# Python Programming/Math

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

v1 = math.sin(10)       # sine
v2 = math.cos(10)       # cosine
v3 = math.tan(10)       # tangent

v4 = math.asin(10)      # arc sine
v5 = math.acos(10)      # arc cosine
v6 = math.atan(10)      # arc tangent

v7 = math.sinh(10)      # hyperbolic sine
v8 = math.cosh(10)      # hyperbolic cosine
v9 = math.tanh(10)      # hyperbolic tangent

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

vG = math.ceil(2.3)     # ceiling
vH = math.floor(2.7)    # floor

vI = math.pi
vJ = math.e
```

## Example code using in-built operators

This code was made to replicate the log function in a calculator

```import time
base_number = input("[A]input base number: ")
new_number = 0
result = input("[end number]input result ")
exponent = 0

while int(new_number) != int(result):
exponent += float("0.0000001")
new_number = int(base_number)**float(exponent)
print(new_number)

else:
print("")
print("The exponent or X is " + str(exponent))
time.sleep(200)
```

## 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
v1 = random.random()     # Uniformly distributed random float >= 0.0 and < 1.0.
v2 = random.random()*10  # Uniformly distributed random float >= 0.0 and < 10.0
v3 = 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
v1 = plainFloat # 0.3333333333333333
decFloat = decimal.Decimal("0.33333333333333333333333333333333333333")
v2 = decFloat   # Decimal('0.33333333333333333333333333333333333333')
decFloat2 = decimal.Decimal(plainFloat)
v3 = 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
v1 = Fraction(0.25)                  # 1/4
v2 = Fraction(floatOneThird)         # 6004799503160661/18014398509481984
v3 = 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
v1 = stats.mean([1, 2, 3, 100]) # 26.5
v2 = stats.median([1, 2, 3, 100]) # 2.5
v3 = stats.mode([1, 1, 2, 3]) # 1
v4 = stats.pstdev([1, 1, 2, 3]) # 0.82915...; population standard deviation
v5 = stats.pvariance([1, 1, 2, 3]) # 0.6875; population variance
```