§
    OŠtj(&  ã                  óB  — U d dl mZ d dlZd dlmZmZ d dlmZ d dlm	Z	 d dl
mZ d dlmZ dd	lmZ dd
lmZmZmZmZmZmZmZmZ m!Z"m#Z$m%Z&m'Z(m)Z*m+Z,m-Z.m/Z0m1Z2m3Z4m5Z6m7Z8m9Z:m;Z<m=Z>m?Z@mAZB g d¢ZCg d¢ZDd„ ZEdZFd„ ZGd„ ZHejI         J                    dd¦  «         K                    ¦   «         ZLdZMdZNeLdv r eGeL¦  «        ZMeM�dZLndZLeLdv r eHeL¦  «        ZNeN�dZLndZLeLdvr ed¦  «         dZLdd ee¦  «        z  dz
  z  dz
  ZOdePd<   eLdk    rçeN€J ‚dZQeNZRdZSdZTeU eVeR W                    d ¦  «        ¦  «        fZXeRjW        ZYeRjZ        Z[eRj        ZeRj        ZeRj        ZeRj\        ZeRj]        ZeRj#        Z#eRj^        ZeRj        ZeRj        ZeRj!        Z!eRj%        Z%eRj'        Z'eRj)        Z)eRj+        Z+d„ Z-eRj/        Z/eRj1        Z1eRj3        Z3eRj5        Z5eRj7        Z7eRj9        Z9eRj;        Z;eRj=        Z=eRj?        Z?eRjA        ZAdS eLdk    r^eM€J ‚eMZQdZRd ZSdZTeUeQj_        fZXeQj_        ZYeQj`        Z[eZeZeZeZd„ Zd „ Z#d!„ Zd"„ Zd#„ Ze"Z!e&Z%e(Z'd$„ Z)e,Z+d%„ Z-e0Z/e2Z1e4Z3e6Z5e8Z7e:Z9e<Z;e>Z=e@Z?eBZAdS eLdk    rCdZQdZRd ZSdZTeUfZXeUZYeZ[eZeZeZeZeZe$Z#eZeZe Ze"Z!e&Z%e(Z'e*Z)e,Z+e.Z-e0Z/e2Z1e4Z3e6Z5e8Z7e:Z9e<Z;e>Z=e@Z?eBZAdS J ‚)&é    )ÚannotationsN)Úc_longÚsizeof)Úreduce)ÚType)Úwarn)Úimport_moduleé   )Ú	PythonMPQ)Ú	bit_scan1Ú	bit_scan0ÚremoveÚ	factorialÚsqrtÚsqrtremÚgcdÚlcmÚgcdextÚ	is_squareÚinvertÚlegendreÚjacobiÚ	kroneckerÚirootÚis_fermat_prpÚis_euler_prpÚis_strong_prpÚis_fibonacci_prpÚis_lucas_prpÚis_selfridge_prpÚis_strong_lucas_prpÚis_strong_selfridge_prpÚis_bpsw_prpÚis_strong_bpsw_prp)ÚGROUND_TYPESÚHAS_GMPYÚ
SYMPY_INTSÚMPQÚMPZr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   )z0.6z0.7z0.8z0.9z0.10c                ób   — |                       d¦  «        d d…         \  }}|› d|› �}|t          v S )Nú.é   )ÚsplitÚ_PYTHON_FLINT_VERSION_NEEDED)Úflint_versionÚmajorÚminorÚ	flint_vers       úQ/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/external/gmpy.pyÚ_flint_version_okayr4   c   sA   € Ø ×&Ò& sÑ+Ô+¨B¨Q¨BÔ/�L€Eˆ5ØÐ"Ð"˜5Ð"Ð"€IØÕ4Ð4Ð4ó    z2.0.0c                óÞ   — | dvrd S 	 dd l }ddl m} n&# t          $ r | dk    rt          d¦  «         Y d S w xY wt	          |¦  «        r|S | dk    rd S t          d|› dt
          › d	�¦  «         |S )
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   sê   € ØÐ!2Ð2Ð2ØˆtðØˆˆˆà7Ð7Ð7Ð7Ð7Ð7Ð7øÝð ð ð Ø Ò(Ð(Ýð Bñ Cô Cð Càˆtˆtð	øøøõ ˜>Ñ*Ô*ð ØˆØ	˜vÒ	%Ð	%Øˆtåð K >ð Kð Kå+GðKð Kð Kñ 	Lô 	Lð 	Lð ˆs   ˆ
