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zFraction.limit_denominatorc C s | j S r )r r r r r r% s zFraction.numeratorc C s | j S r )r rC r r r r& s zFraction.denominatorc C s d| j j| j| jf S )Nz
%s(%s, %s))r6 r8 r r r< r r r __repr__" s zFraction.__repr__c C s( | j dkrt| jS d| j| j f S d S )Nr z%s/%s)r r) r r< r r r __str__' s
zFraction.__str__c sT fdd}d j d |_ j|_ fdd}d j d |_ j|_||fS )Nc sP t |ttfr| |S t |tr0 t| |S t |trH t| |S tS d S r )r" r r r' complexNotImplementedr fallback_operatormonomorphic_operatorr r forward~ s
z-Fraction._operator_fallbacks.<locals>.forward__c sZ t |tjr|| S t |tjr4 t|t| S t |tjrR t|t| S tS d S r )r" r# r$ ZRealr' ComplexrF rG r r rH r r reverse s
z-Fraction._operator_fallbacks.<locals>.reverseZ__r)r8 __doc__)rJ rI rK rO r rH r _operator_fallbacks. s P
z Fraction._operator_fallbacksc C s, | j |j }}t| j| |j| || S r r& r r% r r dadbr r r _add s z
Fraction._addc C s, | j |j }}t| j| |j| || S r rR rS r r r _sub s z
Fraction._subc C s t | j|j | j|j S r r r% r& r r r r _mul s z
Fraction._mulc C s t | j|j | j|j S r rX r r r r _div s
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Fraction._divc C s | j |j | j|j S r r% r& r r r r _floordiv s zFraction._floordivc C s: | j |j }}t| j| ||j \}}|t||| fS r )r& divmodr% r )r r rT rU ZdivZn_modr r r _divmod s zFraction._divmodc C s, | j |j }}t| j| |j| || S r rR rS r r r _mod s z
Fraction._modc C s t |tjr|jdkr|j}|dkr>t| j| | j| ddS | jdkrft| j| | j| ddS t| j | | j | ddS qt| t| S n t| | S d S )Nr r Fr ) r" r# r$ r& r% r r r r' )r r Zpowerr r r __pow__ s&
zFraction.__pow__c C s\ | j dkr | jdkr || j S t|tjr<t|j|j| S | j dkrP|| j S |t| S )Nr r ) r r r" r# r$ r r% r& r' rN r r r __rpow__ s
zFraction.__rpow__c C s t | j| jddS NFr r r r rC r r r __pos__ s zFraction.__pos__c C s t | j | jddS rb rc rC r r r __neg__ s zFraction.__neg__c C s t t| j| jddS rb )r r> r r rC r r r __abs__ s zFraction.__abs__c C s* | j dk r| j | j S | j | j S d S )Nr r rC r r r __trunc__ s
zFraction.__trunc__c C s | j | j S r r[ rC r r r __floor__
s zFraction.__floor__c C s | j | j S r r[ rC r r r __ceil__ s zFraction.__ceil__c C s |d krZt | j| j\}}|d | jk r,|S |d | jkrB|d S |d dkrR|S |d S dt| }|dkrtt| | |S tt| | | S d S )Nr r r r )r] r% r& r> r round)r2 ZndigitsZfloorZ remaindershiftr r r __round__ s zFraction.__round__c C sP t | jtd t}|s t}nt| j| t }| dkr:|n| }|dkrLdS |S )Nr r )powr _PyHASH_MODULUS _PyHASH_INFr> r )r2 ZdinvZhash_resultr r r __hash__, s zFraction.__hash__c C s t |tkr | j|ko | jdkS t|tjrD| j|jkoB| j|jkS t|tj r`|j
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zFraction._richcmpc C s | |tjS r )r| operatorltr r r r __lt__m s zFraction.__lt__c C s | |tjS r )r| r} gtr r r r __gt__q s zFraction.__gt__c C s | |tjS r )r| r} ler r r r __le__u s zFraction.__le__c C s | |tjS r )r| r} ger r r r __ge__y s zFraction.__ge__c C s
t | jS r )boolr rC r r r __bool__} s zFraction.__bool__c C s | j t| ffS r )r6 r) r< r r r
__reduce__ s zFraction.__reduce__c C s t | tkr| S | | j| jS r r
r r6 r r r< r r r __copy__ s zFraction.__copy__c C s t | tkr| S | | j| jS r r )r2 Zmemor r r __deepcopy__ s zFraction.__deepcopy__)r N)r= )N)Br8
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