Your IP : 18.119.166.34
a
R�f_ � @ sx d Z ddlmZ ddlZddlZddlZddlZddlZdgZej j
Zej jZ
e�dejejB �ZG dd� dej�ZdS )z+Fraction, infinite-precision, real numbers.� ��DecimalN�FractionaC
\A\s* # optional whitespace at the start, then
(?P<sign>[-+]?) # an optional sign, then
(?=\d|\.\d) # lookahead for digit or .digit
(?P<num>\d*) # numerator (possibly empty)
(?: # followed by
(?:/(?P<denom>\d+))? # an optional denominator
| # or
(?:\.(?P<decimal>\d*))? # an optional fractional part
(?:E(?P<exp>[-+]?\d+))? # and optional exponent
)
\s*\Z # and optional whitespace to finish
c s� e Zd ZdZdZdRdd�� fdd�Zed d
� �Zedd� �Zd
d� Z dSdd�Z
edd� �Zedd� �Z
dd� Zdd� Zdd� Zdd� Zeeej�\ZZdd� Zeeej�\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/� Z0d0d1� Z1d2d3� Z2d4d5� Z3d6d7� Z4d8d9� Z5dTd:d;�Z6d<d=� Z7d>d?� Z8d@dA� Z9dBdC� Z:dDdE� Z;dFdG� Z<dHdI� Z=dJdK� Z>dLdM� Z?dNdO� Z@dPdQ� ZA� ZBS )Ur a] 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�_denominatorr NT��
_normalizec s" t t| ��| �}|du �rdt|�tu r6||_d|_|S t|tj �rV|j
|_|j|_|S t|tt
f�rx|�� \|_|_|S t|t��rZt�|�}|du r�td| ��t|�d�p�d�}|�d�}|r�t|�}nvd}|�d�}|�rdt|� }|| t|� }||9 }|�d �} | �rBt| �} | d
k�r4|d| 9 }n|d| 9 }|�d�dk�rb| }ntd
��nft|�t u �r�t|�u �r�n nn@t|tj ��r�t|tj ��r�|j
|j |j
|j }}ntd��|d
k�r�td| ��|�rt�||�}
|d
k �r|
}
||
}||
}||_||_|S )a� Constructs 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)
N� z Invalid literal for Fraction: %rZnum�0�denom�decimal�
�expr Zsign�-z2argument should be a string or a Rational instancez+both arguments should be Rational instanceszFraction(%s, 0))�superr �__new__�type�intr r �
isinstance�numbers�Rational� numerator�denominator�floatr �as_integer_ratio�str�_RATIONAL_FORMAT�match�
ValueError�group�len� TypeError�ZeroDivisionError�mathZgcd)�clsr r r �self�mr r
Zscaler �g�� __class__� �./opt/alt/python39/lib64/python3.9/fractions.pyr >