Source code: Lib/fractions.py
The 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
and returns a new Fraction
instance with value numerator/denominator
. If denominator is 0
, it raises a ZeroDivisionError
. The second version requires that other_fraction is an instance of numbers.Rational
and returns a Fraction
instance with the same value. The next two versions accept either a float
or a 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 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 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)
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:
Changed in version 3.2: The Fraction
constructor now accepts float
and decimal.Decimal
instances.
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)
.
from_decimal(dec)
This class method constructs a Fraction
representing the exact value of dec, which must be a decimal.Decimal
instance.
Note
From Python 3.2 onwards, you can also construct a Fraction
instance directly from a decimal.Decimal
instance.
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()
function:
>>> 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()
function.
__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()
function.
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)
returns 0
.
Deprecated since version 3.5: Use math.gcd()
instead.
See also
Module
numbers
© 2001–2018 Python Software Foundation
Licensed under the PSF License.
https://docs.python.org/3.6/library/fractions.html