fractions --- Rational numbers

Code source : Lib/fractions.py

Le module fractions fournit un support de l'arithmétique des nombres rationnels.

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

class fractions.Fraction(numerator=0, denominator=1)
class fractions.Fraction(number)
class fractions.Fraction(string)

The first version requires that numerator and denominator are instances of numbers.Rational and returns a new Fraction instance with a value equal to numerator/denominator. If denominator is zero, it raises a ZeroDivisionError.

The second version requires that number is an instance of numbers.Rational or has the as_integer_ratio() method (this includes float and decimal.Decimal). It returns a Fraction instance with exactly the same value. Assumed, that the as_integer_ratio() method returns a pair of coprime integers and last one is positive. Note that due to the usual issues with binary 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. 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 (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)

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:

Modifié dans la version 3.2: Le constructeur de Fraction accepte maintenant des instances de float et decimal.Decimal.

Modifié dans la version 3.9: The math.gcd() function is now used to normalize the numerator and denominator. math.gcd() always returns an int type. Previously, the GCD type depended on numerator and denominator.

Modifié dans la version 3.11: Underscores are now permitted when creating a Fraction instance from a string, following PEP 515 rules.

Modifié dans la version 3.11: Fraction implements __int__ now to satisfy typing.SupportsInt instance checks.

Modifié dans la version 3.12: Space is allowed around the slash for string inputs: Fraction('2 / 3').

Modifié dans la version 3.12: Fraction instances now support float-style formatting, with presentation types "e", "E", "f", "F", "g", "G" and "%"".

Modifié dans la version 3.13: Formatting of Fraction instances without a presentation type now supports fill, alignment, sign handling, minimum width and grouping.

Modifié dans la version 3.14: The Fraction constructor now accepts any objects with the as_integer_ratio() method.

numerator

Numérateur de la fraction irréductible.

denominator

Denominator of the Fraction in lowest terms. Guaranteed to be positive.

as_integer_ratio()

Return a tuple of two integers, whose ratio is equal to the original Fraction. The ratio is in lowest terms and has a positive denominator.

Ajouté dans la version 3.8.

is_integer()

Return True if the Fraction is an integer.

Ajouté dans la version 3.12.

classmethod from_float(f)

Ce constructeur alternatif accepte (uniquement) des nombres à virgule flottante, de classe float, ou plus généralement des instances de numbers.Integral. Attention, Fraction.from_float(0.3) est différent de Fraction(3, 10).

Note

Depuis Python 3.2, vous pouvez aussi construire une instance de Fraction directement depuis un float.

classmethod from_decimal(dec)

Ce constructeur alternatif accepte (uniquement) les instances de decimal.Decimal ou numbers.Integral.

Note

Depuis Python 3.2, vous pouvez aussi construire une instance de Fraction directement depuis une instance de decimal.Decimal.

classmethod from_number(number)

Alternative constructor which only accepts instances of numbers.Integral, numbers.Rational, float or decimal.Decimal, and objects with the as_integer_ratio() method, but not strings.

Ajouté dans la version 3.14.

limit_denominator(max_denominator=1000000)

Trouve et renvoie la Fraction la plus proche de self qui a au plus max_denominator comme dénominateur. Cette méthode est utile pour trouver des approximations rationnelles de nombres flottants donnés :

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

ou pour retrouver un nombre rationnel représenté par un flottant :

>>> 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__()

Renvoie le plus grand int <= self. Cette méthode peut aussi être utilisée à travers la fonction math.floor() :

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

Renvoie le plus petit int >= self. Cette méthode peut aussi être utilisée à travers la fonction math.ceil().

__round__()
__round__(ndigits)

La première version renvoie l'int le plus proche de self, arrondissant les demis au nombre pair le plus proche. La seconde version arrondit self au plus proche multiple de Fraction(1, 10**ndigits) (logiquement, si ndigits est négatif), arrondissant toujours les demis au nombre pair le plus proche. Cette méthode peut aussi être utilisée à via la fonction round().

__format__(format_spec, /)

Provides support for formatting of Fraction instances via the str.format() method, the format() built-in function, or Formatted string literals.

If the format_spec format specification string does not end with one of the presentation types 'e', 'E', 'f', 'F', 'g', 'G' or '%' then formatting follows the general rules for fill, alignment, sign handling, minimum width, and grouping as described in the format specification mini-language. The "alternate form" flag '#' is supported: if present, it forces the output string to always include an explicit denominator, even when the value being formatted is an exact integer. The zero-fill flag '0' is not supported.

If the format_spec format specification string ends with one of the presentation types 'e', 'E', 'f', 'F', 'g', 'G' or '%' then formatting follows the rules outlined for the float type in the Mini-langage de spécification de format section.

Voici quelques exemples :

>>> from fractions import Fraction
>>> format(Fraction(103993, 33102), '_')
'103_993/33_102'
>>> format(Fraction(1, 7), '.^+10')
'...+1/7...'
>>> format(Fraction(3, 1), '')
'3'
>>> format(Fraction(3, 1), '#')
'3/1'
>>> format(Fraction(1, 7), '.40g')
'0.1428571428571428571428571428571428571429'
>>> format(Fraction('1234567.855'), '_.2f')
'1_234_567.86'
>>> f"{Fraction(355, 113):*>20.6e}"
'********3.141593e+00'
>>> old_price, new_price = 499, 672
>>> "{:.2%} price increase".format(Fraction(new_price, old_price) - 1)
'34.67% price increase'

Voir aussi

Module numbers

Les classes abstraites représentant la hiérarchie des nombres.