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    7^(hS#  ã                   ó‚   — d dl mZ d dlmZmZmZ d dlmZmZm	Z	m
Z
mZmZmZmZ d dlmZ d„ Zd„ Zd„ Zd„ Zd	„ Zd
„ Zd„ Zy)é    )Úring)ÚZZÚQQÚAlgebraicField)Úmodgcd_univariateÚmodgcd_bivariateÚ._chinese_remainder_reconstruction_multivariateÚmodgcd_multivariateÚ_to_ZZ_polyÚ_to_ANP_polyÚfunc_field_modgcdÚ_func_field_modgcd_m)Úsqrtc                  óš  — t        dt        «      \  } }| j                  | j                  }}t        ||«      dk(  sJ ‚| j                  |}}t        ||«      |ddfk(  sJ ‚t        ||«      |ddfk(  sJ ‚| j                  | }}t        ||«      |ddfk(  sJ ‚t        ||«      |ddfk(  sJ ‚d|z   | d«      }}t        ||«      d|dfk(  sJ ‚d|z  dz   d|dz  z  dz
  }}t        ||«      d|z  dz   dd|z  dz
  fk(  sJ ‚|d	z  d
|dz  z  z   d|dz  z  z   d|z  z   d
z   }|dz  d|dz  z  z   d|z  z   dz   }|dz  d|z  z   dz   }|dz  d|z  z   d	z   }|dz   }t        ||«      |||fk(  sJ ‚|d	z  d	z
  }|d	z  d	|dz  z  z   d	z   }|dz  dz   }|dz  dz
  }|dz  dz   }t        ||«      |||fk(  sJ ‚|d
z  |dz  z   d|d	z  z  z
  d|dz  z  z
  d
|dz  z  z   d|z  z   dz
  }d|dz  z  d|d	z  z  z   d	|dz  z  z
  d|z  z
  dz   }d}|}|}t        ||«      |||fk(  sJ ‚d|dz  z  d|dz  z  z   d|dz  z  z   d|dz  z  z   d|dz  z  z
  d|dz  z  z   d|dz  z  z   dz   }d|dz  z  d|dz  z  z   d |dz  z  z
  dz
  }t        ||j	                  |«      «      d   |k(  sJ ‚d!|z  d"z   }d#|z  d$z   }d#|z  d$z   }d%}d}t        ||«      |||fk(  sJ ‚y )&NÚx©r   r   r   r   é   éÿÿÿÿé   é   é   é   é   é   é   é   é   é	   lìÿÿÿ     p¢ƒ>�Zè6-(È·3Ã{ CÃzˆìVgÚsóR&é1   l       À	Í`”ç ò%³'(Õ'»@ó$@¥9$` ÑV é*   l      `µ%³Nw‚g¹ej^íôr�0c’u`Z§hD é#   l      ]%³5…œu[o¦vÈ&Á+Ú/
có>_o],é   l    @ü)-ÀPµ/Í'X=‚vØw+U9+; l    _ÖIÈ	†,ü4~XsRò`Y?t
U¼ é   l   y[Ùpñ?÷uÿ;ÃZàW`±( é   l   ñEÙA‘y·\¼^
l     Àmc@Ats lÍ\o#MkïEœ6w# l    @¼r/sÜL—xFJŽG jëA�l   €3ƒsèd%uÒ%ƒg%9 Œi[T l         qRvl        @Ñû	l        P\l        `àiÂ*  )r   r   Úzeror   Údiff)ÚRr   ÚfÚgÚhÚcffÚcfgs          ú_/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/polys/tests/test_modulargcd.pyÚtest_modgcd_univariate_integersr.      s3  € Ü�”R‹=�D€A€qà�6‰6�1—6‘6€q€AÜ˜Q Ó" iÒ/Ð/Ð/à�6‰6�1€q€AÜ˜Q Ó" q¨!¨Q iÒ/Ð/Ð/Ü˜Q Ó" q¨!¨Q iÒ/Ð/Ð/à�6‰6�A�2€q€AÜ˜Q Ó" q¨!¨R jÒ0Ð0Ð0Ü˜Q Ó" q¨"¨a jÒ0Ð0Ð0àˆQ‰3‘�!“€q€AÜ˜Q Ó" q¨!¨Q iÒ/Ð/Ð/àˆQ‰3�‰7�A�a˜‘d‘F˜Q‘J€q€AÜ˜Q Ó" q¨¡s¨Q¡w°°1°Q±3¸±7Ð&;Ò;Ð;Ð;à	ˆ1‰ˆq��A‘‰v‰˜˜1˜a™4™Ñ " Q¡$Ñ&¨Ñ*€AØ	ˆ1‰ˆq��A‘‰v‰˜˜1™Ñ˜qÑ €Aà	ˆ1‰ˆq�‰s‰
