fractions — Rational numbers¶
소스 코드: Lib/fractions.py
fractions 모듈은 유리수 산술을 지원합니다.
Fraction 인스턴스는 한 쌍의 정수, 다른 유리수 또는 문자열로 만들 수 있습니다.
- class fractions.Fraction(numerator=0, denominator=1)¶
- class fractions.Fraction(other_fraction)
- class fractions.Fraction(float)
- class fractions.Fraction(decimal)
- class fractions.Fraction(string)
The first version requires that numerator and denominator are instances of
numbers.Rationaland returns a newFractioninstance with valuenumerator/denominator. If denominator is0, it raises aZeroDivisionError. The second version requires that other_fraction is an instance ofnumbers.Rationaland returns aFractioninstance with the same value. The next two versions accept either afloator adecimal.Decimalinstance, and return aFractioninstance with exactly the same value. Note that due to the usual issues with binary floating point (see Floating-Point Arithmetic: Issues and Limitations), the argument toFraction(1.1)is not exactly equal to 11/10, and soFraction(1.1)does not returnFraction(11, 10)as one might expect. (But see the documentation for thelimit_denominator()method below.) The last version of the constructor expects a string or unicode instance. The usual form for this instance is:[sign] numerator ['/' denominator]
where the optional
signmay be either ‘+’ or ‘-’ andnumeratoranddenominator(if present) are strings of decimal digits (underscores may be used to delimit digits as with integral literals in code). In addition, any string that represents a finite value and is accepted by thefloatconstructor is also accepted by theFractionconstructor. In either form the input string may also have leading and/or trailing whitespace. Here are some examples:>>> from fractions import Fraction >>> Fraction(16, -10) Fraction(-8, 5) >>> Fraction(123) Fraction(123, 1) >>> Fraction() Fraction(0, 1) >>> Fraction('3/7') Fraction(3, 7) >>> Fraction(' -3/7 ') Fraction(-3, 7) >>> Fraction('1.414213 \t\n') Fraction(1414213, 1000000) >>> Fraction('-.125') Fraction(-1, 8) >>> Fraction('7e-6') Fraction(7, 1000000) >>> Fraction(2.25) Fraction(9, 4) >>> Fraction(1.1) Fraction(2476979795053773, 2251799813685248) >>> from decimal import Decimal >>> Fraction(Decimal('1.1')) Fraction(11, 10)
The
Fractionclass inherits from the abstract base classnumbers.Rational, and implements all of the methods and operations from that class.Fractioninstances are hashable, and should be treated as immutable. In addition,Fractionhas the following properties and methods:버전 3.2에서 변경:
Fraction생성자는 이제float와decimal.Decimal인스턴스를 받아들입니다.버전 3.9에서 변경: The
math.gcd()function is now used to normalize the numerator and denominator.math.gcd()always returns aninttype. Previously, the GCD type depended on numerator and denominator.버전 3.11에서 변경: Underscores are now permitted when creating a
Fractioninstance from a string, following PEP 515 rules.버전 3.11에서 변경:
Fractionimplements__int__now to satisfytyping.SupportsIntinstance checks.버전 3.12에서 변경: Space is allowed around the slash for string inputs:
Fraction('2 / 3').버전 3.12에서 변경:
Fractioninstances now support float-style formatting, with presentation types"e","E","f","F","g","G"and"%"".버전 3.13에서 변경: Formatting of
Fractioninstances without a presentation type now supports fill, alignment, sign handling, minimum width and grouping.- numerator¶
기약 분수로 나타낼 때 Fraction의 분자.
- denominator¶
기약 분수로 나타낼 때 Fraction의 분모.
- as_integer_ratio()¶
Return a tuple of two integers, whose ratio is equal to the original Fraction. The ratio is in lowest terms and has a positive denominator.
Added in version 3.8.
- is_integer()¶
Return
Trueif the Fraction is an integer.Added in version 3.12.
- classmethod from_float(flt)¶
Alternative constructor which only accepts instances of
floatornumbers.Integral. Beware thatFraction.from_float(0.3)is not the same value asFraction(3, 10).
- classmethod from_decimal(dec)¶
Alternative constructor which only accepts instances of
decimal.Decimalornumbers.Integral.참고
파이썬 3.2 이상에서는,
decimal.Decimal인스턴스에서 직접Fraction인스턴스를 생성할 수도 있습니다.
- limit_denominator(max_denominator=1000000)¶
분모가 최대 max_denominator인
self에 가장 가까운Fraction을 찾아서 반환합니다. 이 메서드는 주어진 부동 소수점 수에 대한 유리한 근사를 찾는 데 유용합니다:>>> from fractions import Fraction >>> Fraction('3.1415926535897932').limit_denominator(1000) Fraction(355, 113)
또는 float로 표현된 유리수를 복구할 때 유용합니다:
>>> from math import pi, cos >>> Fraction(cos(pi/3)) Fraction(4503599627370497, 9007199254740992) >>> Fraction(cos(pi/3)).limit_denominator() Fraction(1, 2) >>> Fraction(1.1).limit_denominator() Fraction(11, 10)
- __floor__()¶
가장 큰
int<= self를 반환합니다. 이 메서드는math.floor()함수를 통해 액세스할 수도 있습니다:>>> from math import floor >>> floor(Fraction(355, 113)) 3
- __ceil__()¶
가장 작은
int>= self를 반환합니다. 이 메서드는math.ceil()함수를 통해 액세스할 수도 있습니다.
- __round__()¶
- __round__(ndigits)
첫 번째 버전은
self에 가장 가까운int를 반환하는데, 절반은 짝수로 자리 올림 합니다. 두 번째 버전은self를 가장 가까운Fraction(1, 10**ndigits)의 배수로 자리 올림 하는데 (ndigits가 음수면 논리적으로), 역시 짝수로 자리 올림 합니다. 이 메서드는round()함수를 통해 액세스할 수도 있습니다.
- __format__(format_spec, /)¶
Provides support for formatting of
Fractioninstances via thestr.format()method, theformat()built-in function, or Formatted string literals.If the
format_specformat specification string does not end with one of the presentation types'e','E','f','F','g','G'or'%'then formatting follows the general rules for fill, alignment, sign handling, minimum width, and grouping as described in the format specification mini-language. The “alternate form” flag'#'is supported: if present, it forces the output string to always include an explicit denominator, even when the value being formatted is an exact integer. The zero-fill flag'0'is not supported.If the
format_specformat specification string ends with one of the presentation types'e','E','f','F','g','G'or'%'then formatting follows the rules outlined for thefloattype in the 포맷 명세 미니 언어 section.Here are some examples:
>>> from fractions import Fraction >>> format(Fraction(103993, 33102), '_') '103_993/33_102' >>> format(Fraction(1, 7), '.^+10') '...+1/7...' >>> format(Fraction(3, 1), '') '3' >>> format(Fraction(3, 1), '#') '3/1' >>> format(Fraction(1, 7), '.40g') '0.1428571428571428571428571428571428571429' >>> format(Fraction('1234567.855'), '_.2f') '1_234_567.86' >>> f"{Fraction(355, 113):*>20.6e}" '********3.141593e+00' >>> old_price, new_price = 499, 672 >>> "{:.2%} price increase".format(Fraction(new_price, old_price) - 1) '34.67% price increase'
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- 모듈
numbers 숫자 계층을 구성하는 추상 베이스 클래스.