brief tutorial on functions for GSMST number theory

functions.py

# -----------------------------------------------------------------------------
# A brief tutorial on functions
# by Daniel Connelly (dhconnelly@gmail.com)
# -----------------------------------------------------------------------------

# Sometimes we want to re-use a piece of programming logic.  Copy-and-paste is
# not necessarily a good approach, as it is prone to errors and duplicates
# work.  A good maxim is "Don't Repeat Yourself."  Let's see how we can use
# functions to eliminate repetition.

print
print 'Repeated work...'

# Let's say we're writing a program that involves a lot of exponents.
# First we just want to find a specific result:

base = 3
exp = 5
prod = 1
while exp > 0:
    prod *= base # same as prod = prod * base
    exp -= 1 # same as exp = exp - 1
print '3 ^ 5 =', prod

# Now we want to provide a basic exponent calculator to the user.

while raw_input('Compute an exponent? ') == 'yes':
    base = float(raw_input('Base: '))
    exp = float(raw_input('Pow: '))

    prod = 1
    while exp > 0:
        prod *= base
        exp -= 1

    print prod

# Now we want to print the powers of 2 up to 2^30.

i = 1
while i <= 30:
    prod = 1
    j = 0
    while j < i:
        prod *= 2
        j += 1
    print '2 ^', i, '=', prod
    i += 1

# Alright, that's enough.  You should notice that the procedure for computing
# the exponent was the same each time.  So that we don't accidentally mess it
# up and to eliminate the repeated work, we'll make this a function.

# First we have to define our function.  We'll call it "power".  Right now it
# will never compute the right answer:

def power(a, b):
    return 0

# Before we talk about how this works, let's see what it would *look like* if
# we replaced the code to compute the exponents with a function.

print
print 'Incorrect function definition...'

print '3 ^ 5 =', power(3, 5)

# That was so easy.  We write the "name" of the function we want to use (in
# this case, "power"), write parentheses, and insert the "arguments"--the
# numbers that the function should use to compute the exponent.

while raw_input('Compute an exponent? ') == 'yes':
    base = float(raw_input('Base: '))
    exp = float(raw_input('Pow: '))
    print power(base, exp)

# Also easy.  We replace all the work to compute the exponent with a single
# "call" to the "power" function.

i = 1
while i <= 30:
    print '2 ^', i, '=', power(2, i)
    i += 1

# That worked the same way.

# Now we need to make our function work properly.  Let's examine the "function
# definition" we made before to see what it means:

def power(a, b):
    return 0

# The "def" part means that we are defining a new function.  "def" is *not* a
# function itself--it just means that we're about to write a new function.
#
# The next part, "power", is the name of the function we're defining.
#
# Next we have to write some parentheses: ().  These will surround the 
# "parameters" to the function.  In this case, we want to accept two, which we
# will call "a" and "b".  Those variables are ONLY visible INSIDE the function
# definition--they're what WE will call the two numbers that we're told to
# use.
# 
# Finally, "return" says that whatever follows it should be the value that
# replaces any call to our function.  So anywhere someone uses our "power"
# function, it will be replaced by 0 (right now).  For example, we wrote
# "power(3, 5)" above.  That will be replaced by 0.

# Now that we understand the parts of the function definition, let's make it
# work properly:

def power(a, b):
    prod = 1
    while b > 0:
        prod *= a
        b -= 1
    return prod

# Notice that each time we computed exponents above, it had this basic form.
# We can use this to do all the same work we had before.  Let's see:

print
print 'Correct function definition!'

print '3 ^ 5 =', power(3, 5)

while raw_input('Compute an exponent? ') == 'yes':
    base = float(raw_input('Base: '))
    exp = float(raw_input('Pow: '))
    print power(base, exp)

i = 1
while i <= 30:
    print '2 ^', i, '=', power(2, i)
    i += 1

# Alright, now we understand functions.  (Maybe.)  Let's move on.