Python 標準ライブラリ fractions 有理数

有理数を扱うためのライブラリfractionsを使うと有理数(分数計算)を簡単に行うことができます。

Fractionの宣言

import fractions
from decimal import Decimal

# fractions.Fraction(numerator=0, denominator=1)
fractions.Fraction() # => Fraction(0, 1) 0/1
fractions.Fraction(6) # => Fraction(6, 1) 6/1
fractions.Fraction(6, 12) # => Fraction(1, 2) 1/2

# fractions.Fraction(other_fraction)
fractions.Fraction(fractions.Fraction(6, 12)) # => Fraction(1, 2) 1/2

# fractions.Fraction(float)
fractions.Fraction(1.25) # => Fraction(5, 4) 5/4

# fractions.Fraction(decimal)
fractions.Fraction(Decimal(0.5)) # => Fraction(1, 2) 1/2

# fractions.Fraction(string)
fractions.Fraction('1.75') # => Fraction(7, 4) 7/4

Fractionのメソッド

numerator 既約分数で表示したときの分子

f = fractions.Fraction(6, 12)
f.numerator # => 1

numerator 既約分数で表示したときの分母

f.denominator # => 2

as_integer_ratio() 分子・分母のタプル

f.as_integer_ratio() # => (1, 2)

# 負号は分子につく
fractions.Fraction(-6, 12).as_integer_ratio() # => (-1, 2)

limit_denominator(max_denominator=1000000) 分母がmax_denominator以下の近い有理数を取得

import math
fractions.Fraction(math.pi).limit_denominator() # => Fraction(3126535, 995207)
fractions.Fraction(math.pi).limit_denominator(100) # => Fraction(311, 99)
fractions.Fraction(1.1).limit_denominator() # => Fraction(11, 10)

floor() 対象より小さい最大の整数

fractions.Fraction(201,100).__floor__() # => 2
math.floor(fractions.Fraction(201,100)) # => 2

ceil() 対象より大きい最小の整数

fractions.Fraction(201,100).__ceil__() # => 3
math.ceil(fractions.Fraction(201,100)) # => 3

round() まるめ

fractions.Fraction(201,100).__round__() # => 2
round(fractions.Fraction(201,100)) # => 2

Fractionへの変換

from_float(flt) float値を有理数に変換

fractions.Fraction.from_float(1.1) # => Fraction(2476979795053773, 2251799813685248)

from_decimal(dec) Decimal値を有理数に変換

fractions.Fraction.from_decimal(Decimal(1.1)) # => Fraction(2476979795053773, 2251799813685248)