To me, this seems like very odd behavior

THIS works as expected:

#Import to good stuff
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt

from scipy.special import gamma     # NOTE: Why ius this necessary?

# Print to confirm that the imports were done successfully
print("Skeleton stuff imported OK")

# Start program instructions here
for x in range(5):
    y = sp.special.gamma(x)
    putstr = '   ' + str(x) + ' -> ' + str(y)
    print(putstr)

print('==========================')
print()
while True:
    xs = input('Enter x = ')
    if 'Q' in xs.upper():
        break
    x = eval(xs)

    z = sp.special.entr(x)
    print("entr(%s) = %s" %(x, z))

    w = sp.special.erf(x)
    print("erf(%s) = %s" %(x, w))
        
    y = sp.special.gamma(x)
    print("gamma(%s) = %s" %(x, y))

    print()

BUT, if I delete the line “from scipy.special import gamma”, and try to run, I get the following output:

Traceback (most recent call last):
  File "D:/PYTHON/MyPrograms/Gamma Test-0000.py", line 14, in <module>
    y = sp.special.gamma(x)
AttributeError: module 'scipy' has no attribute 'special'

[rkern]

Just to add an explanation of that implicit side effect:

When we import a subpackage, the Python import system places it in the namespace of the parent package. If you just do import scipy; print(scipy.special), that scipy.special access won’t work. If you do import scipy; from scipy import special; print(scipy.special), that scipy.special access will work because the from scipy import special (or import scipy.special or from scipy.special import gamma) will import the special sub-package and place it in the scipy namespace as a side effect.

This is mostly for caching purposes. I would consider it an implementation detail. I wouldn’t write my code to routinely rely on that implicit side effect. As I stated previously, I would explicitly import the sub-packages that I need and use them explicitly.

[matthew-brett]

It’s fairly standard in big libraries, like Scipy, not to import everything with a top level import like import scipy, because this would make it necessary to import everything from Scipy even if you were only, for example, using the scipy.special sub-package. This in turn would make all Scipy imports slower, as we do (in this case) an unnecessary import of scipy.optimize, scipy.io etc.