0 $lY> je8Cqn1h i?a i_@sxdZddlmZddlZddlZddlZddlZddlZdgZej j Z ej j Z edejejBZGdddejZdS)z+Fraction, infinite-precision, real numbers.DecimalNFractionaC \A\s* # optional whitespace at the start, then (?P[-+]?) # an optional sign, then (?=\d|\.\d) # lookahead for digit or .digit (?P\d*) # numerator (possibly empty) (?: # followed by (?:/(?P\d+))? # an optional denominator | # or (?:\.(?P\d*))? # an optional fractional part (?:E(?P[-+]?\d+))? # and optional exponent ) \s*\Z # and optional whitespace to finish cseZdZdZdZdRddfdd Zed d Zed d Zd dZ dSddZ e ddZ e ddZ ddZddZddZddZeeej\ZZddZeeej\ZZd d!Zeeej\ZZd"d#Zeeej\Z Z!d$d%Z"ee"ej#\Z$Z%d&d'Z&ee&e'\Z(Z)d(d)Z*ee*ej+\Z,Z-d*d+Z.d,d-Z/d.d/Z0d0d1Z1d2d3Z2d4d5Z3d6d7Z4d8d9Z5dTd:d;Z6dd?Z8d@dAZ9dBdCZ:dDdEZ;dFdGZdLdMZ?dNdOZ@dPdQZAZBS)Ura]This class implements rational numbers. In the two-argument form of the constructor, Fraction(8, 6) will produce a rational number equivalent to 4/3. Both arguments must be Rational. The numerator defaults to 0 and the denominator defaults to 1 so that Fraction(3) == 3 and Fraction() == 0. Fractions can also be constructed from: - numeric strings similar to those accepted by the float constructor (for example, '-2.3' or '1e10') - strings of the form '123/456' - float and Decimal instances - other Rational instances (including integers)  _numerator _denominatorrNT _normalizec s"tt||}|durdt|tur6||_d|_|St|tj rV|j |_|j |_|St|t t frx|\|_|_|St|trZt|}|durtd|t|dpd}|d}|rt|}nvd}|d}|rdt|}||t|}||9}|d } | rBt| } | d kr4|d| 9}n|d| 9}|d d krb| }ntd nft|turt|urnnn@t|tj rt|tj r|j |j |j |j }}ntd|d krtd||rt||} |d kr| } || }|| }||_||_|S)aConstructs a Rational. Takes a string like '3/2' or '1.5', another Rational instance, a numerator/denominator pair, or a float. Examples -------- >>> Fraction(10, -8) Fraction(-5, 4) >>> Fraction(Fraction(1, 7), 5) Fraction(1, 35) >>> Fraction(Fraction(1, 7), Fraction(2, 3)) Fraction(3, 14) >>> Fraction('314') Fraction(314, 1) >>> Fraction('-35/4') Fraction(-35, 4) >>> Fraction('3.1415') # conversion from numeric string Fraction(6283, 2000) >>> Fraction('-47e-2') # string may include a decimal exponent Fraction(-47, 100) >>> Fraction(1.47) # direct construction from float (exact conversion) Fraction(6620291452234629, 4503599627370496) >>> Fraction(2.25) Fraction(9, 4) >>> Fraction(Decimal('1.47')) Fraction(147, 100) Nz Invalid literal for Fraction: %rnum0denomdecimal exprsign-z2argument should be a string or a Rational instancez+both arguments should be Rational instanceszFraction(%s, 0))superr__new__typeintrr isinstancenumbersRational numerator denominatorfloatras_integer_ratiostr_RATIONAL_FORMATmatch ValueErrorgrouplen TypeErrorZeroDivisionErrormathgcd) clsrrr selfmr rZscalerg __class__!/usr/lib64/python3.9/fractions.pyr>st