+
    iX                     x   ^ RI t ^ RIt^RIHtHtHtHtHt ]P                  t
/ 3R lt ! R R]4      t]! R4      t]! R4      t]! R4      t]! R	4      t]! R
4      t]! R4      t]! R4      t]! R4      t]! R4      t]! R4      t]! R4      t ^ RIt]P2                  P5                  ]4       R#   ] d     R# i ; i)    N)	int_typesmpf_hashbitcountfrom_man_expHASH_MODULUSc                     W3pW29   d	   W#,          # YrTV'       d   YTV,          rTK  V^8w  d   W,          p W,          p\        \        4      pW3Vn        V^8:  d   \        V^ ,          4      ^d8  d   WbV&   V#    )newmpq_mpq_abs)pq_cachekeyxyvs   &&&    o/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/mpmath/rational.pycreate_reducedr      sp    
$C
}{q
a%1Av		CAdAGAv#c!f+#sH    c                      a  ] tR t^t o RtR.tRR ltR tR tR t	R t
]
tR tR	 tR
 tR tR tR tR tR tR tR tR tR t]tR tR tR t]tR tR tR tRt V t!R# )r   z@
Exact rational type, currently only intended for internal use.
r   c                    \        V4      \        J d   Vw  rM \        VR 4      '       d   VP                  w  r\	        W4      # r   )typetuplehasattrr   r   )clsr   r   s   &&&r   __new__mpq.__new__   s:    7eDAqQ  77DAa##r   c                (    R V P                   ,          # )z
mpq(%s,%s)r   ss   &r   __repr__mpq.__repr__&   s    agg%%r   c                (    R V P                   ,          # )z(%s/%s)r   r#   s   &r   __str__mpq.__str__)   s    177""r   c                .    V P                   w  rW,          # Nr   )r$   abs   &  r   __int__mpq.__int__,   s    wwvr   c                :    \        V P                  ^ ,          4      # r   )boolr   r#   s   &r   __nonzero__mpq.__nonzero__0   s    AGGAJr   c           	        V P                   w  r\        P                  R8  dr   \        V\        ^,
          \        4      pV'       g   \        P
                  P                  pM\        V4      V,          \        ,          pV^ 8  d   V) pVR8X  d   RpV# V^8X  d   \        V4      # W"^,
          ,          '       g&   \        \        V^\        V4      ,
          4      4      # \        W34      # )   r6      )r   sysversion_infopowr   	hash_infoinfr   hashr   r   r   )r$   r,   r-   inversehs   &    r   __hash__mpq.__hash__5   s    wwv%!\!^\:GMM%%Vg%51u1"aBwBHAvAw1IIQ(1+ >??;r   c                    \        V4      pV\        J d   V P                  VP                  8H  # V\        9   d   V P                  w  r4V^8w  d   R# W18H  # \        # )r
   Fr   r   r   r   NotImplementedr$   tttyper,   r-   s   &&   r   __eq__
mpq.__eq__H   sO    QC<77agg%%I77DAAv6Mr   c                    \        V4      pV\        J d   V P                  VP                  8g  # V\        9   d   V P                  w  r4V^8w  d   R# W18g  # \        # )r
   TrF   rH   s   &&   r   __ne__
mpq.__ne__S   sO    QC<77agg%%I77DAAv6Mr   c                    \        V4      pV\        9   d   V P                  w  rEV! WAV,          4      # V\        J d2   V P                  w  rEVP                  w  rgV! WG,          WV,          4      # \        # r+   )r   r   r   r   NotImplementedError)r$   rI   oprJ   r,   r-   cds   &&&     r   _cmpmpq._cmp^   s_    QI77DAa1:C<77DA77DAac13<""r   c                B    V P                  V\        P                  4      # r+   )rU   operatorltr$   rI   s   &&r   __lt__
mpq.__lt__i       QVVAx{{33r   c                B    V P                  V\        P                  4      # r+   )rU   rX   lerZ   s   &&r   __le__
mpq.__le__j   r]   r   c                B    V P                  V\        P                  4      # r+   )rU   rX   gtrZ   s   &&r   __gt__
mpq.__gt__k   r]   r   c                B    V P                  V\        P                  4      # r+   )rU   rX   gerZ   s   &&r   __ge__
