or does someone want to put in place a
> more efficient algorithm?
Far from being an expert there, so just my 1/2 cent ...
I guess we would want to use a newton iteration. Ideally, things would
be done as for lazy power series: have a general tool to define a
power series implicitly, with newton iteration. With this tool tool
all the usual functions (inverse, log, power, exp, sin, ...) can be
implemented in two lines of code each. This further reduces their
complexity to that of the multiplication, which is optimal. So all the
optimization efforts could be focused on the newton iteration and
multiplication). I am not 100% sure it applies perfectly to Laurent
series though.
Best,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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