# Numeric Data Types

type(2)
type(1.5)
type(1+1j)
True + True
type(-True)
1/3 == 0.333333333333333300000  # Beware of approximations
from math import pi, tan
tan(pi/4)

# Dates

from datetime import date
today = date(2013, 9, 25)
freedom = date(2013, 12, 20)
str(freedom - today)
today.year
today.strftime('%A, %B %d')
type(today)

# Rational arithmetic

def add_rational(x, y):
    """Add rational numbers x and y."""
    nx, dx = numer(x), denom(x)
    ny, dy = numer(y), denom(y)
    return rational(nx * dy + ny * dx, dx * dy)

def mul_rational(x, y):
    """Multiply rational numbers x and y."""
    return rational(numer(x) * numer(y), denom(x) * denom(y))

def equal_rational(x, y):
    """Return whether rational numbers x and y are equal."""
    return numer(x) * denom(y) == numer(y) * denom(x)

# Constructor and selectors

from operator import getitem

def rational(n, d):
    """Construct a rational number x that represents n/d."""
    return (n, d)

def numer(x):
    """Return the numerator of rational number x."""
    return getitem(x, 0)

def denom(x):
    """Return the denominator of rational number x."""
    return getitem(x, 1)


# String conversion

def rational_to_string(x):
    """Return a string 'n/d' for numerator n and denominator d."""
    return '{0}/{1}'.format(numer(x), denom(x))


# Improved constructor

from fractions import gcd
def rational(n, d):
    """Construct a rational number x that represents n/d in lowest terms."""
    g = gcd(n, d)
    return (n//g, d//g)


# Functional pair

def pair(x, y):
    """Return a functional pair."""
    def dispatch(m):
        if m == 0:
            return x
        elif m == 1:
            return y
    return dispatch

def getitem_pair(p, i):
    """Return the element at index i of pair p."""
    return p(i)