9.5. fractions — Rational numbers — Python v2.7 documentation (original) (raw)

New in version 2.6.

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 aFraction instance with the same value. The next two versions accept either a float or a decimal.Decimal instance, and return aFraction 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 soFraction(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 ‘-‘ andnumerator 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) [40794 refs] 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 classnumbers.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 methods:

Changed in version 2.7: The Fraction constructor now accepts float anddecimal.Decimal instances.

from_float(flt)¶

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

Note

From Python 2.7 onwards, you can also construct aFraction 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.

Note

From Python 2.7 onwards, you can also construct aFraction instance directly from a decimal.Decimalinstance.

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)

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.