�Q‰€Aà
ˆQ‰$��1‘‰*�q‰.€CØ
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 ˜Q §¡ q£	Ó*¨1Ñ-°Ò2Ð2Ð2à˜qÑ Ð#9Ñ9€AØ˜1ÑÐ1Ñ1€Aà˜1ÑÐ1Ñ1€AØ
€CØ
€Cä˜Q Ó" q¨#¨s mÒ3Ð3Ñ3ó    c                  óš  — t        dt        «      \  } }}| j                  | j                  }}t        ||«      dk(  sJ ‚d|z   | d«      }}t        ||«      d|dfk(  sJ ‚|d|z  z   ||z   }}t        ||«      d||fk(  sJ ‚|dz  d|z  |z  z   |dz  z   |dz  |dz  z   }}t        ||«      ||z   ||z   |dz  ||z  z
  |dz  z   fk(  sJ ‚||dz  z  d|z  |z  z   |z   ||dz  z  |z   }}t        ||«      ||z  |z   |dz   |dz  |z
  dz   fk(  sJ ‚|dz  |dz  z  |dz  |z  z   dz   ||dz  z  ||z  z   dz   }}t        ||«      d||fk(  sJ ‚d|z  |dz  z  d|z  |z  z   d|z  z   |dz  z   d|z  z   dz   }d|z  |dz  z  d|z  z   |dz  z   dz   }t        ||«      d|z  |z  d|z  z   |z   dz   |dz   |dz  |z
  dz   fk(  sJ ‚d|dz  z  d|z  z   dz   |dz   }}t        ||«      |dz   d|z  dz   dfk(  sJ ‚|dz   d|dz  z  d|z  z   dz   }}t        ||«      |dz   dd|z  dz   fk(  sJ ‚d|dz  z  d|z  |z  z   d|z  z
  d|z  z
  }|dz  |z   dz
  }t        ||«      |dz
  d|z  d|z  z   |dz   fk(  sJ ‚d|dz  z  d|z  |z  z   d|z  z
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  }d|z  |z  d|z  z
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  }t        ||«      ||z   d|z  dz
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  fk(  sJ ‚y )Núx,yr   r   r   r   r   )r   r   r%   r   )r'   r   Úyr(   r)   s        r-   Útest_modgcd_bivariate_integersr3   [   så  € Ü�5œ"‹o�G€A€qˆ!à�6‰6�1—6‘6€q€AÜ˜A˜qÓ! YÒ.Ð.Ð.àˆQ‰3‘�!“€q€AÜ˜A˜qÓ! a¨¨A YÒ.Ð.Ð.àˆq�‰s‰7�A˜‘E€q€AÜ˜A˜qÓ! a¨¨A YÒ.Ð.Ð.àˆa‰4�!�A‘#�a‘%‰<˜!˜Q™$Ñ  1¡ q¨!¡t¡€q€AÜ˜A˜qÓ! a¨!¡e¨Q°©U°A°q±D¸1¸Q¹3±JÀÀAÁÑ4EÐ%FÒFÐFÐFàˆQ�‰T‰6�A�a‘C˜‘E‰>˜AÑ˜q  A¡™v¨™z€q€AÜ˜A˜qÓ! a¨¡c¨A¡g¨q°1©u°a¸±d¸Q±hÀ±lÐ%CÒCÐCÐCàˆa‰4��1‘‰9�q˜!‘t˜A‘vÑ Ñ! 1 Q¨¡T¡6¨A¨a©C¡<°!Ñ#3€q€AÜ˜A˜qÓ! a¨¨A YÒ.Ð.Ð.à	ˆ!‰ˆAˆq‰D‰�1�Q‘3�q‘5Ñ˜1˜Q™3Ñ  A¡Ñ%¨¨!©Ñ+¨aÑ/€AØ	ˆ!‰ˆAˆq‰D‰�1�Q‘3‰˜˜A™Ñ Ñ!€AÜ˜A˜qÓ! a¨¡c¨!¡e¨a°©c¡k°A¡o¸Ñ&9¸1¸q¹5À!ÀQÁ$ÈÁ(ÈQÁ,Ð%OÒOÐOÐOàˆQ�‰T‰6�A�a‘C‰<˜!Ñ˜Q ™U€q€AÜ˜A˜qÓ! a¨!¡e¨Q¨q©S°1©W°aÐ%8Ò8Ð8Ð8àˆq‰5�!�A�q‘D‘&˜1˜Q™3‘, Ñ"€q€AÜ˜A˜qÓ! a¨!¡e¨Q°°!±°a±Ð%8Ò8Ð8Ð8à	ˆ!ˆQ‰$‰��1‘�Q‘‰˜˜1™Ñ˜q ™sÑ"€AØ	ˆ1‰ˆq‰�1‰€AÜ˜A˜qÓ! a¨!¡e¨Q¨q©S°1°Q±3©Y¸¸A¹Ð%>Ò>Ð>Ð>à	ˆ!ˆQ‰$‰��1‘�Q‘‰˜˜1™Ñ˜q ™sÑ"€AØ	ˆ!‰ˆA‰��!‘‰�a˜˜1™‘fÑ˜q ™sÑ"€AÜ˜A˜qÓ! a¨!¡e¨Q¨q©S°1©W°a¸±c¸A±gÐ%>Ò>Ð>Ñ>r/   c                  óÜ  — t        dt        «      \  } }}d\  }}|dz  |z  |dz  z