 “6µ6c                óp   — | dvrd S t          dt          dd¬¦  «        }| dk    r|€t          d¦  «         |S )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   ‡   sY   € ØÐ!:Ð:Ð:Øˆtå˜Õ5GØ )ÈðMñ Mô M€Dð ˜VÒ#Ð#¨¨ÝÐQÑRÔRÐ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                ón   — |t           k    rt                               | |¦  «        S t          | |¦  «        S ©N)ÚLONG_MAXrA   r   Úpython_iroot)ÚxÚns     r3   r   r   ß   s1   € ð •Š=ˆ=Ý—:’:˜a Ñ#Ô#Ð#Ý˜A˜qÑ!Ô!Ð!r5   c                óZ   — t                                | ¦  «                             ¦   «         S rN   )r9   ÚfmpzÚisqrt©rQ   s    r3   r   r     s   € Ý�zŠz˜!‰}Œ}×"Ò"Ñ$Ô$Ð$r5   c                ó~   — | dk     rdS t                                | ¦  «                             ¦   «         d         dk    S )Nr   Fr
   ©r9   rT   r   rV   s    r3   r   r     s6   € ØˆqŠ5ˆ5Ø�5Ý�zŠz˜!‰}Œ}×$Ò$Ñ&Ô& qÔ)¨QÒ.Ð.r5   c                óZ   — t                                | ¦  «                             ¦   «         S rN   rX   rV   s    r3   r   r     s   € Ý�zŠz˜!‰}Œ}×$Ò$Ñ&Ô&Ð&r5   c                 ór   — t          t          j        j        | t                               d¦  «        ¦  «        S )Nr   )r   r9   rT   r   ©Úargss    r3   r   r     ó"   € Ý•e”j”n d­E¯JªJ°q©M¬MÑ:Ô:Ð:r5   c                 ór   — t          t          j        j        | t                               d¦  «        ¦  «        S )Nr
   )r   r9   rT   r   r[   s    r3   r   r     r]   r5   c                ó�   — |dk    s|dz  st          d¦  «        ‚t                               | ¦  «                             |¦  «        S )Nr   r,   z#y should be an odd positive integer)Ú
ValueErrorr9   rT   r   )rQ   Úys     r3   r   r     s@   € Ø�Š6ˆ6˜˜Q™ˆ6ÝÐBÑCÔCÐCÝ�zŠz˜!‰}Œ}×#Ò# AÑ&Ô&Ð&r5   c                ó¨   — |t           k    r8t                               | ¦  «                             |¦  «        }|||z  | k    fS t	          | |¦  «        S rN   )rO   r9   rT   ÚrootrP   )rQ   rR   ra   s      r3   r   r     sJ   € Ø•Š=ˆ=Ý—
’
˜1‘”×"Ò" 1Ñ%Ô%ˆAØ�a˜‘d˜a’i�<ÐÝ˜A˜qÑ!Ô!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”      sé  ðØ "Ð "Ð "Ð "Ð "Ð "Ð "Ø 	€	€	€	Ø !Ð !Ð !Ð !Ð !Ð !Ð !Ð !Ø Ð Ð Ð Ð Ð Ø Ð Ð Ð Ð Ð Ø Ð Ð Ð Ð Ð à (Ð (Ð (Ð (Ð (Ð (à  Ð  Ð  Ð  Ð  Ð  ðð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð ð:0ð 0ð 0€ðn  DÐCÐCÐ ð5ð 5ð 5ð Ð ðð ð ð2
ð 
ð 
ð  ”j—n’nÐ%9¸6ÑBÔB×HÒHÑJÔJÐ Ø	€Ø€ð Ð+Ð+Ð+ØˆZÐ+Ñ,Ô,€FØÐØ%ÐÐà$ÐàÐ3Ð3Ð3ØˆJÐ*Ñ+Ô+€EØÐØ$ÐÐà&ÐàÐ9Ð9Ð9Ø€Dð 
Cñ Dô Dð Dà"Ðð �!�F�F˜6‘N”NÑ" QÑ&Ñ'¨1Ñ,€ð Ð Ð Ñ à˜&Ò Ð àÐÐÐà€EØ€Dà€HØ€LØ�t�t˜DŸHšH Q™KœKÑ(Ô(Ð)€JØ
Œ(€CØ
Œ(€Cà”€IØ”€IØŒ[€FØ”€IØŒ:€DØ”€IØŒn€GØ
Œ(€CØ
Œ(€CØŒ[€FØŒ[€FØŒ}€HØŒ[€FØ”€Ið"ð "ð "ð Ô&€MØÔ$€LØÔ&€MØÔ,ÐØÔ$€LØÔ,ÐØÔ2ÐØ"Ô:ÐØÔ"€KØÔ0ÐÐÐà˜GÒ#Ð#àÐÐÐà€EØ€Dà€HØ€LØ�u”zÐ"€JØ
Œ*€CØ
Œ*€Cà €IØ €IØ€FØ €Ið%ð %ð %ð/ð /ð /ð
'ð 'ð 'ð;ð ;ð ;ð;ð ;ð ;ð €FØ€FØ€Hð'ð 'ð 'ð
 !€Ið"ð "ð "ð )€MØ&€LØ(€MØ.ÐØ&€LØ.ÐØ4ÐØ<ÐØ$€KØ2ÐÐÐà˜HÒ$Ð$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2ÐÐÐð ˆ5r5   