#                                                        functions.py

# Let's start with somethig that we are all familiar with.
#
# In Math, we define and apply a function like this:
#
#    Definition:  f(x) = 3x^2 + 2x + 1
#
#    Application: f(2) = 12 + 4 + 1 = 17
#
# In Python, the idea is the same.  We only happen to be using
# a different language: different syntax, same semantics (at 
# least for now):
#
#    Definition:
#
#       def f(x):
#           return 3*x**2 + 2*x + 1
#
#    Application:
#
#       f(2)
#
#       which would return 17 as its value
#
# Let's look at it a little more carefully.
# 
# In Python, a function must be defined using the following syntax:
#
# def NAME(LIST_OF_PARAMETERS):
#     STATEMENTS
#
# You can make up any names you want for the functions you create,
# except that you can't use a name that is a Python keyword.  For
# example, 'def' is a keyward reserved in the language Python, and you
# must avoid using it as a name that you create.

# The list of parameters specifies what information, if any, you
# have to provide in order to use the new function.
#
# There can be one or more of statements inside the function, but
# they must be indented from the def.  In my examples, I will use
# the standard indentation of four spaces.
#
# Function definitions are the first of several compound statements
# we will see, all of which have the same pattern:
#
#  1. A header, which begins with a keyword and ends with a colon (:).
#     In case you have not noticed it, the right parenthsis, the left
#     parenthesis, and the colon are all required.  Seemingly 
#     insignificant letters like them are part of the language syntax
#     and Python just like any other programming language is very picky
#     about the exact syntax.
#
#  2. A body consisting of one or more Python statements, each
#     indented the same amount from the header.
#
# In a function definition, the keyword in the header is def,
# which is followed by the name of the function and a list of
# parameters enclosed in parentheses.  The parameter list may
# be empty, or it may contain any number of parameters.  In 
# either case, the parentheses are required. 

def f(x):
    return 3*x**2 + 2*x + 1

print f(1)

def g(x, y, z):
    return x * y + z

# Run the programs in this file and see what the comma following the second
# double quote does below.  It mearly separates two values that the print
# function prints.  I will often use this sort of output format which will
# make reading the output easier.
print "g(2, 3, 4) = ", g(2, 3, 4)

# pow for power and abs for absolute are two of the many functions that
# are already defined in the language that we can use.  Those language
# provided functions are called built-in functions as opposed to the
# ones that we programmers create, which are called user-defined functions.
# For example, f and g are user-defined functions.
print "f(pow(abs(-2), 3)) = ", f(pow(abs(-2), 3))



# There are some libraries (packages) that need to be 'imported' into the
# language before we can use any function that is defined in the library.
# 'math' is one such library that contains many math related functions.
# We import a library by the 'import' command like below:

import math

# distance computes the distance between two points: p1(x1, y1) and p2(x2, y2)
def distance(x1, y1, x2, y2):
    dx = x2 - x1
    dy = y2 - y1
    dsquared = dx**2 + dy**2
    result = math.sqrt(dsquared)
    return result

print "distance(0, 0, 3, 4) = ", distance(0, 0, 3, 4)


# isEven tells a given number is even or odd.
#   % computes modulo
#   == tests to see if two values are equal or not producing a boolean value,
#      i.e., True or False
def isEven(x):
    return x%2 == 0

print "isEven(3) = ", isEven(3)


def isDivisible(x,y):
    return x%y == 0

print "isDivisible(30, 3) = ", isDivisible(30, 3)



# Exercise 1.
#
# Define a function that converts a Celcius temperature value to a Fehrenheit
# temperature and call it with some values such as 100, 0, -40, etc.
# I will provide my answer to this exercise at the end of this file, but try
# it yourself before you see mine.


# Exercise 2.
#
# This time let us combine functions and input.  Define a function that
# reads a number from the user through keyboard input, calls the function
# that converts the number as Celcius temperature into Fehenheit temperature,
# and returns the computed Fehrenheit temperature.
#
# After that you can run this program three times: once each with 100, 0,
# and -40 as input values.
#
# I will also provide my answer to this exercise at the end of this file, but
# try it yourself before you see mine.


# Exercise 3.
#
# Define a function with three string parameters and returns a string
# that is the result of concatenating the three with a space as a separating
# character between strings.  Now, call the function with three strings as its
# actual arguments.


# Exercise 4.
#
# See Section 3.8 and Section 5.10 of [DEM] if you want to see more exercise
# problems.

















# Sample solution to Exercise 1 above.

def c2f (c):
    return c * (9.0/5.0) + 32


# Sample solution to Exercise 2 above.

def c2ftest ():
    n = input("Enter a number: ")
    n = c2f(n)
    return n

print c2ftest()  # use 100
print c2ftest()  # use 0
print c2ftest()  # use -40



# Note that c2ftest may be rewritten more succinctly this way:

def c2ftest2 ():
    return c2f(input("Enter a number: "))

print c2ftest2()  # use 100
print c2ftest2()  # use 0
print c2ftest2()  # use -40