Ë
    7^(hE’  ã                   ó  — d dl mZ d dlmZ d dlmZ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 d dlmZ d dlmZ d dlmZmZ d dlmZmZmZ d d	l m!Z! d
„ Z"d„ Z#e!d„ «       Z$d„ Z%d„ Z&d„ Z'd„ Z(d„ Z)d„ Z*d„ Z+d„ Z,d„ Z-d„ Z.d„ Z/d„ Z0y)é    )ÚAbs)Úsqrt)ÚSÚRational)Ú	decomposeÚbest_originÚdistance_to_sideÚpolytope_integrateÚ
point_sortÚhyperplane_parametersÚmain_integrate3dÚmain_integrateÚpolygon_integrateÚlineseg_integrateÚintegration_reductionÚintegration_reduction_dynamicÚ	is_vertex)Ú	Segment2D)ÚPolygon)ÚPointÚPoint2D)ÚxÚyÚz)Úslowc                  ó¼  — t        t        «      dt        ik(  sJ ‚t        t        dz  «      dt        dz  ik(  sJ ‚t        t        t        z  «      dt        t        z  ik(  sJ ‚t        t        t        z   «      dt        t        z   ik(  sJ ‚t        t        dz  t        z   «      t        t        dz  dœk(  sJ ‚t        dt        dz  z  dt        z  z   dz   «      ddt        z  dt        dz  z  dœk(  sJ ‚t        t        dz  dt        z  t        z  z   «      dt        dz  dt        z  t        z  z   ik(  sJ ‚t        d	t        dz  z  t        z   dt        z  z   t        dz  z   t        dz  t        z  z   dz   «      ddt        z  t        z   d	t        dz  z  t        dz  t        t        dz  z  z   d
œk(  sJ ‚t        t        d«      t        hk(  sJ ‚t        t        dz  d«      t        dz  hk(  sJ ‚t        t        t        z  d«      t        t        z  hk(  sJ ‚t        t        t        z   d«      t        t        hk(  sJ ‚t        t        dz  t        z   d«      t        t        dz  hk(  sJ ‚t        dt        dz  z  dt        z  z   dz   d«      ddt        z  dt        dz  z  hk(  sJ ‚t        t        dz  dt        z  t        z  z   d«      t        dz  dt        z  t        z  hk(  sJ ‚t        d	t        dz  z  t        z   dt        z  z   t        dz  z   t        dz  t        z  z   dz   d«      dt        dt        z  d	t        dz  z  t        t        dz  z  t        dz  hk(  sJ ‚y )Né   é   ©r   r   é   é   é   ©r   r   r   é   é	   )r   r   r   r$   T)r   r   r   © ó    ú`/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_intpoly.pyÚtest_decomposer)      sû  € Ü”Q‹<˜Aœq˜6Ò!Ð!Ð!Ü”Q˜‘T‹?˜q¤! Q¡$˜iÒ'Ð'Ð'Ü”Q”q‘S‹>˜a¤¤1¡˜XÒ%Ð%Ð%Ü”Qœ‘UÓ ¤1¤q¡5˜zÒ)Ð)Ð)Ü”Q˜‘TœA‘XÓ¤a¬A¨q©D¡/Ò1Ð1Ð1Ü�Q”q˜!‘t‘V˜a¤™c‘\ AÑ%Ó&¨a°A´a±C¸A¼aÀ¹d¹FÑ*CÒCÐCÐCÜ”Q˜‘T˜Aœa™C¤™E‘\Ó" q¬!¨Q©$°´1±´Q±©,Ð&7Ò7Ð7Ð7Ü�Q”q˜!‘t‘Vœa‘Z !¤A¡#Ñ%¬¨1©Ñ,¬q°!©t´A©vÑ5¸Ñ9Ó:Ø�!”A‘#œ‘'˜a¤ 1¡™f¬¨A©´´!°Q±$±©Ñ7ò8ð 8ð 8ô ”Q˜Ó¤! Ò$Ð$Ð$Ü”Q˜!‘V˜TÓ"¤q¨!¡t fÒ,Ð,Ð,Ü”Qœ‘U˜DÓ!¤a¬!¡e WÒ,Ð,Ð,Ü”Qœ‘U˜DÓ!¤a¬ VÒ+Ð+Ð+Ü”Q˜!‘Vœa‘Z Ó&¬1¬a°1©f¨+Ò5Ð5Ð5Ü�Qœ˜a™‘Z !¤a¡%Ñ'¨!Ñ+¨TÓ2°q¸!¼A¹#¸qÄÀAÁ¹vÐ6FÒFÐFÐFÜ”Q˜!‘V˜a¤!™e¤a™iÑ'¨Ó.´1¸±6¸1¼q¹5Ä1¹9Ð2EÒEÐEÐEÜ�Qœ˜a™‘Z¤!‘^ a¬!¡eÑ+¬a°1©fÑ4´q¸A±vÄ±zÑAÀAÑEÀtÓLØŒq�!”A‘#�qœ˜A™‘vœq¤ A¡™v¤q¨!¡tÐ,ò-ð -ñ -r'   c            	      ó*  — t         dz  t        dz  z  t         dz  t        dz  z  z   dt        z  z   t        dz  z   t         dz  t        z  z   } t        t        dd«      t        dd«      «      }t        t        t	        d«      dz  d«      t        t	        d«      dz  d«      «      }t        t        dt	        d«      dz  «      t        dt	        d«      dz  «      «      }t        t        dd«      t        dd«      «      }t        t        dd«      t        dd«      «      }t        t        dd«      t        dd«      «      }t        dd|| «      d	k(  sJ ‚t        d
d|t        dz  «      dk(  sJ ‚t        dd|t        dz  «      dk(  sJ ‚t        dd|t        dz  t         dz  z  «      dk(  sJ ‚t        dd|t        dz  t         dz  z  «      d
k(  sJ ‚t        dd|t        dz  t         dz  z  «      dk(  sJ ‚t        dd|t        dz  t         dz  z  «      d
