Math - Python

Math

The math module, plus statistics and random.

Roots and powers

Python

import math

print(math.sqrt(16))
print(math.pow(2, 10))
print(2 ** 10)
print(math.isqrt(17))

Output

math.pow always gives a float; ** keeps integers as integers. isqrt is the integer square root, rounded down.

Rounding

Python

import math

print(math.floor(3.7), math.floor(-3.2))
print(math.ceil(3.2), math.ceil(-3.7))
print(math.trunc(3.7), math.trunc(-3.7))
print(round(3.7))

Output

Four different answers for four different questions: floor rounds down, ceil rounds up, trunc rounds towards zero, and round rounds to nearest with halves going to even.

Constants

Python

import math

print(math.pi)
print(math.e)
print(math.inf > 10 ** 100)
print(math.isnan(math.nan))

Output

3.141592653589793
2.718281828459045
True
True

nan is never equal to anything, including itself, which is why isnan() exists:

Python

import math
print(math.nan == math.nan)

Output

False

Comparing floats

The fix for the 0.1 + 0.2 problem:

Python

import math

print(0.1 + 0.2 == 0.3)
print(math.isclose(0.1 + 0.2, 0.3))

Output

False
True

Logs and trigonometry

Python

import math

print(math.log(math.e))
print(math.log10(1000))
print(math.log2(8))
print(round(math.sin(math.radians(90)), 10))

Output

1.0
3.0
3.0
1.0

Trigonometric functions work in radians. math.radians() and math.degrees() convert.

Other useful pieces

Python

import math

print(math.gcd(12, 18))
print(math.factorial(5))
print(math.comb(5, 2))
print(math.dist((0, 0), (3, 4)))

Output

statistics

For averages, reach for statistics rather than writing your own:

Python

import statistics

values = [2, 4, 4, 4, 5, 5, 7, 9]
print(statistics.mean(values))
print(statistics.median(values))
print(statistics.mode(values))
print(statistics.stdev(values))

Output

5
4.5
4
2.138089935299395

random

Python

import random

random.seed(1)
first = random.randint(1, 6)
random.seed(1)
again = random.randint(1, 6)

print(first == again)
print(1 <= first <= 6)
print(random.choice(["rock", "paper"]) in ("rock", "paper"))

deck = [1, 2, 3, 4, 5]
random.shuffle(deck)
print(sorted(deck))
print(len(random.sample(range(100), 3)))

Output

True
True
True
[1, 2, 3, 4, 5]
3

seed() fixes the sequence so the output is repeatable. Without it every run differs — which is the point, except when testing.

Python

import secrets
print(len(secrets.token_hex(16)))

Output

Decimal for money

Python

from decimal import Decimal

print(0.1 + 0.2)
print(Decimal("0.10") + Decimal("0.20"))
print(Decimal("1.10") * 3)

Output

0.30000000000000004
0.30
3.30

Build a Decimal from a string. Decimal(0.1) inherits the float's error before it ever gets there.

Test yourself

2 questions

Why does math.nan == math.nan give False?

Show the answer

nan is defined never to equal anything, including itself — That is why math.isnan() exists as a separate function.

Which module should you use for passwords and tokens?

Show the answer

secrets — random is predictable from its seed and is not safe for anything security related.

Next chapter

JSON

Turn Python data into text and back, for files and APIs.