submodule import problem

[deanhystad]

I am having a problem with modules and packages. I can make my imports work outside the package or I can make them work inside the package. I have not figured out a way to make them work in both scopes and I assume this is because I am still rather ignorant about Python.

This demonstrates the problem. I have a program that uses a package:

program.py

import package.b as b
print(b.average(2, 4))

Inside the package I have two modules: a and b.
a.py

def sum(x, y):
    return x + y

b.py

import a
def average(x, y):
    return a.sum(x, y) / 2

The directory structure is:

Output:
program.py
package\
    __init__.py   <-- Empty
    a.py
    b.py

If I run b.py there are no errors. When I run program.py I get the message
File "...\b.py" line 1 in <module>
Module Not Found: No Module named a

I changed module b to use a relative reference:
b.py

from . import a
def average(x, y):
    return a.sum(x, y) / 2

If I run program.py there are no errors. When I run b.py I get the message

Error:
File "....\b.py" line 1 in <module>
    from . import a
ImportError: attempted relative import with no known parent package

I have read dozens of tutorials on how to make a package. I have read dozens of articles about import and __init__.py and PYTHONPATH and setup.py and every topic that looks like it may point toward and answer. I fear I am missing some vital piece Python understanding and this is so trivial that nobody talks about it.