[SciPy-dev] Generic polynomials class (was Re: Volunteer for Scipy Project)

[Anne Archibald]

2009/10/16 Josh Lawrence <josh.k.lawrence at gmail.com>:
> Hey all,
>
> I'm chiming in here after following this post. I am highly interested
> and excited about the resulting tools. Keep up the good work!
>
> On Oct 16, 2009, at 3:58 PM, Anne Archibald wrote:
>
>> * Should we try to accommodate complex variables? Complex
>> coefficients?
>
>
> FWIW, scipy's polynomial stuff would be must less valuable (not quite
> worthless, but close) to me if in general they did not support complex
> domains and ranges. Contour integration stuffs are just too valuable
> for a lot of my research. So a huge +1 to complex domains and ranges
> for these polynomial objects.

Okay, we can definitely allow these, with just a little care about
dtypes. But all the clever stability and approximation work I've seen
has been for real polynomials - for example, the Chebyshev polynomials
are in some sense optimal for approximating real functions, and I
choose points for the Lagrange polynomials so as to get good stability
on a real interval. For really good complex polynomial support we're
going to have to do some reading in the literature - do you have any
suggestions?

For that matter, would you like to describe in a bit more detail how
you'd use a polynomial class and what you want from it? There's
definitely a danger of us producing a polynomial class that does just
the few things we need it to...

Anne