  dz
  }|dz   |z  d|z  |dz  z  z
  dz   }t        ||||«      }|j                  |«      |k(  sJ ‚|j                  |«      |k(  sJ ‚t        d| «      \  }}	d\  }}||z  dz   |	dz  z  |z   }|dz  d|z  z
  |	z  dz   }t        ||||«      }|j                  |«      |k(  sJ ‚|j                  |«      |k(  sJ ‚y )Núx, y)r   r   r   r   r   Úz)r   r$   )r   r   r	   Útrunc_ground)
r'   r   r2   ÚpÚqÚhpÚhqÚhpqÚTr6   s
             r-   Útest_chinese_remainderr>   ƒ   s,  € Ü�6œ2Ó�G€A€qˆ!Ø�D€A€qà	
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F€Cà×Ñ˜AÓ "Ò$Ð$Ð$Ø×Ñ˜AÓ "Ò$Ð$Ñ$r/   c            
      óL
  — t        dt        «      \  } }}| j                  | j                  }}t        ||«      dk(  sJ ‚d|dz  z  d|z  z   dz   |dz   }}t        ||«      |dz   d|z  dz   dfk(  sJ ‚|dz   d|dz  z  d|z  z   dz   }}t        ||«      |dz   dd|z  dz   fk(  sJ ‚d|dz  z  d|z  |z  z   d|z  z
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  d|z  dz
  fk(  sJ ‚||dz  z  d|z  |z  z   |z   ||dz  z  |z   }}t        ||«      ||z  |z   |dz   |dz  |z
  dz   fk(  sJ ‚|dz  |dz  z  |dz  |z  z   dz   ||dz  z  ||z  z   dz   }}t        ||«      d||fk(  sJ ‚|dz  d|dz  z  z   d|dz  z  z   d	|z  z   dz   }|dz  d
|dz  z  z   d|z  z   d
z   }|dz  d|z  z   dz   }|dz  d|z  z   dz   }|dz   }t        ||«      |||fk(  sJ ‚t        dt        «      \  } }}}}	||z   |z   | |z
  |z
  |	z
  }}t        ||«      d||fk(  sJ ‚|	dz  d|	z  z   dz   d|	z  dz   }}t        ||«      |	dz   |	dz   dfk(  sJ ‚|dz  |	dz  z  d|dz  z  |	z  z   |dz  z   ||	z  z   |z   |	dz  d|	z  z   dz   }}|	dz   |dz  |	z  |dz  z   |z   |	dz   }}}t        ||«      |||fk(  sJ ‚t        ||«      |||fk(  sJ ‚t        dt        «      \  } }}}|||z  z
  |||z  z
  }}t        ||«      |||z  z
  ddfk(  sJ ‚| j	                  «       \  }}}t        ||«      \  }
}}|
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|z  |k(  r|
|z  |k(  sJ ‚t        dt        «      \  } }}}}	}| j	                  «       \  }}}t        ||«      \  }
}}|
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|z  |k(  r|
|z  |k(  sJ ‚t        dt        «      \  } }}}}	}}}| j	                  «       \  }}}t        ||«      \  }