k(  sJ ‚y )Nr   é   r"   é   r   r$   r   )r   r   ©r   r$   )r   r   )ç      ø?r   )r   r   )r   r.   ©r   r   r%   )r   r   r   r   r   r   )Úexpr1Úl1Úl2Úl3Úl4Úl5Úl6s          r(   Útest_best_originr7   +   sà  € Ü�‰F”Q˜!‘V‰Oœa 1™f¤q¨A¡v™oÑ-°´A±Ñ5¼¸R¹Ñ?Ä!ÀqÁ&Ì1Á*ÑL€Eä	”5˜˜A“;¤ a¨£Ó	,€BÜ	”5œ˜1› ™ 1Ó%¤u¬Q¨q«T°A©X°qÓ'9Ó	:€BÜ	”5˜œA˜a›D 1™HÓ%¤u¨Q´°!³°q±Ó'9Ó	:€BÜ	”5˜˜A“;¤ a¨£Ó	,€BÜ	”5˜˜A“;¤ a¨£Ó	,€BÜ	”5˜˜A“;¤ a¨£Ó	,€Bä�v˜q " eÓ,°Ò6Ð6Ð6ô �v˜q "¤a¨1¡fÓ-°Ò9Ð9Ð9Ü�v˜q "¤a¨1¡fÓ-°Ò9Ð9Ð9Ü�v˜q "¤a¨1¡f¬q°A©v¡oÓ6¸&Ò@Ð@Ð@Ü�v˜q "¤a¨1¡f¬q°A©v¡oÓ6¸&Ò@Ð@Ð@Ü�v˜q "¤a¨1¡f¬q°A©v¡oÓ6¸&Ò@Ð@Ð@Ü�v˜q "¤a¨1¡f¬q°A©v¡oÓ6¸&Ò@Ð@Ñ@r'   c                  óx'  — t        t        t        dd«      t        dd«      t        dd«      «      d«      dk(  sJ ‚t        t        t        dd«      t        dd«      t        dd«      t        dd«      «      t        t        z  «      t        dd«      k(  sJ ‚t        t        t        dd«      t        dd«      t        dd«      «      dt        dz  z  dt        z  z
  «      t        d	d«      k(  sJ ‚t        t        t        dd«      t        dt        d«      «      t        t        d«      t        d«      «      t        t        d«      d«      «      d«      dk(  sJ ‚t        t        dd«      t        t        d«       dz  t        j                  «      t        t        d«       dz  t        d«      dz  «      t        dd«      t        t        d«      dz  t        d«      dz  «      t        t        d«      dz  t        j                  «      «      } t        | d«      t        dt        d«      z  «      dz  k(  sJ ‚t        g d
¢d«      dk(  sJ ‚t        g d¢t        t        z  «      t        dd«      k(  sJ ‚t        g d¢dt        dz  z  dt        z  z
  «      t        d	d«      k(  sJ ‚t        ddt        d«      fdft        d«      dfdfdgd«      dk(  sJ ‚t        dd«      t        d«       dz  fdfdt        d«      dz  ft        dd«      t        d«      dz  ft        d«      ft        j                  t        d«      dz  ft        d«      fdt        d«      dz  ft        j                  t        d«       dz  fdfg} t        | d«      t        dt        d«      z  «      dz  k(  sJ ‚t        t        t        dd«      t        dd«      t        dd«      t        dd«      t        dd«      «      d«      dk(  sJ ‚t        t        t        dd«      t        dd«      t        dd«      t        dd«      t        dd«      t        dd«      «      d«      dk(  sJ ‚t        g d¢d«      dk(  sJ ‚t        g d¢d«      dk(  sJ ‚t        t        dd«      t        dd«      t        dd«      t        dd«      t        dd«      t        dd«      t        dd «      «      }t        |t        dz  t        t        z  z   t        dz  z   «      t        d!«      d"z  k(  sJ ‚t        t        d#d$«      t        d%d&«      t        d'd(«      t        d)d*«      t        d+d,«      «      }t        |t        dz  t        t        z  z   t        dz  z   «      t        d-«      d.z  k(  sJ ‚t        t        d/d0«      t        d1d2«      t        d3d4«      t        d5d6«      «      }t        |t        dz  t        t        z  z   t        dz  z   «      t        d7«      d"z  k(  sJ ‚t        t        d8d9«      t        d:d;«      t        d<d=«      t        d>d?«      t        d@dA«      «      }t        |t        dz  t        t        z  z   t        dz  z   «      t        dB«      dCz  k(  sJ ‚t        t        dd«      t        dd«      t        dd«      «      }g }t        dDz  t        z  t        dEz  t        dz  z  z   dt        dz  z  t        dFz  z  z   }t        dz  t        dz  z  t        dz  t        dz  z  z   dt        dGz  z  z   }t        dGz  t        dDz  t        z  z   t        dFz  t        dz  z  z   t        dz  t        dz  z  z   }	|j                  |||	f«       t        ||dG¬H«      }
|
|   t        dIdJ«      k(  sJ ‚|
|   t        dKdL«      k(  sJ ‚|
