+
    ‹°³j(&  ã                  óˆ  a € 0 t $ ^ RIHt ^ RIt^ RIHtHt ^ RIHt ^ RI	H
t
 ^ RIHt ^ RIHt ^RIHt ^R	IHtHtHtHtHtHtHtH t!H"t#H$t%H&t'H(t)H*t+H,t-H.t/H0t1H2t3H4t5H6t7H8t9H:t;H<t=H>t?H@tAHBtC . ROtD. ROtER tFRtGR tHR tI]P”                  P—                  RR4      P™                  4       tMRtNRtO]MR 9   d   ]H! ]M4      tN]Ne   RtMMRtM]MR!9   d   ]I! ]M4      tO]Oe   RtMMRtM]MR"9  d   ]! R4       RtM^^]! ]4      ,          ^,
          ,          ^,
          tPR]QR
&   ]MR8X  Ede   ]Of   Q hRtR]OtS^tTRtU]V]W! ]SP±                  ^ 4      4      3tY]SP°                  tZ]SP¶                  t\]SP$                  t]SP(                  t]SP,                  t]SPº                  t]SP¼                  t]SPH                  t$]SP¾                  t]SP<                  t]SP@                  t ]SPD                  t"]SPL                  t&]SPP                  t(]SPT                  t*]SPX                  t,R t.]SP`                  t0]SPd                  t2]SPh                  t4]SPl                  t6]SPp                  t8]SPt                  t:]SPx                  t<]SP|                  t>]SP€                  t@]SP„                  tBR# ]MR8X  dp   ]Nf   Q h]NtRRtS^ tTRtU]V]RPÀ                  3tY]RPÀ                  tZ]RPÂ                  t\]t]t]t]tR tR t$R tR tR t ]#t"]'t&])t(R t*]-t,R t.]1t0]3t2]5t4]7t6]9t8];t:]=t<]?t>]At@]CtBR# ]MR8X  dD   RtRRtS^ tTRtU]V3tY]VtZ]t\]t]t]t]t]t]%t$]t]t]!t ]#t"]'t&])t(]+t*]-t,]/t.]1t0]3t2]5t4]7t6]9t8];t:]=t<]?t>]At@]CtBR# Q h)#é    )ÚannotationsN)Úc_longÚsizeof)Úreduce)ÚType)Úwarn)Úimport_module)Ú	PythonMPQ)Ú	bit_scan1Ú	bit_scan0ÚremoveÚ	factorialÚsqrtÚsqrtremÚgcdÚlcmÚgcdextÚ	is_squareÚinvertÚlegendreÚjacobiÚ	kroneckerÚirootÚis_fermat_prpÚis_euler_prpÚis_strong_prpÚis_fibonacci_prpÚis_lucas_prpÚis_selfridge_prpÚis_strong_lucas_prpÚis_strong_selfridge_prpÚis_bpsw_prpÚis_strong_bpsw_prpÚ
SYMPY_INTSc                óV   € V P                  R 4      R,          w  rV R V 2pV\        9   # )Ú.:Né   N)ÚsplitÚ_PYTHON_FLINT_VERSION_NEEDED)Úflint_versionÚmajorÚminorÚ	flint_vers   &   ÚT/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/external/gmpy.pyÚ_flint_version_okayr/   c   s5   € Ø ×&Ñ& sÓ+¨BÕ/�L€EØ�'˜˜5˜'Ð"€IØÔ4Ñ4Ð4ó    z2.0.0c                óÚ   € V R9  d   R#  ^ RI p^ RI Hp \	        T4      '       d   T# T R 8X  d   R# \        RT R\
