# [Numpy-discussion] Polynomial Improvements

Robert bobbyocean at gmail.com
Tue Apr 20 14:20:59 EDT 2021

```Hi,

I am new to contributing to open source projects and not sure where to begin
(maybe emailing this distro?). In any case, the main improvement I would
like to work on would be adding multivariate polynomials/differentials to
numpy. I would love any insight into the current status and intensions of
numpy polynomial implementations.

1) why do we have np.polynomial and np.lib.polynomial? which one is older?
is there a desire to see these merged?
2) why does np.polynomial.Polynomial have a domain and window? they appear
to have no implementation (except the chebyshev interpolation) as far as I
can tell? what is their intended use? why is their no variable
representation implemented like in np.polynomial and is not installed to
numpy directly, @set_module('numpy')?
3) how many improvements are allowed to be done all at once? is there an
expectation of waiting before improving implementations or code?

Thinking further down the road, how much is too much to add to numpy? I
would like to see multivariate implemented, but after that it would be nice
to have a collection of known polynomials like standard, pochhammer,
cyclotomic, hermite, lauguerre, legendre, chebyshev, jacobi. After that it
would be of interest to extend .diff() to really be a differential operator
(implemented as sequences of polynomials) and to allow differential
constructions. Then things like this would be possible:

x = np.poly1d([1,0])
D = np.diff1d([1,0])
assert Hermite(78) == (2*x - D)(Hermite(77))

Or if series were implemented then we would see things like:

assert Hermite(189) == (-1)**189 * Exp(x**2)*(D**189)(Exp(-x**2))
assert Hermite(189) == Exp(-D**2)(x**189)(2*x)

4) at what point does numpy polynomial material belong in scipy material and
visa-versa? is numpy considered the backend to scipy or visa-versa? at times
it seems like things are double implemented in numpy and scipy, but in
general should not implement things in numpy that already exist in scipy?

Thanks,
Robert

--
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```