[SciPy-dev] FW: RFC: Chebychev polynomials

[Chuck Harris]

Hi all,

I have written a small set of routines for dealing with Chebychev polynomials. I
would like suggestions for improvements, extra functions to include etc. I use 
these functions often myself, and thought they might be useful to include in
scipy. Where they might go is an open question. Perhaps a package of polynomial
routines that also contained divided differences, Lagrange interpolation, Newton
interpolation, a modern root finding routine, a routine for orthogonal polynomials
over a given set of sample points, etc. I have written some of these and wonder
what the general interest is.

A question about power series. There are routines in scipy-base for manipulating
power series, but the coefficients are ordered from high degree to low degree. This
is okay for polynomials, maybe, but doesn't seem the most natural order when dealing
with the initial entries in an infinite series. Is there any settled view on this?
My own routine that converts Chebychev series to power series orders the coefficients
from low degree to high degree and the Chebychev coefficients themselves are ordered in
the same way.

I have a few routines that might go into a misc package, specifically routines for
equivalence relations, very useful for clustering, and a generator for permutations of
a list. Any interest? The contouring functions in xplt have also proved useful as stand
alone functions. It might be nice to break these out into their own module. I think it
might be nice to have separate functions for various spline operations also : B-splines,
splines in tension, not-a-knot end conditions, natural splines, etc. The current single
function call is hard to understand in line, and in any case, python it the natural
language in which to produce such a monstrosity.

I have attached the Chebychev module. Feedback welcome.

Chuck

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