ó
    ‰*£h(&  ã                  óH  • % S SK Jr  S SKrS SKJrJr  S SKJr  S SKJ	r	  S SK
Jr  S SKJr  SS	KJr  SS
KJrJrJrJrJrJrJrJr J!r"J#r$J%r&J'r(J)r*J+r,J-r.J/r0J1r2J3r4J5r6J7r8J9r:J;r<J=r>J?r@JArB  / SQrC/ SQrDS rESrFS rGS rH\R’                  R•                  SS5      R—                  5       rLSrMSrN\LS;   a  \G" \L5      rM\Mb  SrLOSrL\LS;   a  \H" \L5      rN\Nb  SrLOSrL\LS;  a
  \" S5        SrLSS\" \5      -  S-
  -  S-
  rOS\PS'   \LS:X  Gab  \Nc   eSrQ\NrRSrSSrT\U\V" \RR¯                  S 5      5      4rX\RR®                  rY\RR´                  r[\RR"                  r\RR&                  r\RR*                  r\RR¸                  r\RRº                  r\RRF                  r#\RR¼                  r\RR:                  r\RR>                  r\RRB                  r!\RRJ                  r%\RRN                  r'\RRR                  r)\RRV                  r+S r-\RR^                  r/\RRb                  r1\RRf                  r3\RRj                  r5\RRn                  r7\RRr                  r9\RRv                  r;\RRz                  r=\RR~                  r?\RR‚                  rAg\LS:X  am  \Mc   e\MrQSrRS rSSrT\U\QR¾                  4rX\QR¾                  rY\QRÀ                  r[\r\r\r\rS rS  r#S! rS" rS# r\"r!\&r%\(r'S$ r)\,r+S% r-\0r/\2r1\4r3\6r5\8r7\:r9\<r;\>r=\@r?\BrAg\LS:X  aB  SrQSrRS rSSrT\U4rX\UrY\r[\r\r\r\r\r\$r#\r\r\ r\"r!\&r%\(r'\*r)\,r+\.r-\0r/\2r1\4r3\6r5\8r7\:r9\<r;\>r=\@r?\BrAg e)&é    )ÚannotationsN)Úc_longÚsizeof)Úreduce)ÚType)Úwarn)Úimport_moduleé   )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_prp)ÚGROUND_TYPESÚHAS_GMPYÚ
SYMPY_INTSÚ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$   )z0.6z0.7z0.8z0.9z0.10c                óN   • U R                  S5      S S u  pU SU 3nU[        ;   $ )NÚ.é   )ÚsplitÚ_PYTHON_FLINT_VERSION_NEEDED)Úflint_versionÚmajorÚminorÚ	flint_vers       ÚP/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/external/gmpy.pyÚ_flint_version_okayr4   c   s7   € Ø ×&Ñ& sÓ+¨B¨QÐ/�L€EØ�'˜˜5˜'Ð"€IØÔ4Ñ4Ð4ó    z2.0.0c                óÊ   • U S;  a  g  SS K nSSK Jn  [	        U5      (       a  U$ U S:X  a  g [        SU S[
         S	35        U$ ! [         a    U S:X  a  [        S5         g f = f)
N©ÚautoÚflintr   )Ú__version__r9   zjSYMPY_GROUND_TYPES was set to flint but python-flint is not installed. Falling back to other ground types.r8   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+   )r9   r:   ÚImportErrorr   r4   r.   )Úsympy_ground_typesr9   Ú_flint_versions      r3   Ú
_get_flintr>   n   sŒ   € ØÐ!2Ó2ØðÛå7ô ˜>×*Ñ*ØˆØ	˜vÓ	%ØäÐ" >Ð"2ð 3+ä+GÐ*HÈðKô 	Lð ˆøô ó Ø Ó(Üð Bô Cáð	ús   ‰
A ÁA"Á!A"c                ó\   • U S;  a  g [        S[        SSS9nU S:w  a  Uc  [        S5        U$ )N©r8   ÚgmpyÚgmpy2rB   Úversion© )Úmin_module_versionÚmodule_version_attrÚmodule_version_attr_call_argsr8   zBgmpy2 library is not installed, switching to 'python' ground types)r	   Ú_GMPY2_MIN_VERSIONr   )r<   rA   s     r3   Ú
