Basics

Python math works like you would expect.

>>> x = 2
>>> y = 3
>>> z = 5
>>> x * y
6
>>> x + y
5
>>> x * y + z
11
>>> (x + y) * z
25

Note that Python adheres to the PEMDAS order of operations.

Powers

There is a built in exponentiation operator **, which can take either integers, floating point or complex numbers. This occupies its proper place in the order of operations.

>>> 2**8
256

Division and Type Conversion

For Python 2.x, dividing two integers or longs uses integer division, also known as "floor division" (applying the floor function after division. So, for example, 5 / 2 is 2. Using "/" to do division this way is deprecated; if you want floor division, use "//" (available in Python 2.2 and later).

"/" does "true division" for floats and complex numbers; for example, 5.0/2.0 is 2.5.

For Python 3.x, "/" does "true division" for all types.^[1][2]

Dividing by or into a floating point number (Python never uses the fractional type in such a case) will cause Python to use true division. To coerce an integer to become a float, 'float()' with the integer as a parameter

>>> x = 5
>>> float(x)
5.0

This can be generalized for other numeric types: int(), complex(), long().

Beware that due to the limitations of floating point arithmetic, rounding errors can cause unexpected results. For example:

>>> print 0.6/0.2
3.0
>>> print 0.6//0.2
2.0

Modulus

The modulus (remainder of the division of the two operands, rather than the quotient) can be found using the % operator, or by the divmod builtin function. The divmod function returns a tuple containing the quotient and remainder.

>>> 10%7
3
>>> -10%7
4

print (" 10%7 ")

Negation

Unlike some other languages, variables can be negated directly:

>>> x = 5
>>> -x
-5

Comparison

Numbers, strings and other types can be compared for equality/inequality and ordering:

>>> 2 == 3
False
>>> 3 == 3
True
>>> 3 == '3'
False
>>> 2 < 3
True
>>> "a" < "aa"
True

Identity

The operators is and is not test for object identity and stand in contrast to == (equals): x is y is true if and only if x and y are references to the same object in memory. x is not y yields the inverse truth value. Note that an identity test is more stringent than an equality test since two distinct objects may have the same value.

>>> [1,2,3] == [1,2,3]
True
>>> [1,2,3] is [1,2,3]
False

For the built-in immutable data types (like int, str and tuple) Python uses caching mechanisms to improve performance, i.e., the interpreter may decide to reuse an existing immutable object instead of generating a new one with the same value. The details of object caching are subject to changes between different Python versions and are not guaranteed to be system-independent, so identity checks on immutable objects like 'hello' is 'hello', (1,2,3) is (1,2,3), 4 is 2**2 may give different results on different machines.

In some Python implementations, the following results are applicable:

print 8 is 8            # True
print "str" is "str"    # True
print (1, 2) is (1, 2)  # False - whyever, it is immutable
print [1, 2] is [1, 2]  # False
print id(8) == id(8)    # True
int1 = 8
print int1 is 8         # True
oldid = id(int1)
int1 += 2
print id(int1) == oldid # False

Links:

• 3. Data model, python.org
• 2. Built-in Functions # id, python.org
• 5. Expressions # is, python.org

Augmented Assignment

There is shorthand for assigning the output of an operation to one of the inputs:

>>> x = 2
>>> x # 2
2
>>> x *= 3
>>> x # 2 * 3
6
>>> x += 4
>>> x # 2 * 3 + 4
10
>>> x /= 5
>>> x # (2 * 3 + 4) / 5
2
>>> x **= 2
>>> x # ((2 * 3 + 4) / 5) ** 2
4
>>> x %= 3
>>> x # ((2 * 3 + 4) / 5) ** 2 % 3
1

>>> x = 'repeat this  '
>>> x  # repeat this
repeat this
>>> x *= 3  # fill with x repeated three times
>>> x
repeat this  repeat this  repeat this

Boolean

if a or b:
    do_this
else:
    do_this

if a and b:
    do_this
else:
    do_this

if not a:
    do_this
else:
    do_this

Exercises

1. Use Python to calculate ${\displaystyle 2^{2^{2^{2}}}=65536}$.
2. Use Python to calculate ${\displaystyle {\frac {(3+2)^{4}}{7}}\approx 89.285}$.
3. Use Python to calculate 11111111111111111111+22222222222222222222, but in one line of code with at most 15 characters. (Hint: each of those numbers is 20 digits long, so you have to find some other way to input those numbers)
4. Exactly one of the following expressions evaluates to "cat"; the other evaluates to "dog". Trace the logic to determine which one is which, then check your answer using Python.

1 and "cat" or "dog"
0 and "cat" or "dog"

References