fractions — Rational numbers¶
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.Rationaland returns a newFractioninstance with valuenumerator/denominator. If denominator is0, it raises aZeroDivisionError. The second version requires that other_fraction is an instance ofnumbers.Rationaland returns aFractioninstance with the same value. The next two versions accept either afloator adecimal.Decimalinstance, and return aFractioninstance with exactly the same value. Note that due to the usual issues with binary floating point (see Arytmetyka liczb zmiennoprzecinkowych: problemy i ograniczenia), the argument toFraction(1.1)is not exactly equal to 11/10, and soFraction(1.1)does not returnFraction(11, 10)as one might expect. (But see the documentation for thelimit_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
signmay be either «+» or «-» andnumeratoranddenominator(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 thefloatconstructor is also accepted by theFractionconstructor. 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
Fractionclass inherits from the abstract base classnumbers.Rational, and implements all of the methods and operations from that class.Fractioninstances are hashable, and should be treated as immutable. In addition,Fractionhas the following properties and methods:Zmienione w wersji 3.2: The
Fractionconstructor now acceptsfloatanddecimal.Decimalinstances.Zmienione w wersji 3.9: The
math.gcd()function is now used to normalize the numerator and denominator.math.gcd()always returns aninttype. Previously, the GCD type depended on numerator and denominator.Zmienione w wersji 3.11: Underscores are now permitted when creating a
Fractioninstance from a string, following PEP 515 rules.Zmienione w wersji 3.11:
Fractionimplements__int__now to satisfytyping.SupportsIntinstance checks.Zmienione w wersji 3.12: Space is allowed around the slash for string inputs:
Fraction('2 / 3').Zmienione w wersji 3.12:
Fractioninstances now support float-style formatting, with presentation types"e","E","f","F","g","G"and"%"".Zmienione w wersji 3.13: Formatting of
Fractioninstances without a presentation type now supports fill, alignment, sign handling, minimum width and grouping.- numerator¶
Numerator of the Fraction in lowest term.
- denominator¶
Denominator of the Fraction in lowest term.
- 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.
Dodane w wersji 3.8.
- is_integer()¶
Return
Trueif the Fraction is an integer.Dodane w wersji 3.12.
- classmethod from_float(flt)¶
Alternative constructor which only accepts instances of
floatornumbers.Integral. Beware thatFraction.from_float(0.3)is not the same value asFraction(3, 10).
- classmethod from_decimal(dec)¶
Alternative constructor which only accepts instances of
decimal.Decimalornumbers.Integral.Informacja
From Python 3.2 onwards, you can also construct a
Fractioninstance directly from adecimal.Decimalinstance.
- limit_denominator(max_denominator=1000000)¶
Finds and returns the closest
Fractiontoselfthat 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 themath.floor()function:>>> from math import floor >>> floor(Fraction(355, 113)) 3
- __ceil__()¶
Returns the least
int>= self. This method can also be accessed through themath.ceil()function.
- __round__()¶
- __round__(ndigits)
The first version returns the nearest
inttoself, rounding half to even. The second version roundsselfto the nearest multiple ofFraction(1, 10**ndigits)(logically, ifndigitsis negative), again rounding half toward even. This method can also be accessed through theround()function.
- __format__(format_spec, /)¶
Provides support for formatting of
Fractioninstances via thestr.format()method, theformat()built-in function, or Formatted string literals.If the
format_specformat 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_specformat specification string ends with one of the presentation types'e','E','f','F','g','G'or'%'then formatting follows the rules outlined for thefloattype in the Format Specification Mini-Language section.Here are some examples:
>>> 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'
Zobacz także
- Module
numbers The abstract base classes making up the numeric tower.