}}|
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|z  |k(  r|
|z  |k(  sJ ‚t        dt        «      \
  } }}}}	}}}}}| j	                  «       \  }}}t        ||«      \  }
}}|
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|z  |k(  r|
|z  |k(  sJ ‚t        dt        «      \  } }}}| j                  «       \  }}}t        ||«      \  }
}}|
|k(  r|
|z  |k(  r|
|z  |k(  sJ ‚| j                  «       \  }}}t        ||«      \  }
}}|
|k(  r|
|z  |k(  r|
|z  |k(  sJ ‚t        dt        «      \  } }}}}| j                  «       \  }}}t        ||«      \  }
}}|
|k(  r|
|z  |k(  r|
|z  |k(  sJ ‚y )Nr1   r   r   r   r   r   r   r   r   r   r   r   zx,y,z,uzx,y,zz	x,y,z,u,vzx,y,z,u,v,a,bzx,y,z,u,v,a,b,c,dzx,y,z,t)r   r   r%   r
   Úfateman_poly_F_1Úfateman_poly_F_2Úfateman_poly_F_3)r'   r   r2   r(   r)   r*   r+   r,   r6   ÚuÚHÚvÚaÚbÚcÚdÚts                    r-   Ú!test_modgcd_multivariate_integersrK   ›   s´  € Ü�5œ"‹o�G€A€qˆ!à�6‰6�1—6‘6€q€AÜ˜q !Ó$¨	Ò1Ð1Ð1àˆQ�‰T‰6�A�a‘C‰<˜!Ñ˜Q ™U€q€AÜ˜q !Ó$¨¨Q©°°!±°a±¸Ð(;Ò;Ð;Ð;àˆq‰5�!�A�q‘D‘&˜1˜Q™3‘, Ñ"€q€AÜ˜q !Ó$¨¨Q©°°1°Q±3¸±7Ð(;Ò;Ð;Ð;à	ˆ!ˆQ‰$‰��1‘�Q‘‰˜˜1™Ñ˜q ™sÑ"€AØ	ˆ!‰ˆA‰��!‘‰�a˜˜1™‘fÑ˜q ™sÑ"€AÜ˜q !Ó$¨¨Q©°°!±°a±¸¸1¹¸q¹Ð(AÒAÐAÐAàˆQ�‰T‰6�A�a‘C˜‘E‰>˜AÑ˜q  A¡™v¨™z€q€AÜ˜q !Ó$¨¨1©¨q©°!°a±%¸¸A¹À¹ÀA¹Ð(FÒFÐFÐFàˆa‰4��1‘‰9�q˜!‘t˜A‘vÑ Ñ! 1 Q¨¡T¡6¨A¨a©C¡<°!Ñ#3€q€AÜ˜q !Ó$¨¨A¨q¨	Ò1Ð1Ð1à	ˆ1‰ˆq��A‘‰v‰˜˜1˜a™4™Ñ " Q¡$Ñ&¨Ñ*€AØ	ˆ1‰ˆq��A‘‰v‰˜˜1™Ñ˜qÑ €Aà	ˆ1‰ˆq�‰s‰
�Q‰€Aà
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ˆa‰%€Cä˜q !Ó$¨¨C°¨Ò5Ð5Ð5ä˜¤BÓ'�M€A€qˆ!ˆQ�àˆq‰5�1‰9�q�b˜1‘f˜q‘j 1‘n€q€AÜ˜q !Ó$¨¨A¨q¨	Ò1Ð1Ð1àˆa‰4�!�A‘#‰:˜‰>˜1˜Q™3 ™7€q€AÜ˜q !Ó$¨¨Q©°°A±°qÐ(9Ò9Ð9Ð9àˆa‰4��1‘‰9�q˜˜A™‘v˜a‘xÑ ! Q¡$Ñ&¨¨1©Ñ,¨qÑ0°!°Q±$¸¸1¹±*¸q±.€q€AØ�a‘%˜˜A™˜a™ ! Q¡$™¨Ñ*¨A°©EˆC€s€Aä˜q !Ó$¨¨C°¨Ò5Ð5Ð5Ü˜q !Ó$¨¨C°¨Ò5Ð5Ð5ä�gœrÓ"�J€A€qˆ!ˆQàˆq�‰s‰7�A˜˜!™‘G€q€AÜ˜q !Ó$¨¨Q¨q©S©°!°Q¨Ò7Ð7Ð7à× Ñ Ó"�G€A€qˆ!Ü% a¨Ó+�K€A€sˆCà�Š6�a˜‘e˜q’j Q s¡U¨a¢ZÐ/Ð/ä˜K¬Ó,Ñ€A€qˆ!ˆQ��1à× Ñ Ó"�G€A€qˆ!Ü% a¨Ó+�K€A€sˆCà�Š6�a˜‘e˜q’j Q s¡U¨a¢ZÐ/Ð/ä! /´2Ó6Ñ€A€qˆ!ˆQ��1�a˜à× Ñ Ó"�G€A€qˆ!Ü% a¨Ó+�K€A€sˆCà�Š6�a˜‘e˜q’j Q s¡U¨a¢ZÐ/Ð/ä#'Ð(;¼RÓ#@Ñ €A€qˆ!ˆQ��1�a˜˜A˜qà× Ñ Ó"�G€A€qˆ!Ü% a¨Ó+�K€A€sˆCà�Š6�a˜‘e˜q’j Q s¡U¨a¢ZÐ/Ð/ä�gœrÓ"�J€A€qˆ!ˆQà× Ñ Ó"�G€A€qˆ!Ü% a¨Ó+�K€A€sˆCà�Š6�a˜‘e˜q’j Q s¡U¨a¢ZÐ/Ð/à× Ñ Ó"�G€A€qˆ!Ü% a¨Ó+�K€A€sˆCà�Š6�a˜‘e˜q’j Q s¡U¨a¢ZÐ/Ð/ä˜¤BÓ'�M€A€qˆ!ˆQ�à× Ñ Ó"�G€A€qˆ!