|	   t        dMdN«      k(  sJ ‚t        t        dd«      t        dd«      t        dd«      «      }t        dEz  t        dz  z  dt        dz  z  t        dz  z  z   }t        dz  t        dz  z  t        dz  t        dz  z  z   dt        dGz  z  z   }t        dGz  t        dDz  t        z  z   t        dFz  t        dz  z  z   t        dz  t        dz  z  z   }	|j                  |||	f«       t        ||dD¬H«      t        dEz  t        z  dt        dz  z  t        dz  z  z   t        dOdD«      ik(  sJ ‚t        t        t        dd«      t        dd«      t        dd«      t        dd«      «      d¬H«      i dd“dd“t        t        j                  “t        dz  t        dz  z  t        j                  dDz  “t        dz  t        j                  dz  “t        dz  t        j                  dz  “t        t        j                  “t        t        dz  z  t        j                  dz  “t        dz  t        j                  dz  “t        dz  t        j                  dz  “t        dz  t        z  t        j                  dz  “t        dz  t        z  t        j                  dFz  “t        t        z  t        j                  dz  “t        dz  t        j                  dz  “t        dz  t        j                  dz  “t        t        dz  z  t        j                  dFz  “k(  sJ ‚g dP¢g dQ¢g dR¢g dS¢g dT¢g dU¢g dV¢g}t        |d«      t        dW«      k(  sJ ‚g dX¢g dY¢g dZ¢g d[¢g d\¢g d]¢g d^¢g}g d_¢g d`¢g da¢g db¢g dc¢g dd¢g de¢g df¢g dg¢g	}dhdidjdkt        j                  dz  t        j                  dz  t        j                  dz  fgg dl¢g dm¢g dn¢g do¢g dp¢g dq¢g dr¢g}t        |t        dz  t        dz  z   t        t        z  z   t        dz  z   «      t        dsd«      k(  sJ ‚t        |t        dz  t        dz  z   t        t        z  z   t        dz  z   «      t        dt«      duz  k(  sJ ‚t        |t        dz  t        dz  z   t        t        z  z   t        dz  z   «      t        dv«      dwz  k(  sJ ‚t        j                  t        d«      z  ddfdt        j                  t        d«      z  dfddt        j                  t        d«      z  fddt        j                  t        d«      z  fdt        j                  t        d«      z  dft        j                  t        d«      z  ddfgg dx¢g dy¢g dz¢g d{¢g d|¢g d}¢g d~¢g d¢g	}t        |d«      t        d«      dz  k(  sJ ‚g d€¢g d�¢g d‚¢g dƒ¢g d„¢g d…¢g d†¢g d‡¢g dˆ¢g d‰¢g dŠ¢g d‹¢g dŒ¢g}t        t        |d«      d�z
  «      dŽk  sJ ‚t        dz  t        dz  z   t        dz  z   }g g d�¢‘g d�¢‘g d‘¢‘g d’¢‘g d“¢‘g d”¢‘g d•¢‘g d–¢‘g d—¢‘g d˜¢‘g d™¢‘g dš¢‘g d›¢‘g dœ¢‘g d�¢‘g dž¢‘g dŸ¢‘g d ¢‘g d¡¢‘g d¢¢‘g d£¢‘g d¤¢‘g d¥¢‘g d¦¢‘g d§¢‘g d¨¢‘g d©¢‘g dª¢‘g d«¢‘g d¬¢‘g d­¢‘g d®¢‘g d¯¢‘g d°¢‘g d±¢‘g d²¢‘g d³¢‘g d´¢‘g dµ¢‘g d¶¢‘g d·¢‘}t        t        ||«      «      d¸z
  d¹k  sJ ‚g g dº¢‘g d»¢‘g d¼¢‘g d½¢‘g d¾¢‘g d¿¢‘g dÀ¢‘g dÁ¢‘g dÂ¢‘g dÃ¢‘g dÄ¢‘g dÅ¢‘g dÆ¢‘g dÇ¢‘g dÈ¢‘g dÉ¢‘g dÊ¢‘g dË¢‘g dÌ¢‘g dÍ¢‘g dÎ¢‘g dÏ¢‘g dÐ¢‘g dÑ¢‘g dÒ¢‘g dÓ¢‘g dÔ¢‘g dÕ¢‘g dÖ¢‘g d×¢‘g dØ¢‘}t        t        ||«      dÙz
  «      dŽk  sJ ‚g g dÚ¢‘g dÛ¢‘g dÜ¢‘g dÝ¢‘g dÞ¢‘g dß¢‘g dà¢‘g dá¢‘g dâ¢‘g dã¢‘g dä¢‘g då¢‘g dæ¢‘g dç¢‘g dè¢‘g dé¢‘g dê¢‘g dë¢‘g dì¢‘g dí¢‘g dî¢‘g dï¢‘g dð¢‘g dñ¢‘g dò¢‘g dó¢‘g dô¢‘g dõ¢‘g dö¢‘g d÷¢‘g dø¢‘g dù¢‘g dú¢‘g dû¢‘g dü¢‘g dý¢‘g dþ¢‘g dÿ¢‘g �d ¢‘g �d¢‘g �d¢‘g �d¢‘g �d¢‘g �d¢‘g �d¢‘g �d¢‘g �d¢‘g �d	¢‘g �d
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   ©Ú
max_degreei´$iR  iPÇ é   i‡tiœ  i.w )©r   r   r   )r   r9   r9   )r9   r9   r9   )r$   r9   r   )r   r9   r   )r9   r   r9   )r$   r   r   )r   r   r9   )r   r   r$   r!   )r$   r   r+   r9   )r   r"   r+   r   )r   r9   r+   r"   )r   r!   r   r"   )r   r!   r$   r9   é¢   ©rN   ©r   r   r+   ©r   r+   r   ©r   r+   r+   ©r+   r   r   ©r+   r   r+   ©r+   r+   r   ©r+   r+   r+   )r$   r"   r9   r   )r   r+   r"   r$   )r+   r!   r9   r"   )r   r!   r+   r   )r   r   r   r$   )r   r9   r!   r   )rN   rT   )r+   r!   r   )r$   r   r   )r$   r+   r   rR   rQ   rU   )r+   r!   r+   )r$   r   r+   )r$   r+   r+   rS   )r9   é   r+   r   )r   r"   r9   r   )r+   r!   r$   r   r   r   )rX   rJ   r!   r+   )rJ   r%   r$   r!   )r%   r    r   r$   )r    r"   r   r   )r"   r    r%   rJ   rX   r9   rN   ©r   r   r   ©r   r   r   ©r   r   r   )r   r   r   )r   r$   r   )r!   r   r$   )r!   r$   r   r#   )r   r!   r   )r   r$   r   i	=  i+„  r,   é%   iÀ  )r$   r!   r+   )r$   r+   r   )r$   r   r   )r$   r   r!   )r!   r   r   )r!   r   r+   )r   r   r   )r+   r   r   ))g¯aIû{ËÔ¿r   çäFˆ8Û?)g¯aIû{ËÔ?r   çäFˆ8Û¿)çS¡ÊÒà¿r   ç×ˆò?0´¹?)