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(number)
class fractions.Fraction(string)

The first version requires that numerator and denominator are instances of numbers.Rational and returns a new Fraction instance with value numerator/denominator. If denominator is 0, it raises a ZeroDivisionError.

The second version requires that number is an instance of numbers.Rational or has the as_integer_ratio() method (this includes float and decimal.Decimal). It returns a Fraction instance with exactly the same value. Assumed, that the as_integer_ratio() method returns a pair of coprime integers and last one is positive. Note that due to the usual issues with binary point (see Floating-Point Arithmetic: Issues and Limitations), the argument to Fraction(1.1) is not exactly equal to 11/10, and so Fraction(1.1) does not return Fraction(11, 10) as one might expect. (But see the documentation for the limit_denominator() method below.)

The last version of the constructor expects a string. The usual form for this instance is:

[sign] numerator ['/' denominator]

where the optional sign may be either ‘+’ or ‘-’ and numerator and denominator (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 the float constructor is also accepted by the Fraction constructor. 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 Fraction class inherits from the abstract base class numbers.Rational, and implements all of the methods and operations from that class. Fraction instances are hashable, and should be treated as immutable. In addition, Fraction has the following properties and methods:

버전 3.2에서 변경: Fraction 생성자는 이제 float와 decimal.Decimal 인스턴스를 받아들입니다.

버전 3.9에서 변경: The math.gcd() function is now used to normalize the numerator and denominator. math.gcd() always returns an int type. Previously, the GCD type depended on numerator and denominator.

버전 3.11에서 변경: Underscores are now permitted when creating a Fraction instance from a string, following PEP 515 rules.

버전 3.11에서 변경: Fraction implements __int__ now to satisfy typing.SupportsInt instance checks.

버전 3.12에서 변경: Space is allowed around the slash for string inputs: Fraction('2 / 3').

버전 3.12에서 변경: Fraction instances now support float-style formatting, with presentation types "e", "E", "f", "F", "g", "G" and "%"".

버전 3.13에서 변경: Formatting of Fraction instances without a presentation type now supports fill, alignment, sign handling, minimum width and grouping.

버전 3.14에서 변경: The Fraction constructor now accepts any objects with the as_integer_ratio() method.

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 True if the Fraction is an integer.

Added in version 3.12.

classmethod from_float(flt)

Alternative constructor which only accepts instances of float or numbers.Integral. Beware that Fraction.from_float(0.3) is not the same value as Fraction(3, 10).

참고

파이썬 3.2 이상에서는, float에서 직접 Fraction 인스턴스를 생성할 수도 있습니다.

classmethod from_decimal(dec)

Alternative constructor which only accepts instances of decimal.Decimal or numbers.Integral.

참고

파이썬 3.2 이상에서는, decimal.Decimal 인스턴스에서 직접 Fraction 인스턴스를 생성할 수도 있습니다.

classmethod from_number(number)

Alternative constructor which only accepts instances of numbers.Integral, numbers.Rational, float or decimal.Decimal, and objects with the as_integer_ratio() method, but not strings.

Added in version 3.14.

limit_denominator(max_denominator=1000000)

분모가 최대 max_denominator인 self에 가장 가까운 Fraction을 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 메서드는 math.floor() 함수를 통해 액세스할 수도 있습니다:

>>> from math import floor
>>> floor(Fraction(355, 113))
3
__ceil__()

가장 작은 int >= self를 반환합니다. 이 메서드는 math.ceil() 함수를 통해 액세스할 수도 있습니다.

__round__()
__round__(ndigits)

첫 번째 버전은 self에 가장 가까운 int를 반환하는데, 절반은 짝수로 자리 올림 합니다. 두 번째 버전은 self를 가장 가까운 Fraction(1, 10**ndigits)의 배수로 자리 올림 하는데 (ndigits가 음수면 논리적으로), 역시 짝수로 자리 올림 합니다. 이 메서드는 round() 함수를 통해 액세스할 수도 있습니다.

__format__(format_spec, /)

Provides support for formatting of Fraction instances via the str.format() method, the format() built-in function, or Formatted string literals.

If the format_spec format 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_spec format specification string ends with one of the presentation types 'e', 'E', 'f', 'F', 'g', 'G' or '%' then formatting follows the rules outlined for the float type 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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