         R24       T#   \         d    T R8X  d   \        R4        R# i ; i)	ÚautoÚflintN)Ú__version__zjSYMPY_GROUND_TYPES was set to flint but python-flint is not installed. Falling back to other ground types.zUsing python-flint zp because SYMPY_GROUND_TYPES is set to flint but this version of SymPy is only tested with python-flint versions r&   ©r2   r3   )r3   r4   ÚImportErrorr   r/   r)   )Úsympy_ground_typesr3   Ú_flint_versions   &  r.   Ú
_get_flintr9   n   sŒ   € ØÐ!2Ô2ÙðÛå7ô ˜>×*Ò*ØˆØ	˜vÔ	%ÙäÐ" >Ð"2ð 3+ä+GÐ*HÈðKô 	Lð ˆøô ô Ø Ô(Üð Bô Câð	ús   ‹
A	 Á	A*Á)A*c                ój   € V R9  d   R# \        R\        RRR7      pV R 8w  d   Vf   \        R4       V# )r2   Úgmpy2NÚversion)Úmin_module_versionÚmodule_version_attrÚmodule_version_attr_call_argszBgmpy2 library is not installed, switching to 'python' ground types©r2   Úgmpyr;   © )r	   Ú_GMPY2_MIN_VERSIONr   )r7   rA   s   & r.   Ú
_get_gmpy2rD   ‡   s?   € ØÐ!:Ô:Ùä˜Ô5GØ )ÈôM€Dð ˜VÔ#¨ªÜÐQÔRà€Kr0   ÚSYMPY_GROUND_TYPESr2   r3   rA   ÚpythonzmSYMPY_GROUND_TYPES environment variable unrecognised. Should be 'auto', 'flint', 'gmpy', 'gmpy2' or 'python'.ztuple[Type, ...]c                óX   € V\         8:  d   \        P                  W4      # \        W4      # ©N)ÚLONG_MAXrA   r   Úpython_iroot)ÚxÚns   &&r.   r   r   ß   s%   € ð ”Œ=Ü—:‘:˜aÓ#Ð#Ü˜AÓ!Ð!r0   c                óH   € \         P                  V 4      P                  4       # rH   )r3   ÚfmpzÚisqrt©rK   s   &r.   r   r     s   € Ü�z‰z˜!‹}×"Ñ"Ó$Ð$r0   c                ón   € V ^ 8  d   R# \         P                  V 4      P                  4       ^,          ^ 8H  # )r   F©r3   rN   r   rP   s   &r.   r   r     s-   € ØˆqŒ5ÙÜ�z‰z˜!‹}×$Ñ$Ó& qÕ)¨QÑ.Ð.r0   c                óH   € \         P                  V 4      P                  4       # rH   rR   rP   s   &r.   r   r     s   € Ü�z‰z˜!‹}×$Ñ$Ó&Ð&r0   c                 ór   € \        \        P                  P                  V \        P                  ^ 4      4      # )r   )r   r3   rN   r   ©Úargss   *r.   r   r     ó!   € Ü”e—j‘j—n‘n d¬E¯J©J°q«MÓ:Ð:r0   c                 ór   € \        \        P                  P                  V \        P                  ^4      4      # )é   )r   r3   rN   r   rU   s   *r.   r   r     rW   r0   c                óŒ   € V^ 8:  g   V^,          '       g   \        R4      h\        P                  V 4      P                  V4      # )r   z#y should be an odd positive integer)Ú