çS¡ÊÒà?r   ç×ˆò?0´¹¿)rb   çPé/7ïÆÓ¿r]   )rb   çPé/7ïÆÓ?r]   )r`   rc   r^   )r`   rd   r^   )ç¯aIû{ËÄ¿ç      à¿r`   )re   ç      à?r`   )ç¯aIû{ËÄ?rf   rb   )rh   rg   rb   )r^   rc   rb   )r^   rd   rb   )çS¡ÊÒÐ¿ça- ‘!rÈ?r^   )ri   ça- ‘!rÈ¿r^   )çS¡ÊÒÐ?rj   r]   )rl   rk   r]   )r]   rc   r`   )r]   rd   r`   )r,   r$   r   r9   é   )é   r"   r   r$   é   )r%   r9   r   r"   r    )é   r   r   r!   é   )é   r+   r   r   é   )rX   r!   r   r+   rJ   )r    rs   r   rp   r%   )rJ   ro   r$   r,   rX   )rm   rq   r!   rX   r,   )ro   rJ   r+   rr   rn   )rq   rm   r9   r%   rp   )rs   r    r"   rn   rr   gZÂžáÄ?gê-�™—q=))r   gÍ;fž æ¿r   )r   gÍ;fž æ?r   )çØ¨ô/‹h½?çÍ;fž Ö¿çH¥Hî~?ã¿)rt   çÍ;fž Ö?rv   )ç%ö–D¸ÊÇ?çœü·SNâ¿ç%ö–D¸Ê×?)rx   çœü·SNâ?rz   )çH¥Hî~?Ó?çÙz5øË¿çH¥Hî~?ã?)r|   çÙz5øË?r~   )ç[ ”Û$ß?ru   ç%ö–D¸Ê×¿)r€   rw   r�   )rv   r   r�   )çH¥Hî~?Ó¿r}   rv   )r‚   r   rv   )r~   r   rz   )ç~ÏEº¡™Ú?ry   r   )rƒ   r{   r   )rz   r   rv   )ç~ÏEº¡™Ú¿ry   r   )r„   r{   r   )ç·Ío™…å¿r}   r   )r…   r   r   )ç·Ío™…å?r}   r   )r†   r   r   )r�   r   r~   )ç[ ”Û$ß¿ru   rz   )r‡   rw   rz   )ç%ö–D¸ÊÇ¿ry   r�   )rˆ   r{   r�   )çØ¨ô/‹h½¿ru   r~   )r‰   rw   r~   )r   rJ   rm   )é   rJ   r   )rm   ro   r   )r   ro   rŠ   )rm   rJ   r   )r   rJ   rŠ   )r   ro   rm   )rŠ   ro   r   )r   r!   rs   )é   r!   r   )r   rs   rM   )rM   r‹   r   )é   r+   r$   )r$   r+   é   )é   rŒ   r$   )r$   r�   rŽ   )é   rs   r!   )r!   r‹   r�   )r+   rŒ   é   )r�   r�   r+   )r9   r    rr   )rn   r    r9   )r9   rr   é   )r‘   rn   r9   )rq   r%   r"   )r"   r%   rp   )é   rq   r"   )r"   rp   r’   )r    r,   rr   )rn   r,   r    )rq   rX   r%   )r%   rX   rp   )rX   rq   r’   )r’   rp   rX   )r‘   rr   r,   )r,   rn   r‘   )r�   rM   rs   )rŒ   rŽ   r�   )r�   rŽ   r�   )r‹   rM   r�   g¤ÅÃœ Ö?g�íµ ÷Æ°>))re   rf   çy«s©æ¿)re   rg   r“   )rh   rf   çy«s©æ?)rh   rg   r”   )r_   r   r“   )ra   r   r”   )ri   ç¨ô—›wãé¿re   )ri   ç¨ô—›wãé?re   )rl   r•   rh   )rl   r–   rh   )r^   rc   r”   )r^   rd   r”   )r]   rc   r“   )r]   rd   r“   )r“   rf   rh   )r“   rg   rh   )r”   rf   re   )r”   rg   re   )çåFˆ8ë¿r   re   )çäFˆ8ë?r   rh   )rp   rJ   r$   r"   )ro   rs   r    r   )rp   r   r    rJ   )r$   rs   ro   r"   )rp   r"   ro   r   )r    rs   r$   rJ   )r9   r   rX   rp   )r   r%   rs   r,   )rX   r%   r   rp   )r9   r,   rs   r   )r   r,   r9   rp   )rX   r   rs   r%   )r!   rq   rX   r"   )rn   r+   r    r,   )r!   r,   r    rq   )rX   r+   rn   r"   )r!   r"   rn   r,   )r    r+   rX   rq   )r9   rJ   rr   r!   )ro   r%   r+   rm   )rr   r%   ro   r!   )r9   rm   r+   rJ   )ro   rm   r9   r!   )rr   rJ   r+   r%   )rq   rr   r   r   )rm   rn   r$   r   )rq   r   r$   rr   )r   rn   rm   r   )rq   r   rm   r   )r$   rn   r   rr   g      ô?)\)r   r   ç�¿ÊOëÀ)r   r   ç�¿ÊOë@)r   çTúËÍ»ñÀr™   )r   r›   rš   )r   çTúËÍ»ñ@r™   )r   rœ   rš   )çwöVnÀçTúËÍ»ñô¿r™   )r�   rž   rš   )r�   çTúËÍ»ñô?r™   )r�   rŸ   rš   )çwöVn@rž   r™   )r    rž   rš   )r    rŸ   r™   )r    rŸ   rš   )r™   ç~÷±´™jÀr™   )r™   r¡   rš   )r™   ç~÷±´™j@r™   )r™   r¢   rš   )rš   r¡   r™   )rš   r¡   rš   )rš   r¢   r™   )rš   r¢   rš   )çækå)#ÞÀr•   çµV‰öÐñ¿)r£   r–   r¤   )çækå)#Þ@r•   ç¶V‰öÐñ?)r¥   r–   r¦   )ç¨1©š*ÀçTúËÍ»ñ Àr¦   )r§   çTúËÍ»ñ @r¦   )ç¨1©š*@r¨   r¤   )rª   r©   r¤   )gr,EËÓÀr   ç‘Íq¹
À)gr,EËÓ@r   ç‘Íq¹
@)r«   r¡   r¦   )r«   r¢   r¦   )r¬   r¡   r¤   )r¬   r¢   r¤   )ç”A(Ì`RÀr¨   r¬   )r­   r©   r¬   )ç”A(Ì`R@r¨   r«   )r®   r©   r«   )çµV‰öÐÀr   r¤   )r¯   r›   r¤   )r¯   rœ   r¤   )ç¶V‰öÐ@r   r¦   )r°   r›   r¦   )r°   rœ   r¦   )çr,EËÓü¿rž   r¦   )r±   rŸ   r¦   )çr,EËÓü?rž   r¤   )r²   rŸ   r¤   )çy«s©ö¿r   r£   )r³   r   rl   )çy«s©ö?r   r¥   )r´   r   ri   )r¤   r¡   r«   )r¤   r•   r¥   )r¤   r•   ri   )r¤   r–   r¥   )r¤   r–   ri   )r¤   r¢   r«   )r¦   r¡   r¬   )r¦   r•   r£   )r¦   r•   rl   )r¦   r–   r£   )r¦   r–   rl   )r¦   r¢   r¬   )r—   r   r¦   )r˜   r   r¤   )r“   rf   r¤   )r“   rg   r¤   )r“   çTúËÍ»ñÀr¤   )r“   r¨   r¤   )r“   r©   r¤   )r“   çTúËÍ»ñ@r¤   )r”   rf   r¦   )r”   rg   r¦   )r”   rµ   r¦   )r”   r¨   r¦   )r”   r©   r¦   )r”   r¶   r¦   )r^   rž   r£   )r^   rž   rl   )r^   rŸ   r£   )r^   rŸ   rl   )ri   r•   r¦   )ri   r–   r¦   )rl   r•   r¤   )rl   r–   r¤   )r]   rž   r¥   )r]   rž   ri   )r]   rŸ   r¥   )r]   rŸ   ri   )r%   éB   é/   )é,   é>   éM   )rŒ   é[   é1   )é!   r¸   éS   )r$   r»   éT   )r,   r½   é5   )é$   rÀ   r·   )r�   rÁ   rº   )éI   r¿   r¼   )rr   rÀ   é.   )r‘   é@   é+   )rm   é:   éH   )rŽ   rÄ   é3   )rX   rÆ   éJ   )r!   rÈ   r¼   )é<   rÊ   rÀ   )é#   r¼   rÅ   )rŠ   rÉ   rÇ   )rs   rÊ   r»   )éO   r¿   éN   )r9   é8   r:   )éL   r»   éQ   )r�   rÎ   éK   )r    r:   rÇ   )é   rÒ   rÊ   )é*   rÇ   r¿   )é)   rÑ   rÏ   )ro   rÒ   rÆ   )rM   rÉ   r¸   )r   éY   éG   )r’   rÆ   rº   )rn   r¸   éU   )rq   r×   rÏ   )éA   rØ   rÒ   )r‹   rÏ   rÉ   )é"   rº   rÖ   )r+   rØ   rÎ   )é    rÑ   rÄ   )rJ   rÁ   é0   )é-   rÎ   rÅ   )r"   rÄ   r·   )rp   rÜ   rÖ   )r\   r·   rØ   )éF   rÖ   rÑ   )r�   rÅ   rÁ   )éX   rÊ   r   )é&   éC   rÜ   )rÔ   r¿   rÈ   )é9   r   rØ   )rÚ   rÜ   rº   )é;   rÈ   éW   )rs   rº   rÊ   )é?   rä   rá   )rn   rØ   r¿   )é4   rÒ   r   )é'   rä   r½   )r‹   rÉ   r:   )é7   r   r·   )r�   r½   rÅ   )é   r:   éE   )ro   rÅ   rÒ   )éR   rê   rä   )r"   r·   rÉ   )éZ   rØ   r   )rã   rê   rÈ   )rÞ   rÑ   r×   )rß   r   rÀ   )rÃ   rÈ   r¿   )é6   r×   éD   )r+   r¿   rØ   )é2   rî   rê   )r$   rÀ   rÑ   )râ   r·   r   )ré   rî   r:   )r�   rº   rÜ   )ræ   r   rÊ   )rŠ   r:   rÉ   )rà   rÜ   éV   )r%   rÉ   r·   )éP   rð   rî   )rX   rÊ   rº   )rè   rÀ   r   )rí   rð   r×   )rÌ   rÅ   r½   )rì   r   rÒ   )rÕ   r×   rÑ   )rç   r½   rá   )rr   rÑ   rÀ   )é=   rá   rð   )r�   rÒ   rÅ   )r’   rÁ   rÆ   )rï   rê   r   )r\   rØ   r¸   )rÓ   rÆ   rÒ   )rò   r   rá   )rM   r¸   rÇ   )rJ   rá   rÁ   )r    rÇ   rê   )rì   rÒ   rØ   )rÝ   r¼   rÎ   )rñ   rî   r   )rÂ   r·   rÄ   )rÙ   rÎ   rØ   )rå   r   rä   )rÛ   rÄ   rÏ   )rŒ   rä   r¼   )rq   rÏ   rî   )râ   rØ   r·   )r¾   rÇ   r¸   )rò   rð   r   )rË   rÀ   r»   )r\   r¸   r·   )rë   r   rê   )r¹   r»   rÖ   )rm   rê   rÇ   )rp   rÖ   rð   )rè   r·   rÀ   )rŽ   rÏ   rÄ   )rå   rá   r   )rÓ   rÊ   rÆ   )rÂ   rÄ   rÀ   )rï   r   rî   )r‘   rÆ   rÁ   )r9   rî   rÏ   )r,   rÁ   rá   )rß   rÀ   rÊ   )rÐ   rÖ   r»   )rë   rä   r   )rÙ   rÒ   rÎ   )rË   r»   rÊ   )rñ   r   rð   )rÍ   rÎ   r¼   )r   rð   rÖ   )r!   r¼   rä   )ræ   rÊ   rÒ   )r�   rÅ   rÎ   )rp   rð   rÜ   )rŠ   rÇ   r:   )r+   rÎ   r¿   )r�   rÜ   rÁ   )r9   r:   rî   )r‘   rÁ   rÅ   )rí   rî   rð   )r¾   r¿   rÇ   )rn   r¿   r¸   )r,   rá   r½   )rÕ   rÏ   r×   )r%   r¸   rÉ   )rÌ   r½   r¼   )r   r×   rð   )rÍ   r¼   r¿   )rà   rð   rá   )rŽ   rÉ   rÏ   )r"   rÉ   rÄ   )r!   rä   rÈ   )rÚ   rÖ   rÜ   )rr   rÄ   rÑ   )rÔ   rÈ   rÇ   )rJ   rÜ   rá   )rM   rÇ   rÉ   )rç   rá   rä   )rÐ   rÑ   rÖ   )r$   rÑ   r»   )r    rê   r:   )r�   rÁ   r½   )rs   r»   rº   )r‹   r:   rÏ   )rŒ   r½   rä   )rÛ   rÏ   rÑ   )rã   rä   rê   )r’   rº   rÁ   )rX   rº   rÆ   )rq   rî   r×   )rÃ   r¼   rÈ   )ro   rÆ   rÅ   )rÞ   r×   rÖ   )rm   rÈ   rê   )r¹   rÖ   rº   )ré   rê   rî   )rÝ   rÅ   r¼   gØfð³I@gè×1:²o@i5  é}   iq  )r
   r   r   r   r   r   r   r   ÚHalfÚextendÚOner   ÚNegativeOner   )ÚhexagonÚfig1Úfig2Úfig3Úfig4ÚtriÚpolysr0   Úexpr2Úexpr3Úresult_dictÚcube1Úcube2Úcube3Úcube4Ú
octahedronÚgreat_stellated_dodecahedronÚexprÚoctahedron_five_compoundÚcube_five_compoundÚechidnahedrons                        r(   Útest_polytope_integrater  @   s–  € ô œg¤e¨A¨q£k´5¸¸A³;Ü&+¨A¨q£kó3Ø45ó7Ø:;ò<ð <ð <äœg¤e¨A¨q£k´5¸¸A³;Ü&+¨A¨q£k´5¸¸A³;ó@ÜABÄQÁóHä&.¨q°!£nò5ð 5ð 5ô œg¤e¨A¨q£k´5¸¸A³;ÄÀaÈÃÓLØ¤ 1¡™f r¬!¡t™mó-Ü08¸¸qÓ0AòBð Bð Bô œg¤e¨A¨q£k´5¸¼DÀ»GÓ3DÜ&+¬D°«G´T¸!³WÓ&=Ü&+¬D°«G°QÓ&7ó9à:;ó=à@AòBð Bð Bô ”e˜A˜q“k¤5¬$¨q«'¨°A©´q·v±vÓ#>ÜœT !›W˜H q™L¬!¨A«$°©(Ó3´U¸1¸a³[ÜœD ›G a™K¬¨1«°©Ó2´E¼$¸q»'ÀA¹+ÄqÇvÁvÓ4NóP€Gô ˜g qÓ)¬Q¨q´°a³©y«\¸AÑ-=Ò=Ð=Ð=ô ò -Ø./ó1Ø45ò6ð 6ð 6äò :Ü;<¼q¹5óBÜEMÈaÐQRÃ^òTð Tð Täò /Ø01´!°Q±$±¸¼A¹±ó?ÜBJÈ4ÐQRÓBSòTð Tð Tä˜|¨q´$°q³'¨l¸AÐ->Ü!% a£¨! ¨aÐ0°,ð@ØABóDØGHòIð Ið Iô ˜"˜a“¤4¨£7 (¨Q¡,Ð/°Ð3Øœ˜a› 1™Ð%Ü˜"˜a“¤$ q£'¨A¡+Ð.´°Q³Ð8Ü—‘œ˜a› 1™Ð%¤t¨A£wÐ/Øœ˜Q› !™Ð$Ü—‘œ$˜q›'˜ A™Ð&¨Ð*ð,€Gô ˜g qÓ)¬Q¨q´°a³©y«\¸AÑ-=Ò=Ð=Ð=ô œg¤e¨B°£m´U¸2¸q³\Ü&+¨A¨q£k´5¸¸A³;Ü&+¨A¨r£ló4à56ó8à;<ò=ð =ð =ô œg¤e¨B°£m´U¸2¸q³\Ü&+¨A¨q£k´5¸¸A³;Ü&+¨A¨r£l´E¸!¸Q³KóAàBCóEàHIòJð Jð Jô ò :Ø;<ó>ØABòCð Cð Cäò -à./ó1à45ò6ð 6ð 6ô ”5˜ Ó'¬¨v°vÓ)>Ü˜ Ó(¬%°¸Ó*?Ü˜ Ó#¤U¨6°5Ó%9Ü˜ Ó&ó(€Dô ˜d¤A q¡D¬1¬Q©3¡J´°A±Ñ$5Ó6Ü	Ð
