Source code: 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)
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
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:
Numerator of the Fraction in lowest term.
Denominator of the Fraction in lowest term.
Finds and returns the closest
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)
>>> from math import floor >>> floor(Fraction(355, 113)) 3
The first version returns the nearest
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
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.
Deprecated since version 3.5: Use
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