Dear Mike, dear Henryk,
What's the status of the merge of your implementations of power
series? I need a couple functionalities not yet in Mike's
implementation, and mainly:
- conversion from a polynomial
- division
On Thu, Oct 30, 2008 at 06:29:35AM -0700, Henryk Trappmann wrote:
> On Oct 30, 1:14 pm, "Mike Hansen" <mhan...@gmail.com> wrote:
> > When I said recursively defined streams, I meant something a little
> > more general. For example, if f is a power series and g is exp(f),
> > then g satisfies g = \int g*f'. This translates to the following code
> > for the exponential of power series:
> >
> > g.define( (f.derivative()*g).integral(base_ring(1)) )
>
> If that works, the better.
>
> >
> > The benefit of this is that it reduces the complexity of
> > exponentiation to that of multiplication for which there are fast
> > algorithms. Generally, you want to reduce everything (composition,
> > division, logs, etc) to multiplication in order to get asymptotically
> > fast algorithms.
>
> Sure, but I would say functionality before performance.
This approach gives both: it's a very powerful way to define most of
the operations in very few lines, while giving optimal complexity (it
can be seen as a newton iteration in disguise).
<snip>
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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