Ó˜XÑ&ò'ð 'ð 'ô ”5˜ Ó&¬¨e°VÓ(<Ü˜ Ó(¬%°¸Ó*?Ü˜ Ó'ó)€Dô ˜d¤A q¡D¬1¬Q©3¡J´°A±Ñ$5Ó6Ü	ˆ/Ó˜IÑ&ò'ð 'ð 'ô ”5˜ Ó(¬%°¸Ó*>Ü˜ Ó(¬%°¸Ó*?óA€Dä˜d¤A q¡D¬1¬Q©3¡J´°A±Ñ$5Ó6Ü	ˆ/Ó˜HÑ%ò&ð &ð &ô ”5˜ Ó'¬¨v°uÓ)=Ü˜ Ó&¬¨e°VÓ(<Ü˜ Ó(ó*€Dô ˜d¤A q¡D¬1¬Q©3¡J´°A±Ñ$5Ó6Ü	ˆ/Ó˜FÑ#ò$ð $ð $ô ”%˜˜1“+œu Q¨›{¬E°!°Q«KÓ
8€CØ€EÜˆq‰D”‰F”Q˜‘Tœ!˜Q™$‘YÑ ¤1 a¡4¡¬¨1©¡Ñ,€EÜˆq‰D”�A‘‰Iœ˜1™œQ ™T™	Ñ! A¤a¨¡e¡GÑ+€EÜˆr‰E”A�q‘Dœ‘F‰NœQ ™T¤! Q¡$™YÑ&¬¨A©¬a°©d©Ñ2€EØ	‡L�L�%˜ Ð&Ô'Ü$ S¨%¸BÔ?€KØ�uÑ¤¨)°SÓ!9Ò9Ð9Ð9Ø�uÑ¤¨(°BÓ!7Ò7Ð7Ð7Ø�uÑ¤¨*°cÓ!:Ò:Ð:Ð:ä
”%˜˜1“+œu Q¨›{¬E°!°Q«KÓ
8€CÜˆq‰D”�A‘‰I˜œ!˜Q™$™œq !™t™Ñ#€EÜˆq‰D”�A‘‰Iœ˜1™œQ ™T™	Ñ! A¤a¨¡e¡GÑ+€EÜˆr‰E”A�q‘Dœ‘F‰NœQ ™T¤! Q¡$™YÑ&¬¨A©¬a°©d©Ñ2€EØ	‡L�L�%˜ Ð&Ô'Ü˜c 5°QÔ7Ü	
ˆA‰Œa‰�!”A�q‘D‘&œ˜A™‘+Ñ	œx¨°Ó2Ð3ò4ð 4ð 4ô
 œg¤e¨A¨q£k´5¸¸A³;Ü&+¨A¨q£k´5¸¸A³;ó@à)*ô,ð0G°°1ð 0G°a¸ð 0G¼A¼q¿v¹vð 0GÜ01°Q±¼¸a¹±ÄÇÁÈÁð0Gä01°Q±¼¿¹À¹	ð0Gô 12°Q±¼¿¹À¹	ð0Gô 12´1·6±6ð	0Gô
 12´A¸±F±
¼A¿E¹EÀA¹Ið0Gô 12°Q±¼¿¹À¹	ð0Gô 12°Q±¼¿¹À¹	ð0Gô 12°Q±¼±
¼A¿E¹EÀA¹Ið0Gô 12°Q±¼±
¼A¿E¹EÀA¹Ið0Gô 12´A±´q·u±u¸q±yð0Gô 12°Q±¼¿¹À¹	ð0Gô 12°Q±¼¿¹À¹	ð0Gô 12´A¸±F±
¼A¿E¹EÀA¹Ið0GòGð Gð Gò$:âš<ª²|Úš<ð)€Eô ˜e QÓ'¬1¨S«6Ò1Ð1Ð1ò.âš<ª²|Úš<ð)€Eò
$ò šLÒ*<ºnÚšLª,Ò8Lð	N€Eð ˜ I¨yÜ�u‰u�q‰yœ!Ÿ%™% !™)¤Q§U¡U¨Q¡YÐ/ð1âš	¢9ªiÚš	¢9ð.€Eô
 ˜e¤Q¨!¡V¬a°1©f¡_´q¼1±uÑ%<¼qÀA¹vÑ%EÓFÜ�E˜1Óòð ð ä˜e¤Q¨!¡V¬a°1©f¡_´q¼1±uÑ%<¼qÀA¹vÑ%EÓFÜˆU‹8�b‰=òð ð ä˜e¤Q¨!¡V¬a°1©f¡_´q¼1±uÑ%<¼qÀA¹vÑ%EÓFÜˆR‹5�3‰;òð ð ô —M‘M¤D¨£GÑ+¨Q°Ð2°Q¼¿¹ÄÀQÃ¹ÈÐ4KØ�qœ!Ÿ-™-¬$¨q«'Ñ1Ð2°Q¸¼1¿5¹5Ä4ÈÃ7¹?Ð4KØ”q—}‘}¤t¨A£wÑ.°Ð2´Q·U±U¼TÀ!»W±_ÀaÈÐ4KðMò šYª	²9ºiÚšYª	ð	3€Jô ˜j¨!Ó,´°Q³¸!±Ò;Ð;Ð;ò
Tò( 
Ò-Ú	Ò+Ú	Ò-Ú	Ò/Ú	Ò1Ú	Ò/ð3	1ð !ô8 Ô!Ð">ÀÓBØñó Ø"ò#ð #ð #ô ˆq‰5”1˜‘6‰>œA ™FÑ"€Dð; /ò -!:ð ; /ò\ "-ð]; /ò\ /:ð]; /ò\ <Gð]; /ò^ "-ð_; /ò^ /:ð_; /ò^ <Gð_; /ò` "-ða; /ò` /:ða; /ò` <Fða; /òb ",ðc; /òb .9ðc; /òb ;Fðc; /òd ",ðe; /òd .8ðe; /òd :Eðe; /òf "-ðg; /òf /:ðg; /òf <Gðg; /òh "-ði; /òh /:ði; /òh <Fði; /òj ",ðk; /òj .9ðk; /òj ;Fðk; /òl ",ðm; /òl .8ðm; /òl :Eðm; /òn "-ðo; /òn /:ðo; /òn <Gðo; /òp "-ðq; /òp /:ðq; /òp <Hðq; /òr ".ðs; /òr 0<ðs; /òr >Jðs; /òt ".ðu; /òt 0<ðu; /òt >Jðu; /òv ".ðw; /Ðôx Ô!Ð":¸DÓAÓBÀXÑMØ
òð ð ð%Jò Nð %Jò8 )ð9%Jò8 +9ð9%Jò8 ;Ið9%Jò: )ð;%Jò: +9ð;%Jò: ;Ið;%Jò< )ð=%Jò< +9ð=%Jò< ;Ið=%Jò> )ð?%Jò> +9ð?%Jò> ;Ið?%Jò@ )ðA%Jò@ +9ðA%Jò@ ;IðA%JòB )ðC%JòB +9ðC%JòB ;IðC%JòD )ðE%JòD +9ðE%JòD ;IðE%JòF )ðG%JòF +9ðG%JòF ;IðG%JòH )ðI%JòH +9ðI%JòH ;IðI%JòJ )ðK%JòJ +9ðK%JòJ ;IðK%JÐôL Ô!Ð"4°dÓ;¸dÑBÓCÀeÒKÐKÐKðHNò [`ð HNòx "ðyHNòx $0ðyHNòx 2>ðyHNòx @LðyHNòz "ð{HNòz $0ð{HNòz 2>ð{HNòz @Lð{HNò| #ð}HNò| %1ð}HNò| 3?ð}HNò| AMð}HNò~ #ðHNò~ %1ðHNò~ 3>ðHNò~ @LðHNò@ #ðAHNò@ %1ðAHNò@ 3?ðAHNò@ AMðAHNòB "ðCHNòB $0ðCHNòB 2>ðCHNòB @KðCHNòD #ðEHNòD %1ðEHNòD 3?ðEHNòD AMðEHNòF #ðGHNòF %0ðGHNòF 2>ðGHNòF @LðGHNòH #ðIHNòH %1ðIHNòH 3?ðIHNòH AMðIHNòJ "ðKHNóJ $0ðKHNóJ 2>ðKHNóJ @LðKHNóL "ðMHNóL $0ðMHNóL 2>ðMHNóL @LðMHNóN #ðOHNóN %0ðOHNóN 2>ðOHNóN @LðOHNóP "ðQHNóP $0ðQHNóP 2>ðQHNóP @LðQHNóR #ðSHNóR %1ðSHNóR 3>ðSHNóR @LðSHNóT #ðUHNóT %0ðUHNóT 2>ðUHNóT @LðUHNóV #ðWHNóV %1ðWHNóV 3>ðWHNóV @KðWHNóX #ðYHNóX %1ðYHNóX 3>ðYHNóX @LðYHNóZ #ð[HNóZ %0ð[HNóZ 2>ð[HNóZ @Kð[HNó\ "ð]HNó\ $0ð]HNó\ 2>ð]HNó\ @Kð]HNó^ #ð_HNó^ %1ð_HNó^ 3>ð_HNó^ @Lð_HNó` #ðaHNó` %0ðaHNó` 2>ðaHNó` @LðaHNób "ðcHNób $0ðcHNób 2>ðcHNób @LðcHNód #ðeHNód %1ðeHNód 3?ðeHNód ALðeHNóf #ðgHNóf %1ðgHNóf 3>ðgHNóf @LðgHNóh #ðiHNóh %0ðiHNóh 2>ðiHNóh @LðiHNój "ðkHNój $0ðkHNój 2>ðkHNój @KðkHNól #ðmHNól %1ðmHNól 3?ðmHNól AMðmHNón #ðoHNón %0ðoHNón 2>ðoHNón @LðoHNóp "ðqHNóp $0ðqHNóp 2>ðqHNóp @LðqHNór #ðsHNór %1ðsHNór 3>ðsHNór @LðsHNót #ðuHNót %0ðuHNót 2>ðuHNót @KðuHNóv #ðwHNóv %1ðwHNóv 3?ðwHNóv ALðwHNóx #ðyHNóx %1ðyHNóx 3>ðyHNóx @LðyHNóz "ð{HNóz $/ð{HNóz 1=ð{HNóz ?Kð{HNó| #ð}HNó| %1ð}HNó| 3>ð}HNó| @Lð}HNó~ "ðHNó~ $0ðHNó~ 2>ðHNó~ @LðHNó@ #ðAHNó@ %1ðAHNó@ 3?ðAHNó@ ALðAHNóB #ðCHNóB %0ðCHNóB 2>ðCHNóB @LðCHNóD #ðEHNóD %0ðEHNóD 2=ðEHNóD ?KðEHNóF #ðGHNóF %1ðGHNóF 3?ðGHNóF AMðGHNóH #ðIHNóH %1ðIHNóH 3>ðIHNóH @KðIHNóJ #ðKHNóJ %1ðKHNóJ 3?ðKHNóJ AMðKHNóL #ðMHNóL %1ðMHNóL 3?ðMHNóL AMðMHNóN #ðOHNóN %1ðOHNóN 3?ðOHNóN AMðOHNóP #ðQHNóP %1ðQHNóP 3?ðQHNóP AMðQHN€MôT Ô! -°Ó3Ñ6FÑFÓGÈ%ÒOÐOÐOÜÔ! -°Ó6Ñ9IÑIÓJØ	ò
