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

Charles R Harris charlesr.harris@gmail....
Tue Oct 6 21:00:19 CDT 2009

On Tue, Oct 6, 2009 at 7:37 PM, Anne Archibald <peridot.faceted@gmail.com>wrote:

> 2009/10/6 David Goldsmith <d.l.goldsmith@gmail.com>:
> > IMO this thread has matured to the point where someone(s) should formally
> > propose a feature spec/object structure for community vetting. :-)
> http://www.scipy.org/NewPolynomials
> I don't propose an object structure, because I'm not sure how that
> should look, and I'm also not sure how reasonable my various
> requirements and restrictions are. On the other hand I did list at the
> end some references I found in a quick literature search; it appears
> the wisdom is that for general polynomial manipulation it's best to
> use the Bernstein basis (the same used in Bezier splines) or the
> Lagrange basis (representing polynomials by (x,y) pairs). In either
> case papers are available describing algorithms for all the basic
> polynomial operations.
Bernstein and Lagrange would both be defined on interval domains, [0,1] and
[-1,1] respectively, and that would define both center and scaling if
arbitrary intervals are mapped to those domains, just like for the Chebyshev
polynomials. Hmm...

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