How to do basic mathematical computations (in Python, using NumPy)

Task

How do we write the most common mathematical operations in a given piece of software? For example, how do we write multiplication, or exponentiation, or logarithms, in Python vs. R vs. Excel, and so on?

Solution

This answer assumes you have imported NumPy as follows.

import numpy as np

Mathematical notation	Python code	Requires NumPy?
$x + y$	`x+y`	no
$x - y$	`x-y`	no
$x y$	`x*y`	no
$\frac{x}{y}$	`x/y`	no
$⌊ \frac{x}{y} ⌋$	`x//y`	no
$⌊ \frac{x}{y} ⌋$	`np.floor_divide(x,y)`	yes
remainder of $x \div y$	`x%y`	no
remainder of $x \div y$	`np.remainder(x,y)`	yes
$x^{y}$	`x**y`	no
$\| x \|$	`abs(x)`	no
$\| x \|$	`np.abs(x)`	yes
$\ln x$	`np.log(x)`	yes
$\log_{a} b$	`np.log(b)/np.log(a)`	yes
$e^{x}$	`np.exp(x)`	yes
$π$	`np.pi`	yes
$\sin x$	`np.sin(x)`	yes
$\sin^{- 1} x$	`np.asin(x)`	yes
$\sqrt{x}$	`x**0.5`	no
$\sqrt{x}$	`np.sqrt(x)`	yes

Other trigonometric functions are also available besides just np.sin, including np.cos, np.tan, etc.

NumPy automatically applies any of these functions to all entries of a NumPy array or pandas Series, but the built-in Python functions do not have this feature. For example, to square all numbers in an array, see below.

import numpy as np
example_array = np.array( [ -3, 2, 0.5, -1, 10, 9.2, -3.3 ] )
example_array ** 2

array([  9.  ,   4.  ,   0.25,   1.  , 100.  ,  84.64,  10.89])

Content last modified on 24 July 2023.

See a problem? Tell us or edit the source.

Contributed by Nathan Carter (ncarter@bentley.edu)