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zFraction.limit_denominatorc C s | j S r5 )r r; r. r. r/ r s zFraction.numeratorc C s | j S r5 )r r> r. r. r/ r s zFraction.denominatorc C s d| j j| j| jf S )Nz
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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 r5 )r r r r complexNotImplementedr; bfallback_operatormonomorphic_operatorr. r/ forwardd s
z-Fraction._operator_fallbacks..forward__c sZ t |tjr|| S t |tjr4 t|t| S t |tjrR t|t| S tS d S r5 )r r r ZRealr ComplexrA rB rD r; rE r. r/ reversep s
z-Fraction._operator_fallbacks..reverseZ__r)r1 __doc__)rG rF rH rL r. rE r/ _operator_fallbacks s P
z Fraction._operator_fallbacksc C s, | j |j }}t| j| |j| || S r5 r r r r; rD dadbr. r. r/ _add s z
Fraction._addc C s, | j |j }}t| j| |j| || S r5 rO rP r. r. r/ _sub s z
Fraction._subc C s t | j|j | j|j S r5 r r r rC r. r. r/ _mul s z
Fraction._mulc C s t | j|j | j|j S r5 rU rC r. r. r/ _div s
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Fraction._divc C s | j |j | j|j S r5 r r rC r. r. r/ _floordiv s zFraction._floordivc C s: | j |j }}t| j| ||j \}}|t||| fS r5 )r divmodr r )r; rD rQ rR ZdivZn_modr. r. r/ _divmod s zFraction._divmodc C s, | j |j }}t| j| |j| || S r5 rO rP 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; rD Zpowerr. r. r/ __pow__ s&
zFraction.__pow__c C s\ | j dkr | jdkr || j S t|tjr r. r. r/ __pos__ s zFraction.__pos__c C s t | j | jddS r_ r` r> r. r. r/ __neg__ s zFraction.__neg__c C s t t| j| jddS r_ )r r8 r r r> r. r. r/ __abs__ s zFraction.__abs__c C s* | j dk r| j | j S | j | j S d S )Nr r r> r. r. r/ __trunc__ s
zFraction.__trunc__c C s | j | j S r5 rX r> r. r. r/ __floor__ s zFraction.__floor__c C s | j | j S r5 rX r> r. r. r/ __ceil__ s zFraction.__ceil__c C s |d u rZt | j| j\}}|d | jk r,|S |d | jkrB|d S |d dkrR|S |d S dt| }|dkrtt| | |S tt| | | S d S )N r
r r )rZ r r r8 r round)r) ndigitsfloor remaindershiftr. r. r/ __round__ s zFraction.__round__c C sd zt | jdt}W n ty( t}Y n0 ttt| j| }| jdkrN|n| }|dkr`dS |S )Nr )powr _PyHASH_MODULUSr! _PyHASH_INFhashr8 r )r) ZdinvZhash_resultr. r. r/ __hash__ s
zFraction.__hash__c C s t |tu r | j|ko | jdkS t|tjrD| j|jkoB| j|jkS t|tj r`|j
dkr`|j }t|t rt
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zFraction.__eq__c C sh t |tjr&|| j|j | j|j S t |tr`t |sDt
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zFraction._richcmpc C s | |tjS r5 )r~ operatorltrC r. r. r/ __lt__^ s zFraction.__lt__c C s | |tjS r5 )r~ r gtrC r. r. r/ __gt__b s zFraction.__gt__c C s | |tjS r5 )r~ r lerC r. r. r/ __le__f s zFraction.__le__c C s | |tjS r5 )r~ r gerC r. r. r/ __ge__j s zFraction.__ge__c C s
t | jS r5 )boolr r> r. r. r/ __bool__n s zFraction.__bool__c C s | j t| ffS r5 )r- r r6 r. r. r/
__reduce__v s zFraction.__reduce__c C s t | tkr| S | | j| jS r5 r r r- r r r6 r. r. r/ __copy__y s zFraction.__copy__c C s t | tkr| S | | j| jS r5 r )r) memor. r. r/ __deepcopy__~ s zFraction.__deepcopy__)r N)r7 )N)Br1
__module__ __qualname__ __slots__r classmethodr3 r4 r r= propertyr r r? r@ rN rS r add__add____radd__rT sub__sub____rsub__rV mul__mul____rmul__rW truediv __truediv__ __rtruediv__rY floordiv __floordiv__
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