Ü% a¨Ó+�K€A€sˆCà�Š6�a˜‘e˜q’j Q s¡U¨a¢ZÐ/Ð/ Zr/   c                  óð  — t        t        t        d«      «      } t        d| «      \  }}|t        d«      dz   z  }t        dt        «      \  }}}||z  |z   }t        ||«      |k(  sJ ‚t        ||«      |k(  sJ ‚t        d| «      \  }}}}	||dz  z  ||	z  z   t        d«      z   }t        dt        «      \  }
}}t        d|
«      \  }}}|dz  |z   |z  |z   }t        ||«      |k(  sJ ‚t        ||«      |k(  sJ ‚y )Nr   r   r   zx_, z_zx, t, szt_, s_)r   r   r   r   r   r   r   )ÚAr'   r   r(   r=   Úx_Úz_Úf_rJ   ÚsÚDÚt_Ús_s                r-   Útest_to_ZZ_ANP_polyrU   ü   s  € Ü”rœ4 ›7Ó#€AÜ��Q‹<�D€A€qØ	Œ4�‹7�Q‰;‰€Aä�XœrÓ"�I€A€rˆ2Ø	ˆB‰�‰€Bä�q˜!Ó Ò"Ð"Ð"Ü˜˜AÓ !Ò#Ð#Ð#ä�i Ó#�J€A€qˆ!ˆQØ	ˆ!ˆQ‰$‰��1‘‰”t˜A“wÑ€Aä�XœrÓ"�I€A€rˆ2Ü�X˜qÓ!�I€A€rˆ2Ø
ˆa‰%�"‰*�b‰˜2Ñ	€Bä�q˜!Ó Ò"Ð"Ð"Ü˜˜AÓ !Ò#Ð#Ñ#r/   c            	      óæ  — t        t        t        d«      «      } t        d| «      \  }}| j                  }d|z   |d«      }}t        ||«      |||fk(  sJ ‚d|z   |t        d«      «      }}t        ||«      |||fk(  sJ ‚d|z  dz   d|dz  z  dz
  }}t        ||«      |dz    |d«      d|z  dz
  fk(  sJ ‚t        d| «      \  }}}|t        d«      |z  z   ||z   }}t        ||«      |||fk(  sJ ‚||z  t        d«      |dz  z  z    |t        d«      «      |z  }}t        ||«      ||t        d«      |z  z    |t        d«      «      fk(  sJ ‚|dz  dt        d«      z  |z  |z  z   d|dz  z  z   |t        d«      |z  z   }}t        ||«      |||fk(  sJ ‚t        t        t        d«      t        d«      «      } t        d| «      \  }}}}|dz  |dz  z  t        d«      d	z  |z  z   }|d
|dz  z  dz   z  |||z   z  }}t        ||«      |d
|dz  z  dz   ||z   fk(  sJ ‚|dz  |dz  z  d|dz  z  z   dt        d«      z  z   }||dz   z  |t        d«      z  t        d«      z  }}t        ||«      ||dz    |t        d«      t        d«      z  «      fk(  sJ ‚t        t        t        d«      dz  t        d«      z  «      } t        d| «      \  }}|dz   |dz
  }}t        ||«      | j                  ||fk(  sJ ‚y )Nr   r   r   r   r5   r   zx, y, zr$   r   é   é   g      à?é
   r   )r   r   r   r   Úoner   )	rM   r'   r   rZ   r(   r)   r2   r6   r*   s	            r-   Útest_modgcd_algebraic_fieldr[     s7  € Ü”rœ4 ›7Ó#€AÜ��Q‹<�D€A€qØ
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