BUG: Polynomial.fit(...).window.dtype inconsistent with Polynomial(...).dtype

[SV-97]

Describe the issue:

When using np.polynomial.Polynomial.fit to fit a polynomial to some data, the dtype of the window of the resulting np.polynomial.Polynomial is different than the one of an instance constructed directly via np.polynomial.Polynomial.

This leads to polynomials effectively having the same window but still being incompatible because of the windows equality comparison evaluating to False.

I locally tested modifying the dtype of polydomain here by setting polydomain = np.array([-1., 1.]) which fixed the issue for me - however I have no idea if this raises other problems in other places.

Reproduce the code example:

import numpy as np

xs1 = np.array([0.0]) 
ys1 = np.array([1.0])

# fit a constant polynomial to (xs1, ys1)
p1 = np.polynomial.Polynomial(np.mean(ys1))

xs2 = np.array([0.0, 1.0])
ys2 = np.array([0.0, 2.0])

# fit a linear polynomial to (xs2, ys2)
p2 = np.polynomial.Polynomial.fit(xs2, ys2, deg=1)

print(p1.window.dtype, p2.window.dtype)
assert(p1.window.dtype != p2.window.dtype) # this assertion should Error but it doesn't

Error message:

No response

NumPy/Python version information:

1.23.5 3.10.6 | packaged by conda-forge | (main, Aug 22 2022, 20:36:39) [GCC 10.4.0]

Context for the issue:

Since np.polynomial.Polynomial can't fit constant polynomials, a wrapping fitting function has to construct some polynomials via the default constructor and others via .fit. My work requires finding (poly_1 - poly_2)**2 which fails because of incompatible windows.

This can be worked around by manually setting the windows on either instance.

[SV-97]

I just noticed that a similar problem affects the domains as well.