ð 
ð 
ô ˜e¤a¨¡d¬A¬a©C [¸QÔ?Ü	
ŒQ‰‘”q˜“t‘œQ !™V¡T¬A¨a«D¡[Ð1ò2ð 2ð 2ô ˜e°Ô2Ø	
‰C”‘Cœ!˜A›$‘J¤¤A¡¡t¬a°«d¡{´A±s¼Q¸q»T±zÜ	
ŒQ‰‘”q˜“t‘œQ !™V¡T¬A¨a«D¡[´!°q±&¹$ÄÀ1Ã¹+Ü	
‰C”!�A“$‰JœœA™™t¤a¨£d™{¬A°©F±D¼1¸Q»4±Kð	AòAð Añ Ar'   c                  ó^  — t        t        dd«      t        dd«      t        dd«      g«      t        dd«      t        dd«      t        dd«      gk(  sJ ‚t        ddd«      } t	        | t
        t        z  «      t        dd«      k(  sJ ‚t	        | t
        t        z  d¬	«      t        dd«      k(  sJ ‚y )
Nr   r   ©r   r   rC   r/   r=   r    T)Ú	clockwise)r   r   r   r   r
   r   r   r   )Úfig6s    r(   Útest_point_sortr  þ  sž   € Ü”u˜Q “{¤E¨!¨Q£K´°q¸!³Ð=Ó>Ü	��A‹œ  1›¤w¨q°!£}Ð5ò6ð 6ð 6ô �6˜6 6Ó*€DÜ˜d¤A¤a¡CÓ(¬H°R¸«OÒ;Ð;Ð;Ü˜d¤A¤a¡C°TÔ:¼hÀqÈ!»nÒLÐLÑLr'   c                  ó:  — t        t        dd«      t        dd«      t        dd«      t        dd«      t        d	d
«      t        dd«      t        dd«      t        dd«      «      } t        | t        dz  t        t        z  z   t        dz  z   «      t        d«      dz  k(  sJ ‚t        t        dd«      t        dd«      t        dd«      t        dd«      t        dd«      «      }t        |t        dz  t        t        z  z   t        dz  z   «      t        d«      dz  k(  sJ ‚y ) Ng)\�Âõ¨Àg9´Èv¾Ÿê¿gòÒMbXÀgJ+‡ù?gTã¥›Ä 
ÀgX9´Èvô?gq=
×£pñ¿g¤p=
×£ Àg/Ý$�
@gB`åÐ"Ûå¿gÝ$�•C@rI   g®Gáz”Àg\�Âõ(\@gé&1¬ð¿g9´Èv¾Ÿ
Àr   l   #ShK6. l     ó^OWg¾Ÿ/Ý$Àg1¬ZäÀg‘í|?5^º¿g /Ý$@g®Gáz®ù¿gX9´ÈvÀgªñÒMb@gyé&1¬è¿gZd;ßÏ@gd;ßO�—Þ?l   QMüQº@ l    0Þ{é
)r   r   r
   r   r   r   )Úfig5r  s     r(   Ú!test_polytopes_intersecting_sidesr    s  € Ü”5˜ Ó(¬%°¸Ó*>Ü˜ Ó'¬¨v°vÓ)>Ü˜ Ó'¬¨u°fÓ)=Ü˜ Ó'¬¨v°vÓ)>ó@€Dô ˜d¤A q¡D¬1¬Q©3¡J´°A±Ñ$5Ó6Ü	Ð
Ó˜YÑ'ò(ð (ð (ô ”5˜ Ó(¬%°¸Ó*>Ü˜ Ó(¬%°°vÓ*>Ü˜ Ó&ó(€Dô ˜d¤A q¡D¬1¬Q©3¡J´°A±Ñ$5Ó6Ü	ˆ.Ó˜8Ñ$ò%ð %ñ %r'   c                  óÀ  — t        dddd«      } dt        t        t        t        z  t        dz  t        z  t        t        dz  z  g}t        | |d¬«      ddt        t        j
                  t        t        j
                  t        t        z  t        dd	«      t        dz  t        z  t        dd
«      t        t        dz  z  t        dd
«      ik(  sJ ‚t        | |d¬«      ddt        t        j
                  t        t        j
                  t        t        z  t        dd	«      ik(  sJ ‚t        | |d¬«      ddt        t        j
                  t        t        j
                  ik(  sJ ‚y )Nr  rA   r/   rC   r   r   r$   rK   r!   r9   )r   r   r   r
   r   rô   r   ©Úpolygonrþ   s     r(   Útest_max_degreer    s  € Ü�f˜f f¨fÓ5€GØ””1”aœ‘cœ1˜a™4¤™6¤1¤Q¨¡T¡6Ð*€EÜ˜g u¸Ô;Ø	
ˆAŒq”!—&‘&œ!œQŸV™V¤Q¤q¡S¬(°1°a«.¼!¸Q¹$¼q¹&Ä(È1ÈaÃ.ÔRSÔTUÐWXÑTXÑRXÔZbÐcdÐfgÓZhÐiòjð jð jä˜g u¸Ô;Ø	
ˆAŒq”!—&‘&œ!œQŸV™V¤Q¤q¡S¬(°1°a«.Ð9ò:ð :ð :ä˜g u¸Ô;Ø	
ˆAŒq”!—&‘&œ!œQŸV™VÐ$ò%ð %ñ %r'   c                  ó  — g d¢g d¢g d¢g d¢g d¢g d¢g d¢g} | d   }| d	d  }t        ||«      }t        d	|||«      d
k(  sJ ‚t        d	|||d	¬«      d	d
t        t        dd«      t        t        dd«      t
        t        dd«      ik(  sJ ‚y )NrP   ©r   r9   r"   r$   ©r$   r"   r+   r   ©r"   r9   r!   r+   ©r   r+   r!   r   ©r$   r   r   r   ©r   r!   r9   r   r   r   iƒÿÿÿrK   i�ýÿÿr   )r   r   r   r   r   r   )ÚcubeÚverticesÚfacesÚ	hp_paramss       r(   Útest_main_integrate3dr$  !  s£   € ò.âš,ª²lÚš,ð(€Dð �A‰w€HØ��ˆH€EÜ% e¨XÓ6€IÜ˜A˜u h°	Ó:¸dÒBÐBÐBÜ˜A˜u h°	ÀaÔHØ	
ˆD”!”X˜d AÓ&¬¬8°D¸!Ó+<¼aÄÈ$ÐPQÓARÐSòTð Tñ Tr'   c            
      ó$  — t        ddd«      } | j                  }t        | «      }t        t        dz  t
        dz  z   ||«      t        dd«      k(  sJ ‚t        t        dz  t
        dz  z   ||d¬«      d	d	dd
t
        t        dd«      t        dik(  sJ ‚y )Nr-   )r+   r$   r/   r   iE  r9   r   rK   r   r+   rÌ   r$   rJ   )r   Úsidesr   r   r   r   r   )ÚtriangleÚfacetsr#  s      r(   Útest_main_integrater)  .  s�   € Ü�v˜v vÓ.€HØ�^‰^€FÜ% hÓ/€IÜœ!˜Q™$¤ A¡™+ v¨yÓ9¼XÀcÈ1Ó=MÒMÐMÐMÜœ!˜Q™$¤ A¡™+ v¨yÀQÔGØ	
