< Python Programming

For basic math including addition, subtraction, multiplication and the like, see Basic Math and Operators chapters. For quick reference, the built-in Python math operators include addition (+), subtraction (-), multiplication (*), division (/), floor division (//), modulo (%), and exponentiation (**). The built-in Python math functions include rounding (round()), absolute value (abs()), minimum (min()), maximum (max()), division with a remainder (divmod()), and exponentiation (pow()). Sign function can be created as "sign = lambda n: 1 if n > 0 else -1 if n < 0 else 0".

Math

A range of mathematical functions is available from math module of the standard library:

import math

print math.sin(10)       # sine
print math.cos(10)       # cosine
print math.tan(10)       # tangent 

print math.asin(10)      # arc sine
print math.acos(10)      # arc cosine
print math.atan(10)      # arc tangent

print math.sinh(10)      # hyperbolic sine    
print math.cosh(10)      # hyperbolic cosine
print math.tanh(10)      # hyperbolic tangent

print math.pow(2, 4)     # 2 raised to 4
print math.exp(4)        # e ^ 4
print math.sqrt(10)      # square root
print math.pow(5, 1/3.0) # cubic root of 5
print math.log(3)        # ln; natural logarithm
print math.log(100, 10)  # base 10

print math.ceil(2.3)    # ceiling
print math.floor(2.7)   # floor

print math.pi
print math.e

Cmath

The cmath module provides similar functions like the math module but for complex numbers, and then some.

Random

Pseudo-random generators are available from the random module:

import random
print random.random()     # Uniformly distributed random float >= 0.0 and < 1.0.
print random.random()*10  # Uniformly distributed random float >= 0.0 and < 10.0
print random.randint(0,9) # Uniformly distributed random int >= 0 and <=9
li=[1, 2, 3]; random.shuffle(li); print li # Randomly shuffled list

Decimal

The decimal module enables decimal floating point arithmethic, avoiding certain artifacts of the usual underlying binary representation of floating point numbers that are unintuitive to humans.

import decimal
plainFloat = 1/3.0
print plainFloat # 0.3333333333333333
decFloat = decimal.Decimal("0.33333333333333333333333333333333333333")
print decFloat   # Decimal('0.33333333333333333333333333333333333333')
decFloat2 = decimal.Decimal(plainFloat)
print decFloat2  # Decimal('0.333333333333333314829616256247390992939472198486328125')

Fractions

The fractions module provides fraction arithmetic via Fraction class. Compared to floating point numbers representing fractions, Fraction fractions do not lose precision.

from fractions import Fraction
oneThird = Fraction(1, 3)
floatOneThird = 1/3.0
print Fraction(0.25)                  # 1/4
print Fraction(floatOneThird)         # 6004799503160661/18014398509481984
print Fraction(1, 3) * Fraction(2, 5) # 2/15

Statistics

The statistics module, available since Python 3.4, provides some basic statistical functions. It only provides basics; it does not replace full-fledged 3rd party libraries such as numpy. For Python 2.7, the statistics module can be installed from pypi.

import statistics as stats
print stats.mean([1, 2, 3, 100]) # 26.5
print stats.median([1, 2, 3, 100]) # 2.5
print stats.mode([1, 1, 2, 3]) # 1
print stats.pstdev([1, 1, 2, 3]) # 0.82915...; population standard deviation
print stats.pvariance([1, 1, 2, 3]) # 0.6875; population variance
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