9.5. fractions — 有理数 ¶

源代码： Lib/fractions.py

fractions module provides support for rational number arithmetic.

A Fraction instance can be constructed from a pair of integers, from another rational number, or from a string.

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.Rational 并返回新 Fraction instance with value numerator/denominator 。若 denominator is 0 , it raises a ZeroDivisionError . The second version requires that other_fraction 是实例化的 numbers.Rational and returns a Fraction instance with the same value. The next two versions accept either a float 或 decimal.Decimal instance, and return a Fraction instance with exactly the same value. Note that due to the usual issues with binary floating-point (see 浮点算术：问题和局限性 ), 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 or unicode instance. 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. 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)
									

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:

3.2 版改变： Fraction constructor now accepts float and decimal.Decimal 实例。

numerator ¶

Numerator of the Fraction in lowest term.

denominator ¶

Denominator of the Fraction in lowest term.

from_float ( flt ) ¶

This class method constructs a Fraction representing the exact value of flt , which must be a float . Beware that Fraction.from_float(0.3) is not the same value as Fraction(3, 10) .

注意

From Python 3.2 onwards, you can also construct a Fraction instance directly from a float .

from_decimal ( dec ) ¶

This class method constructs a Fraction representing the exact value of dec , which must be a decimal.Decimal 实例。

注意

From Python 3.2 onwards, you can also construct a Fraction instance directly from a decimal.Decimal 实例。

limit_denominator ( max_denominator=1000000 ) ¶

Finds and returns the closest Fraction to self that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number:

>>> from fractions import Fraction
>>> Fraction('3.1415926535897932').limit_denominator(1000)
Fraction(355, 113)
											

or for recovering a rational number that’s represented as a float:

>>> 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__ ( ) ¶

Returns the greatest int <= self . This method can also be accessed through the math.floor() 函数：

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

__ceil__ ( ) ¶

Returns the least int >= self . This method can also be accessed through the math.ceil() 函数。

__round__ ( ) ¶

__round__ ( ndigits )

The first version returns the nearest int to self , rounding half to even. The second version rounds self to the nearest multiple of Fraction(1, 10**ndigits) (logically, if ndigits is negative), again rounding half toward even. This method can also be accessed through the round() 函数。

fractions. gcd ( a , b ) ¶

Return the greatest common divisor of the integers a and b . If either a or b is nonzero, then the absolute value of gcd(a, b) is the largest integer that divides both a and b . gcd(a,b) has the same sign as b if b is nonzero; otherwise it takes the sign of a . gcd(0, 0) 返回 0 .

从 3.5 版起弃用： 使用 math.gcd() 代替。

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