mpq.__ge__l   r]   r   c                f    V P                   w  rV^ 8  d   V # \        \        4      pV) V3Vn         V# r1   r   r   r   r$   r,   r-   r   s   &   r   __abs__mpq.__abs__n   s4    ww6HH"a%r   c                T    V P                   w  r\        \        4      pV) V3Vn         V# r+   rk   rl   s   &   r   __neg__mpq.__neg__v   s(    wwH"a%r   c                    V # r+    r#   s   &r   __pos__mpq.__pos__|   s    r   c                :   \        V4      pV\        J dB   V P                  w  r4VP                  w  rV\        W6,          WE,          ,           WF,          4      # V\        9   d6   V P                  w  r4\        \        4      pW4V,          ,           V3Vn        V# \        # r+   r   r   r   r   r   r   rG   r$   rI   rJ   r,   r-   rS   rT   r   s   &&      r   __add__mpq.__add__   w    QC<77DA77DA!!#ac'13//I77DACA!eQhAGHr   c                :   \        V4      pV\        J dB   V P                  w  r4VP                  w  rV\        W6,          WE,          ,
          WF,          4      # V\        9   d6   V P                  w  r4\        \        4      pW4V,          ,
          V3Vn        V# \        # r+   rw   rx   s   &&      r   __sub__mpq.__sub__   r{   r   c                :   \        V4      pV\        J dB   V P                  w  r4VP                  w  rV\        WE,          W6,          ,
          WF,          4      # V\        9   d6   V P                  w  r4\        \        4      pWA,          V,
          V3Vn        V# \        # r+   rw   rx   s   &&      r   __rsub__mpq.__rsub__   sw    QC<77DA77DA!!#ac'13//I77DACAc!eQhAGHr   c                    \        V4      pV\        J d5   V P                  w  r4VP                  w  rV\        W5,          WF,          4      # V\        9   d!   V P                  w  r4\        W1,          V4      # \
        # r+   r   r   r   r   r   rG   r$   rI   rJ   r,   r-   rS   rT   s   &&     r   __mul__mpq.__mul__   a    QC<77DA77DA!!#qs++I77DA!!#q))r   c                    \        V4      pV\        J d5   V P                  w  r4VP                  w  rV\        W6,          WE,          4      # V\        9   d!   V P                  w  r4\        W4V,          4      # \
        # r+   r   r   s   &&     r   __div__mpq.__div__   sa    QC<77DA77DA!!#qs++I77DA!!qS))r   c                    \        V4      pV\        J d5   V P                  w  r4VP                  w  rV\        WE,          W6,          4      # V\        9   d!   V P                  w  r4\        WA,          V4      # \
        # r+   r   r   s   &&     r   __rdiv__mpq.__rdiv__   r   r   c                    \        V4      pV\        9   dO   V P                  w  r4V'       d3   V^ 8  d   YCV) rp\        \        4      pW1,          WA,          3Vn        V# \
        h\        # r1   )r   r   r   r   r   ZeroDivisionErrorrG   )r$   rI   rJ   r,   r-   r   s   &&    r   __pow__mpq.__pow__   s\    QI77DAq5QB!AH$*##r   rs   Nr	   )"__name__
__module____qualname____firstlineno____doc__	__slots__r    r%   r(   r.   r3   __bool__rC   rK   rN   rU   r[   r`   rd   rh   rm   rp   rt   ry   __radd__r}   r   r   __rmul__r   r   r   __static_attributes____classdictcell__)__classdict__s   @r   r   r      s      	I$&#  H&			# 4333 H	 H		 r   r   )r
   r
   )r   r
   )r
   r8   r7   )r
      )r
      )r6   r   )   r8   )r6   r   )   r   )r   r   )rX   r;   libmpr   r   r   r   r   objectr    r   r   r   mpq_1mpq_0mpq_1_2mpq_3_2mpq_1_4mpq_1_16mpq_3_16mpq_5_2mpq_3_4mpq_7_4mpq_5_4numbersRationalregisterImportErrorrs   r   r   <module>r      s     
 L Lnn " "~& ~B 	E
E

e*
e*
e*v;v;
e*
e*
e*
e*	c" 		s   B. .B98B9