ValueErrorr3   rN   r   )rK   Úys   &&r.   r   r     s6   € Ø�Œ6˜˜QŸœÜÐBÓCÐCÜ�z‰z˜!‹}×#Ñ# AÓ&Ð&r0   c                ó�   € V\         8:  d2   \        P                  V 4      P                  V4      pW"V,          V 8H  3# \	        W4      # rH   )rI   r3   rN   ÚrootrJ   )rK   rL   r\   s   && r.   r   r     s<   € Ø”Œ=Ü—
‘
˜1“×"Ñ" 1Ó%ˆAØ˜•d˜a‘i�<ÐÜ˜AÓ!Ð!r0   )ÚGROUND_TYPESÚHAS_GMPYr$   ÚMPQÚMPZr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   )z0.6z0.7z0.8z0.9z0.10r5   r@   )r3   rA   rF   )bÚ__conditional_annotations__Ú
__future__r   ÚosÚctypesr   r   Ú	functoolsr   Útypingr   Úwarningsr   Úsympy.externalr	   Ú	pythonmpqr
   Úntheoryr   Úpython_bit_scan1r   Úpython_bit_scan0r   Úpython_remover   Úpython_factorialr   Úpython_sqrtr   Úpython_sqrtremr   Ú
python_gcdr   Ú
python_lcmr   Úpython_gcdextr   Úpython_is_squarer   Úpython_invertr   Úpython_legendrer   Úpython_jacobir   Úpython_kroneckerr   rJ   r   Úpython_is_fermat_prpr   Úpython_is_euler_prpr   Úpython_is_strong_prpr   Úpython_is_fibonacci_prpr   Úpython_is_lucas_prpr   Úpython_is_selfridge_prpr    Úpython_is_strong_lucas_prpr!   Úpython_is_strong_selfridge_prpr"   Úpython_is_bpsw_prpr#   Úpython_is_strong_bpsw_prpÚ__all__r)   r/   rC   r9   rD   ÚenvironÚgetÚlowerÚ_SYMPY_GROUND_TYPESÚ_flintÚ_gmpyrI   Ú__annotations__r3   rA   r`   r_   ÚintÚtypeÚmpzr$   rb   Úmpqra   ÚfacrO   Ú	isqrt_remrN   Úfmpq)rc   s   @r.   Ú<module>r”      sù  øðß "Ð "Û 	ß !Ý Ý Ý å (å  ÷÷ ÷ ÷ ÷ ÷ õ ò:0€òn  DÐ ò5ð Ð òò2
ð  —j‘j—n‘nÐ%9¸6ÓB×HÑHÓJÐ Ø	€Ø€ð Ð+Ô+ÙÐ+Ó,€FØÒØ%Ñà$ÐàÐ3Ô3ÙÐ*Ó+€EØÒØ$Ñà&ÐàÐ9Ô9Ùð 
Cô Dà"Ðð �!‘F˜6“NÕ" QÕ&Õ'¨1Õ,€ð Ó à˜&Õ àÒÐÐà€EØ€Dà€HØ€LØ‘t˜DŸH™H Q›KÓ(Ð)€JØ
�(‰(€CØ
�(‰(€Cà—‘€IØ—‘€IØ�[‰[€FØ—‘€IØ�:‰:€DØ—‘€IØ�n‰n€GØ
�(‰(€CØ
�(‰(€CØ�[‰[€FØ�[‰[€FØ�}‰}€HØ�[‰[€FØ—‘€Iò"ð ×&Ñ&€MØ×$Ñ$€LØ×&Ñ&€MØ×,Ñ,ÐØ×$Ñ$€LØ×,Ñ,ÐØ×2Ñ2ÐØ"×:Ñ:ÐØ×"Ñ"€KØ×0Ñ0Òà˜GÔ#àÒÐÐà€EØ€Dà€HØ€LØ�u—z‘zÐ"€JØ
�*‰*€CØ
�*‰*€Cà €IØ €IØ€FØ €Iò%ò/ò
'ò;ò;ð €FØ€FØ€Hò'ð
 !€Iò"ð )€MØ&€LØ(€MØ.ÐØ&€LØ.ÐØ4ÐØ<ÐØ$€KØ2Òà˜HÔ$à€EØ€Dà€HØ€LØ�€JØ
€CØ
€Cà €IØ €IØ€FØ €IØ€DØ €IØ€GØ
€CØ
€CØ€FØ€FØ€HØ€FØ €IØ€EØ(€MØ&€LØ(€MØ.ÐØ&€LØ.ÐØ4ÐØ<ÐØ$€KØ2Òð ˆ5r0   