_get_gmpy2rI   ‡   s?   € ØÐ!:Ó:Øä˜Ô5GØ )ÈñM€Dð ˜VÓ#¨©ÜÐQÔRà€Kr5   ÚSYMPY_GROUND_TYPESr8   r7   r9   r@   rA   Úpython)r9   rA   rK   zmSYMPY_GROUND_TYPES environment variable unrecognised. Should be 'auto', 'flint', 'gmpy', 'gmpy2' or 'python'.é   ztuple[Type, ...]r'   r,   c                óV   • U[         ::  a  [        R                  X5      $ [        X5      $ ©N)ÚLONG_MAXrA   r   Úpython_iroot)ÚxÚns     r3   r   r   ß   s%   € ð ”‹=Ü—:‘:˜aÓ#Ð#Ü˜AÓ!Ð!r5   c                óH   • [         R                  U 5      R                  5       $ rN   )r9   ÚfmpzÚisqrt©rQ   s    r3   r   r     s   € Ü�z‰z˜!‹}×"Ñ"Ó$Ð$r5   c                ób   • U S:  a  g[         R                  U 5      R                  5       S   S:H  $ )Nr   Fr
   ©r9   rT   r   rV   s    r3   r   r     s-   € Øˆq‹5ØÜ�z‰z˜!‹}×$Ñ$Ó& qÑ)¨QÑ.Ð.r5   c                óH   • [         R                  U 5      R                  5       $ rN   rX   rV   s    r3   r   r     s   € Ü�z‰z˜!‹}×$Ñ$Ó&Ð&r5   c                 ór   • [        [        R                  R                  U [        R                  S5      5      $ )Nr   )r   r9   rT   r   ©Úargss    r3   r   r     ó!   € Ü”e—j‘j—n‘n d¬E¯J©J°q«MÓ:Ð:r5   c                 ór   • [        [        R                  R                  U [        R                  S5      5      $ )Nr
   )r   r9   rT   r   r[   s    r3   r   r     r]   r5   c                ó€   • US::  d
  US-  (       d  [        S5      e[        R                  U 5      R                  U5      $ )Nr   r,   z#y should be an odd positive integer)Ú
ValueErrorr9   rT   r   )rQ   Úys     r3   r   r     s4   € Ø�‹6˜˜QŸÜÐBÓCÐCÜ�z‰z˜!‹}×#Ñ# AÓ&Ð&r5   c                ó†   • U[         ::  a-  [        R                  U 5      R                  U5      nX"U-  U :H  4$ [	        X5      $ rN   )rO   r9   rT   ÚrootrP   )rQ   rR   ra   s      r3   r   r     s<   € Ø”‹=Ü—
‘
˜1“×"Ñ" 1Ó%ˆAØ˜‘d˜a‘i�<ÐÜ˜AÓ!Ð!r5   )aÚ
__future__r   ÚosÚctypesr   r   Ú	functoolsr   Útypingr   Úwarningsr   Úsympy.externalr	   Ú	pythonmpqr   Úntheoryr   Úpython_bit_scan1r   Úpython_bit_scan0r   Úpython_remover   Úpython_factorialr   Úpython_sqrtr   Úpython_sqrtremr   Ú
python_gcdr   Ú
python_lcmr   Úpython_gcdextr   Úpython_is_squarer   Úpython_invertr   Úpython_legendrer   Úpython_jacobir   Úpython_kroneckerr   rP   r   Úpython_is_fermat_prpr   Úpython_is_euler_prpr   Úpython_is_strong_prpr   Úpython_is_fibonacci_prpr   Úpython_is_lucas_prpr    Úpython_is_selfridge_prpr!   Úpython_is_strong_lucas_prpr"   Úpython_is_strong_selfridge_prpr#   Úpython_is_bpsw_prpr$   Úpython_is_strong_bpsw_prpÚ__all__r.   r4   rH   r>   rI   ÚenvironÚgetÚlowerÚ_SYMPY_GROUND_TYPESÚ_flintÚ_gmpyrO   Ú__annotations__r9   rA   r&   r%   ÚintÚtypeÚmpzr'   r)   Úmpqr(   ÚfacrU   Ú	isqrt_remrT   ÚfmpqrD   r5   r3   Ú<module>r”      sõ  ðÞ "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+Ó+ÙÐ+Ó,€FØÑØ%Ñà$ÐàÐ3Ó3ÙÐ*Ó+€EØÑØ$Ñà&ÐàÐ9Ó9Ùð 
Cô Dà"Ðð �!‘F˜6“NÑ" QÑ&Ñ'¨1Ñ,€ð Ó à˜&Ô àÑÐÐà€EØ€Dà€HØ€LØ‘t˜DŸH™H Q›KÓ(Ð)€JØ
�(‰(€CØ
�(‰(€Cà—‘€IØ—‘€IØ�[‰[€FØ—‘€IØ�:‰:€DØ—‘€IØ�n‰n€GØ
�(‰(€CØ
�(‰(€CØ�[‰[€FØ�[‰[€FØ�}‰}€HØ�[‰[€FØ—‘€Iò"ð ×&Ñ&€MØ×$Ñ$€LØ×&Ñ&€MØ×,Ñ,ÐØ×$Ñ$€LØ×,Ñ,ÐØ×2Ñ2ÐØ"×:Ñ:ÐØ×"Ñ"€KØ×0Ñ0Ñà˜GÓ#àÑÐÐà€EØ€Dà€HØ€LØ�u—z‘zÐ"€JØ
�*‰*€CØ
�*‰*€Cà €IØ €IØ€FØ €Iò%ò/ò
'ò;ò;ð €FØ€FØ€Hò'ð
 !€Iò"ð )€MØ&€LØ(€MØ.ÐØ&€LØ.ÐØ4ÐØ<ÐØ$€KØ2Ñà˜HÓ$à€EØ€Dà€HØ€LØ�€JØ
€CØ
€Cà €IØ €IØ€FØ €IØ€DØ €IØ€GØ
€CØ
€CØ€FØ€FØ€HØ€FØ €IØ€EØ(€MØ&€LØ(€MØ.ÐØ&€LØ.ÐØ4ÐØ<ÐØ$€KØ2Ñð ˆ5r5   