Course Nine - Use numbers with Python

May 02, 2023

Use numbers with Python

By ienex

In Python, numeric data types are used to store numeric values. These values are immutable, meaning that changing a value creates a new object in memory rather than modifying the existing one.

Creating Numeric Objects

Numeric objects are created when a value is assigned to a variable:

var1 = 1
var2 = 10

You can also delete numeric objects using the del statement:

del var1
del var_a, var_b

Numeric Data Types in Python

Python supports four primary numeric types:

Integer (int): Whole numbers, positive or negative, without a decimal point.
Long integer (long): Integers of unlimited size. Denoted with L at the end (preferably uppercase to avoid confusion with the digit 1).
Floating point (float): Real numbers with a decimal point. Can also be expressed using scientific notation (5e2 = 5 × 10²).
Complex numbers (complex): Numbers in the form a + bj, where a is the real part, b is the imaginary part, and j represents the square root of -1.

Examples of numbers:

Complex	Float	Long	Int
3.14j	0.0	51924361L	10
45.j	15.20	-0x19323L	100
9.322e-36j	-21.9	0122L	786
.876j	32.3 + e18	0xDEFABCECBDAECBFBAEL	080
-6.545+0J	-90.5346…L	-0490	…
3e+26J	-32.54e100	-052318172735L	-0x260
4.53e-7j	70.2-E12	-7421885298529L	0x69

Converting Between Number Types

Python allows conversion between numeric types using:

int(x)      # Convert x to integer
long(x)     # Convert x to long integer
float(x)    # Convert x to floating point
complex(x,y) # Convert x and y to a complex number (real=x, imaginary=y)

Common Mathematical Functions

Python provides built-in functions for performing various calculations:

Function	Description
`abs(x)`	Returns the absolute value of `x`.
`ceil(x)`	Returns the smallest integer greater than or equal to `x`.
`cmp(x, y)`	Returns -1 if x<y, 0 if x==y, 1 if x>y.
`exp(x)`	Returns e^x.
`fabs(x)`	Returns the absolute value of x as a float.
`floor(x)`	Returns the largest integer less than or equal to x.
`log(x)`	Natural logarithm of x.
`log10(x)`	Base-10 logarithm of x.
`max(x1, x2, …)`	Returns the largest value.
`min(x1, x2, …)`	Returns the smallest value.
`modf(x)`	Returns fractional and integer parts of x as a tuple.
`pow(x, y)`	Returns x raised to the power y.
`round(x [,n])`	Rounds x to n decimal places.
`sqrt(x)`	Returns the square root of x.

Working with Random Numbers

Python’s random module provides tools for generating random numbers:

Function	Description
`choice(seq)`	Returns a random element from a sequence.
`randrange([start,] stop [, step])`	Returns a randomly selected element from a range.
`random()`	Returns a random float in [0.0, 1.0).
`seed([x])`	Initializes the random number generator.
`shuffle(lst)`	Shuffles a list in place.
`uniform(x, y)`	Returns a random float r such that x ≤ r < y.

Trigonometric Functions

Python provides several functions to handle trigonometric calculations:

Function	Description
`acos(x)`	Returns the inverse cosine of x (in radians).
`asin(x)`	Returns the inverse sine of x (in radians).
`atan(x)`	Returns the inverse tangent of x (in radians).
`atan2(y, x)`	Returns atan(y/x) in radians.
`cos(x)`	Returns the cosine of x (in radians).
`hypot(x, y)`	Returns sqrt(xx + yy).
`sin(x)`	Returns the sine of x (in radians).
`tan(x)`	Returns the tangent of x (in radians).
`degrees(x)`	Converts radians to degrees.
`radians(x)`	Converts degrees to radians.

Mathematical Constants

Python provides important mathematical constants:

pi: The value of π.
e: The base of natural logarithms.

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