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d� dej�ZdS )z+Fraction, infinite-precision, real numbers.� )�DecimalN�Fraction�gcdc C sf ddl }|jdtd� t| �t ko0t|�kn r\|p<| dk rPtj| |� S tj| |�S t| |�S )z�Calculate the Greatest Common Divisor of a and b.
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\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
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(?:\.(?P<decimal>\d*))? # an optional fractional part
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dd� Zdd� Zdd� Zeeej�\ZZdd� Zeeej�\ZZdd � Zeeej�\ZZd!d"� Zeeej�\ZZ d#d$� Z!d%d&� Z"d'd(� Z#d)d*� Z$d+d,� Z%d-d.� Z&d/d0� Z'd1d2� Z(d3d4� Z)d5d6� Z*d7d8� Z+d9d:� Z,dVd;d<�Z-d=d>� Z.d?d@� Z/dAdB� Z0dCdD� Z1dEdF� Z2dGdH� Z3dIdJ� Z4dKdL� Z5dMdN� Z6dOdP� Z7dQdR� Z8� Z9S )Wr 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)
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}||_||_|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)
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zFraction.__new__c C sD t |tj�r| |�S t |t�s8td| j|t|�jf ��| |j� � S )z�Converts a finite float to a rational number, exactly.
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z.%s.from_float() only takes floats, not %r (%s))r r �Integralr"