ˆAˆq�!”Qœ  Q›¬¨BÐ/ò0ð 0ñ 0r'   c            	      ó€   — g d¢g d¢g d¢g d¢g d¢g d¢g d¢g} | d   }| dd  }| d	   }t        |d
dgd	||dd	«      dk(  sJ ‚y )NrP   r  r  r  r  r  r  r   r   rZ   r+   içÿÿÿ)r   )r   Úfacetr(  r!  s       r(   Útest_polygon_integrater,  7  s_   € ò.âš,ª²lÚš,ð(€Dð �‰G€EØ�!�"ˆX€FØ�A‰w€HÜ˜U Y° N°A°v¸xÈÈAÓNÐRUÒUÐUÑUr'   c                  óJ   — d} t        | ddgd«      t        d«       dz  k(  sJ ‚y )NrN   r[   rZ   rY   r   )r	   r   )Úpoints    r(   Útest_distance_to_sider/  B  s.   € Ø€EÜ˜E I¨yÐ#9¸9ÓEÌ$ÈqË'ÈÐRSÉÒSÐSÑSr'   c                  ód   — g d¢} ddg}t        | d|dd«      dk(  sJ ‚t        | d|dd«      dk(  sJ ‚y )N)rR   rV   rW   rS   rR   rV   r   r   r+   )r   )r  Úline_segs     r(   Útest_lineseg_integrater2  G  sG   € Ú:€GØ˜9Ð%€HÜ˜W a¨°1°aÓ8¸AÒ=Ð=Ð=Ü˜W a¨°1°aÓ8¸AÒ=Ð=Ñ=r'   c            	      ó  — t        t        dd«      t        dd«      t        dd«      «      } | j                  }t        | «      d   \  }}t	        |d||dt
        t        fd«      dk(  sJ ‚t	        |d||dt
        t        fd«      dk(  sJ ‚y )Nr   r$   r+   r   )r   r   r&  r   r   r   r   )r'  r(  ÚaÚbs       r(   Útest_integration_reductionr6  N  s„   € Ü”u˜Q “{¤E¨!¨Q£K´°q¸!³Ó=€HØ�^‰^€FÜ  Ó*¨1Ñ-�D€A€qÜ  ¨¨A¨q°!´a¼°V¸QÓ?À1ÒDÐDÐDÜ  ¨¨A¨q°!´a¼°V¸QÓ?À1ÒDÐDÑDr'   c                  ó   — t        t        dd«      t        dd«      t        dd«      «      } | j                  }t        | «      d   \  }}|d   j                  d   }g d¢g d¢t
        dddgt        ddd gg}t        |d||t        dt        t
        fddd||d«      t        dd	«      k(  sJ ‚t        |d||ddt        t
        fddd||d«      dk(  sJ ‚y )
Nr   r$   r+   r   )r   r   r   r   )r   r   r   r+   rr   r‘   r   )	r   r   r&  r   Úpointsr   r   r   r   )r'  r(  r4  r5  Úx0Úmonomial_valuess         r(   Ú"test_integration_reduction_dynamicr;  V  s÷   € Ü”u˜Q “{¤E¨!¨Q£K´°q¸!³Ó=€HØ�^‰^€FÜ  Ó*¨1Ñ-�D€A€qØ	�‰×	Ñ	˜!Ñ	€BÚ#¢\Ü˜1˜a �}¤q¨!¨Q° oð7€Oô )¨°°A°q¼!¸QÄÄAÀÈØ)*¨A¨r°?ÀAóGÜJRÐSUÐWXË/òZð Zð Zä(¨°°A°q¸!¸QÄÄAÀÈØ)*¨A¨r°?ÀAóGØJKòLð Lñ Lr'   c                  ó®   — t        d«      du sJ ‚t        d«      du sJ ‚t        t        dd«      «      du sJ ‚t        d«      du sJ ‚t        d«      du sJ ‚y )Nr   F)r   r$   Tr$   )r   r$   r!   )r   r$   r!   r+   )r   r   r&   r'   r(   Útest_is_vertexr=  d  sf   € Ü�Q‹<˜5Ñ Ð Ð Ü�VÓ Ñ$Ð$Ð$Ü”U˜1˜a“[Ó! TÑ)Ð)Ð)Ü�YÓ 4Ñ'Ð'Ð'Ü�\Ó" eÑ+Ð+Ñ+r'   c                  óŒ  — t        t        dd«      t        dd«      t        dd«      t        dd«      «      } dt        t        t        t        z  t        dz  t        z  t        t        dz  z  g}t	        | |«      ddt        t
        j                  t        t
        j                  t        t        z  t        dd«      t        dz  t        z  t        dd«      t        t        dz  z  t        dd«      ik(  sJ ‚dt        t        t        t        z  dt        dz  t        z  z   t        t        t        dz  z  z   g}t	        | |«      ddt        t
        j                  t        t
        j                  t        t        z  t        dd«      t        dz  t        z  dz   t        dd«      t        t        dz  z  t        z   t        dd«      ik(  sJ ‚y )Nr   r   r   r!   r9   r$   rs   )r   r   r   r   r
   r   rô   r   r  s     r(   Útest_issue_19234r?  l  sg  € Ü”e˜A˜q“k¤5¨¨A£;´°a¸³¼UÀ1Àa»[ÓI€GØ”!”Qœœ!™œQ ™T¤!™V¤Q¤q¨!¡t¡VÐ,€EÜ˜g uÓ-Ø	
ˆAŒq”!—&‘&œ!œQŸV™V¤Q¤q¡S¬(°1°a«.¼!¸Q¹$¼q¹&Ä(È1ÈaÃ.ÔRSÔTUÐWXÑTXÑRXÔZbÐcdÐfgÓZhÐiòjð jð jà”!”Qœœ!™˜Q¤ A¡¤a¡™Z¬¬Q¬q°!©t©V©Ð4€EÜ˜g uÓ-Ø	
ˆAŒq”!—&‘&œ!œQŸV™V¤Q¤q¡S¬(°1°a«.¼!¸Q¹$¼q¹&À1¹*ÄhÈrÐSTÃoÔWXÔYZÐ\]ÑY]ÑW]Ô`aÑWaÔckÐlmÐopÓcqÐròsð sñ sr'   N)1Ú$sympy.functions.elementary.complexesr   Ú(sympy.functions.elementary.miscellaneousr   Ú
sympy.corer   r   Úsympy.integrals.intpolyr   r   r	   r
   r   r   r   r   r   r   r   r   r   Úsympy.geometry.liner   Úsympy.geometry.polygonr   Úsympy.geometry.pointr   r   Ú	sympy.abcr   r   r   Úsympy.testing.pytestr   r)   r7   r  r  r  r  r$  r)  r,  r/  r2  r6  r;  r=  r?  r&   r'   r(   ú<module>rI     s¡   ðÝ 4Ý 9ç "÷O÷ O÷ Oõ Oõ *Ý *ß /ß Ñ å %ò-ò,Að* ñ{Aó ð{AòzMò%ò%ò
Tò0òVòTò
>òEòLò,ósr'   