Mathematical Functions in Python

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Introduction

Python has a built-in module math which defines various mathematical functions. In addition to math module, there is a fundamental package for scientific computing in Python named NumPy (Numerical Python). It is an open source Python library and contains multidimensional array and matrix data structures. In this section, examples of both methods will be presented.

For using math, we must first import this module:

import math

For using `NumPy`, we must first install it. There is no prerequisite for installing NumPy except Python itself. We can use `pip` or `conda` for this purpose:

'pip'

pip install numpy

'conda'

conda install numpy

We must import `numpy` to access it and its functions. We also shorten the imported name to `np` for better readability of code using NumPy:

import numpy as np

Mathematical Functions

Basic Functions

Some basic functions for my fellow students. Some functions need the module `math`. Please check out the introduction at the top. :)

math	Description
math.ceil(x)	Rounds the number x up to the next integer
math.floor(x)	Rounds the number x down to the next integer
math.com (n,k)	Binomial Coefficient: number of possible k choose n without order
math,factorial(n)	Returns n factorial if n >= 0
abs(x)	Returns the absolute value of x

math.ceil(5.3)

6

math.floor(173.123)

173

math.factorial(4)

24

abs(-17.2)

17.2

Power Functions

built-in function	math	numpy	Description
pow(x, y, mod)	math.pow(x, y, mod)	np.power(x1, x2,...)	x to the power of y. x1, x2 array_like

Examples

pow (2,2)=4
##Square

pow (2,3)=8

##=Cube

pow (3,4, mode: 10)

The value of (3**4) % 10 is = 1

##The exponents of two 1-Darray

ar1 = [3, 5, 7, 2, 4]

ar2 = [6, 2, 5, 3, 5]

arr = np.power(ar1,ar2)

arr: array([  729,    25, 16807,     8,  1024], dtype=int32)

##The power vales of 2-D array

ar1 = np.array([[3,4,3],[6,7,5]])

ar2 =np.array([[4,2,7],[4,2,1]])

arr = np.power(ar1,ar2)

arr: array([[  81,   16, 2187],

       [1296,   49,    5]], dtype=int32)

Root Functions

To implement root funtions in python we can use the built-in power function. Alternatively we can use 'math' or 'numpy'.

built-in power function	math	numpy	Description
x**(1/2)	math.sqrt(x)	np.sqrt(x)	Returns the square root of x
x**(1/3)	math.powe(x, 1/3)	np.cbrt(x)	Returns the cube root of x
x**(1/n)	math.pow(x, 1/n)	np.power(x, 1/n)	Returns the nth root of x

Examples

• 'built-in function'

0** (1/2)

0.0

9** (1/3)

2.0

120** (1/10)

1.6140542384620635

• 'math'

math.sqrt(0)

0.0

math.pow(9, 1/3)

2.0

math.pow(120, 1/10)

1.6140542384620635

• 'numpy'

np.sqrt(0)

0.0

np.cbrt(9)

2.0

np.power(120, 1/10)

1.6140542384620635

Exponential Functions

math	numpy	Description
math.exp(x)	np.exp()	The math.exp() method returns E raised to the power of x (Ex).‘E’ is the base of the natural system of logarithms and x is the number passed to it, return value: Float

Examples

math.exp(66) or np.exp(66)

4.607186634331292e+28

DELETE?

math.exp(66) or np.exp(66)

214643579785916.06

Log Functions

math	numpy	Description
math.log(x, base)	np.log(x)	The natural logarithm log is the inverse of the exponential function, The math.log() method returns the natural logarithm of a number, or the logarithm of number to base.base value is optional and the default is e.

Examples

# get the log value of an array with base 2

arr = np.array([1, 4, 6])

arr1 = np.log2(arr)

print(arr1)

​

# Output :

# [0.        2.        2.5849625]

# get the log value of an array with base 10

arr = np.array([1, 4, 6])

arr1 = np.log10(arr)

print(arr1)

​

# Output :

# [0.         0.60205999 0.77815125]

Trigonometric Functions

math	numpy	Description
math.cos(x)	np.cos(x)	Return the cosine of x radians.
math.sin(x)	np.sin(x)	Return the sine of x radians.
math.tan(x)	np.tan(x)	Return the tangent of x radians.

Examples

We use math.pi or np.pi methods for defining pi(π) in Python.

• math

math.cos(math.pi)

-1.0

math.sin(math.pi/2)

1.0

• numpy

np.cos(math.pi)

-1.0

np.sin(math.pi/2)

1.0

References

1.https://docs.python.org/3/library/math.html

2.https://numpy.org/doc/stable/reference/routines.math.html#extrema-finding

The author of this entry is XX. Edited by Milan Maushart