How to do basic mathematical computations
Description
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, in Excel
Each of the formulas shown on the right of the table below is valid code for use in Excel formulas, in cells in a worksheet.
| Mathematical notation | Excel notation | Example |
|---|---|---|
| $x+y$ | x+y |
=A1+B1 |
| $x-y$ | x-y |
=A1-B1 |
| $xy$ | x*y |
=A1*B1 |
| $\frac xy$ | x/y |
=A1/B1 |
| $x^y$ | x^y |
=A1^B1 |
| $\vert x\vert$ | ABS(x) |
=ABS(A1) |
| $\ln x$ | LN(x) |
=LN(A1) |
| $\log_a b$ | LOG(b,a) |
=LOG(A1,B1) |
| $e^x$ | EXP(x) |
=EXP(A1) |
| $\pi$ | PI() |
=PI() |
| $\sin x$ | SIN(x) |
=SIN(A1) |
| $\sin^{-1} x$ | ASIN(x) |
=ASIN(A1) |
| $\sqrt x$ | SQRT(x) |
=SQRT(A1) |
Other trigonometric functions are also available besides just SIN,
including COS, TAN, etc.
Content last modified on 24 July 2023.
See a problem? Tell us or edit the source.
Solution, in Julia
| Mathematical notation | Julia code |
|---|---|
| $x+y$ | x+y |
| $x-y$ | x-y |
| $xy$ | x*y |
| $\frac xy$ | x/y (or y\x) |
| $\left\lfloor\frac xy\right\rfloor$ | x÷y |
| remainder of $x\div y$ | x%y |
| $x^y$ | x^y |
| $\vert x\vert$ | abs(x) |
| $\ln x$ | log(x) |
| $\log_a b$ | log(a,b) |
| $e^x$ | exp(x) |
| $\pi$ | pi |
| $\sin x$ | sin(x) |
| $\sin^{-1} x$ | asin(x) |
| $\sqrt x$ | sqrt(x) |
Other trigonometric functions are also available besides just sin
including cos, tan, etc.
Content last modified on 24 July 2023.
See a problem? Tell us or edit the source.
Using NumPy, in Python
This answer assumes you have imported NumPy as follows.
1
import numpy as np
| Mathematical notation | Python code | Requires NumPy? |
|---|---|---|
| $x+y$ | x+y |
no |
| $x-y$ | x-y |
no |
| $xy$ | x*y |
no |
| $\frac xy$ | x/y |
no |
| $\left\lfloor\frac xy\right\rfloor$ | x//y |
no |
| $\left\lfloor\frac xy\right\rfloor$ | 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 |
| $\vert x\vert$ | abs(x) |
no |
| $\vert x\vert$ | 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 |
| $\pi$ | 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.
1
2
3
import numpy as np
example_array = np.array( [ -3, 2, 0.5, -1, 10, 9.2, -3.3 ] )
example_array ** 2
1
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.
Using SymPy, in Python
This answer assumes you have imported SymPy as follows.
1
2
from sympy import * # load all math functions
init_printing( use_latex='mathjax' ) # use pretty math output
| Mathematical notation | Python code | Requires SymPy? |
|---|---|---|
| $x+y$ | x+y |
no |
| $x-y$ | x-y |
no |
| $xy$ | x*y |
no |
| $\frac xy$ | x/y |
no |
| $\left\lfloor\frac xy\right\rfloor$ | x//y |
no |
| remainder of $x\div y$ | x%y |
no |
| $x^y$ | x**y |
no |
| $\vert x\vert$ | abs(x) |
no |
| $\ln x$ | log(x) |
yes |
| $\log_a b$ | log(b,a) |
yes |
| $e^x$ | E |
yes |
| $\pi$ | pi |
yes |
| $\sin x$ | sin(x) |
yes |
| $\sin^{-1} x$ | asin(x) |
yes |
| $\sqrt x$ | sqrt(x) |
yes |
Other trigonometric functions are also available besides just sin,
including cos, tan, etc.
Note that SymPy gives precise answers to mathematical queries, which may not be what you want.
1
sqrt(2)
$\displaystyle \sqrt{2}$
If you want a decimal approximation instead, you can use the N function.
1
N(sqrt(2))
$\displaystyle 1.4142135623731$
Or you can use the evalf function.
1
sqrt(2).evalf()
$\displaystyle 1.4142135623731$
By contrast, if you need an exact rational number when Python gives you
an approximation, you can use the Rational function to build one.
Note the differences below:
1
1/3
$\displaystyle 0.333333333333333$
1
Rational(1,3)
$\displaystyle \frac{1}{3}$
Content last modified on 24 July 2023.
See a problem? Tell us or edit the source.
Solution, in Python
For those expressions that need the Python math package, use the code
import math beforehand to ensure that package is loaded. Alternatively,
you can write from math import * and thus drop the math prefixes in
the table below.
| Mathematical notation | Python code | Requires math package? |
|---|---|---|
| $x+y$ | x+y |
no |
| $x-y$ | x-y |
no |
| $xy$ | x*y |
no |
| $\frac xy$ | x/y |
no |
| $\left\lfloor\frac xy\right\rfloor$ | x//y |
no |
| remainder of $x\div y$ | x%y |
no |
| $x^y$ | x**y |
no |
| $\vert x\vert$ | abs(x) |
no |
| $\ln x$ | math.log(x) |
yes |
| $\log_a b$ | math.log(b,a) |
yes |
| $e^x$ | math.exp(x) |
yes |
| $\pi$ | math.pi |
yes |
| $\sin x$ | math.sin(x) |
yes |
| $\sin^{-1} x$ | math.asin(x) |
yes |
| $\sqrt x$ | x**0.5 |
no |
| $\sqrt x$ | math.sqrt(x) |
yes |
Other trigonometric functions are also available besides just math.sin,
including math.cos, math.tan, etc.
Content last modified on 24 July 2023.
See a problem? Tell us or edit the source.
Solution, in R
For those expressions that need the Python math package, use the code
import math beforehand to ensure that package is loaded. Alternatively,
you can write from math import * and thus drop the math prefixes in
the table below.
| Mathematical notation | R code |
|---|---|
| $x+y$ | x+y |
| $x-y$ | x-y |
| $xy$ | x*y |
| $\frac xy$ | x/y |
| $x^y$ | x^y |
| $\vert x\vert$ | abs(x) |
| $\ln x$ | log(x) |
| $\log_a b$ | log(b,a) |
| $e^x$ | exp(x) |
| $\pi$ | pi |
| $\sin x$ | sin(x) |
| $\sin^{-1} x$ | asin(x) |
| $\sqrt x$ | sqrt(x) |
Other trigonometric functions are also available besides just sin,
including cos, tan, etc.
R naturally applies these functions across vectors. For example, you can square all the entries in a vector as in the example below.
1
2
example.vector <- c( -3, 2, 0.5, -1, 10, 9.2, -3.3 )
example.vector ^ 2
1
[1] 9.00 4.00 0.25 1.00 100.00 84.64 10.89
Content last modified on 24 July 2023.
See a problem? Tell us or edit the source.