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Math

In Python we discover many built-in mathematical functions. Consider a square root—we just call math.sqrt. No custom code is required.

Function notes

We can apply floors and ceilings to reduce, and increase, fractional numbers. With sum() and fsum we can add up numbers.

`Floor`, ceil

Two common math functions are floor and ceil. Floor removes the digits past the decimal place. In this example it changes 100.7 to 100.

And Ceil() rounds the number up to the next highest one. A ceiling is always above us.

Tip When using methods like floor and ceil, consistency is helpful. If some parts of the program use these methods, others should too.

import math

# Fractional number.
n = 100.7

# Absolute value.
print(math.floor(n))
print(math.ceil(n))100
101

Sum, `fsum`

With sum, we add together the elements in a list. Fsum is a more accurate way to sum floating-point numbers. On integers, the methods are equal. But fsum is better for floats.

Tip Sum and fsum can be used on any iterable collection. This includes the list, tuple and set.

Warning If the iterable contains a non-numeric value, a TypeError will occur. We handle this in an except statement.

Here In this example, the sum() method causes a rounding error to occur. The fsum() method returns a better sum.

import math

# Input list.
values = [0.9999999, 1, 2, 3]

# Sum values in list.
r = sum(values)
print(r)

# Sum values with fsum.
r = math.fsum(values)
print(r)6.999999900000001
6.9999999

Truncate

Truncating a number removes everything past the decimal place. This does not round the number. Instead it just eliminates the fractional part.

Note The number before the decimal place is never changed with math.trunc. This is similar to casting to (int) in C-like languages.

import math

# Truncate this value.
value1 = 123.45
truncate1 = math.trunc(value1)
print(truncate1)

# Truncate another value.
value2 = 345.67
truncate2 = math.trunc(value2)
print(truncate2)123
345

`Pow` built-in

Exponentiation multiplies a number by itself a certain number of times. With math.pow we apply this operation. Math.pow is similar to the ** operator.

But When math.pow is applied, the result is always converted to a float. This is not the case with the ** operator.

import math

# Use math.pow method.
a = math.pow(2, 3)

# Use operator.
b = 2 ** 3

# Print results.
print(a)
print(b)8.0
8

`Sqrt`

In most programs, we do not need square roots. But when we do, the math.sqrt method is useful. It receives one argument. It returns the square root (in floating-point form).

Tip If your program often uses square roots, a cache or lookup table may be helpful. You could memoize the result of math.sqrt for speed.

import math

value1 = 9
value2 = 16
value3 = 100

# Use sqrt method.
print(math.sqrt(value1))
print(math.sqrt(value2))
print(math.sqrt(value3))3.0
4.0
10.0

Pi, E

You probably know the approximate values of E and pi. And you could specify these directly in a Python program. But with math.e and math.pi, we avoid this hassle.

import math

# This returns the value of e.
print(math.e)

# And this is pi.
print(math.pi)2.718281828459045
3.141592653589793

Summary

It is possible to directly compute mathematical functions. We could add methods that use arithmetic operators. But this adds complexity—it bloats programs.

Instead, we can use built-ins

These are found in the default and math modules. This approach is more effective. It is simpler, and it makes programs easier to understand and maintain.