Mathematical Functions in Python

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Introduction

Python has a built-in module math which defines various mathematical functions. In addition to the 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-D arrays

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 values of a 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 functions 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