fractions
— 有理数
¶
源代码： Lib/fractions.py
fractions
模块提供有理数算术支持。
Fraction 实例可以构造自一对整数、另一有理数或字符串。
第 1 个版本要求
numerator
and
denominator
是实例化的
numbers.Rational
并返回新的
Fraction
实例采用值
numerator/denominator
。若
denominator
is
0
，引发
ZeroDivisionError
。第 2 个版本要求
other_fraction
是实例化的
numbers.Rational
并返回
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]
其中可选
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)
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
构造函数现在接受
float
and
decimal.Decimal
实例。
3.9 版改变：
math.gcd()
function is now used to normalize the
numerator
and
denominator
.
math.gcd()
always return a
int
type. Previously, the GCD type depended on
numerator
and
denominator
.
3.11 版改变：
Underscores are now permitted when creating a
Fraction
instance from a string, following
PEP 515
规则。
3.11 版改变：
Fraction
实现
__int__
now to satisfy
typing.SupportsInt
instance checks.
Numerator of the Fraction in lowest term.
Denominator of the Fraction in lowest term.
Return a tuple of two integers, whose ratio is equal to the Fraction and with a positive denominator.
3.8 版新增。
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)
.
注意
From Python 3.2 onwards, you can also construct a
Fraction
instance directly from a
float
.
Alternative constructor which only accepts instances of
decimal.Decimal
or
numbers.Integral
.
注意
From Python 3.2 onwards, you can also construct a
Fraction
instance directly from a
decimal.Decimal
实例。
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)
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
Returns the least
int
>= self
. This method can also be accessed through the
math.ceil()
函数。
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。
另请参阅
numbers
组成数值塔的抽象基类。