ENH: Change default values for "domain" and "window" parameters of Polynomial class

[KrisMinchev]

Proposed new feature or change:

The current default values for both domain and window parameters are both np.array([-1, 1]). On the other hand, if we call __init__ with 3 parameters, then domain and window always get cast to double. This leads to the following behaviour:

>>> p1 = P(np.array([1,2,3]))
>>> p1
Polynomial([1., 2., 3.], domain=[-1,  1], window=[-1,  1], symbol='x')
>>> p2 = P(np.array([1,2,3]), np.array([-1, 1]), np.array([-1,1]))
>>> p2
Polynomial([1., 2., 3.], domain=[-1.,  1.], window=[-1.,  1.], symbol='x')
>>> p1.domain.dtype
dtype('int64')
>>> p2.domain.dtype
dtype('float64')

Changing the default values of the parameters domain and window to np.array([-1., 1.]) will increase consistency between constructors Polynomial(coef) and Polynomial(coef, domain, window).

[eendebakpt]

The conversion of the input arguments happens in numpy.polynomial.polyutils.as_series. Besides checking dimensions, it converts all input to a numpy array of type double, complex double or object.

Note that also numpy.polynomial.polyzero is of integer type, even though the zero polynomial has coefficients np.array([0.]). (similar for numpy.polynomial.polyone and numpy.polynomial.polyx).

It is indeed odd that one cannot create the polynomial p1 by setting the domain and window directly. Changing the code (e.g. main...eendebakpt:polynomial_float_domain) and running unit testing results in no errors (expect for a test on the representation).

Maybe there are cases with custom objects where the difference matters, but I could not find any examples. I tried creating something with fractions.Fraction, but that seems to work exactly the same (with either integer or float domain). For example

import fractions
from numpy.polynomial import Polynomial

f=fractions.Fraction(2,3)
one=fractions.Fraction(1,1)
zero=fractions.Fraction(0,1)
p=Polynomial([f, f])
print(p)
print(p.domain)
y=p(f)
print(y)
print(type(y))

p=Polynomial([f, f], domain=[zero, one], window=[zero, one])
print(p)
print(p.domain)
y=p(f)
print(y)
print(type(y))

has output

2/3 + 2/3 x
[-1  1]
1.1111111111111112
<class 'numpy.float64'>
2/3 + 2/3 x
[Fraction(0, 1) Fraction(1, 1)]
10/9
<class 'fractions.Fraction'>