Ë
    7^(h0\  ã                   ó   — d dl Z d dlZd dlZd dlmZ d dlmZmZmZ d dl	m
Z
mZ d dlmZ d dlmZ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mZmZ d dl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+ d dl,m-Z-m.Z.m/Z/m0Z0m1Z1 d dl2m3Z3 d dl4m5Z5 d dl6m7Z8 d dl9m:Z: d dlm;Z; d dlm<Z< d dl=m>Z>  e>d«      Z?ddhZ@ddhZAdhZBg ddfd„ZCd„ ZDd„ ZEd„ ZFd „ ZGd!„ ZHd"„ ZId#„ ZJd$„ ZKd%„ ZLd&„ ZMd'„ ZNd(„ ZOd)„ ZPd*„ ZQd+„ ZRd d,lSmTZT d-„ ZUd d.lVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZm€Z€m�Z�m‚Z‚mƒZƒm„Z„m…Z…m†Z†m‡Z‡mˆZˆm‰Z‰mŠZŠm‹Z‹mŒZŒm�Z�mŽZŽm�Z�m�Z�m‘Z‘ d/„ Z’d d0l“m”Z” d d1l•m–Z– d d2l—m˜Z˜m™Z™ d d3lšm›Z›mœZœm�Z�mžZž d d4lŸm Z m¡Z¡m¢Z¢ d5„ Z£d d6l¤m¥Z¥ d7„ Z¦d d8l§m¨Z¨ d9„ Z©d d:lªm«Z«m¬Z¬ d;„ Z­d d<l®m¯Z¯ d=„ Z°d d>l±m²Z² d d?lm³Z³ d@„ Z´edA„ «       ZµedB„ «       Z¶d dCl·m¸Z¸ d dDl¹mºZº d dEl»m¼Z¼ d dFl½m¾Z¾ dG„ Z¿dH„ ZÀedI„ «       ZÁdJ„ ZÂdK„ ZÃdL„ ZÄdM„ ZÅdN„ ZÆdO„ ZÇdP„ ZÈd dQlÉmÊZÊ d dRlËmÌZÌmÍZÍ d dSlÎmÏZÏ d dTlÐmÑZÑmÒZÒ d dUlÓmÔZÔ d dVlÕmÖZÖ dW„ Z×edX„ «       ZØedY„ «       ZÙedZ„ «       ZÚd d[lÛmÜZÜ d d\lÝmÞZÞ d]„ Zßd d^làmáZá d d_lâmãZã d`„ Zäda„ Zådb„ Zædc„ Zçy)dé    N)Úmeter)ÚXFAILÚraisesÚignore_warnings)ÚAtomÚBasic)ÚSingletonRegistry)ÚStrÚDummyÚSymbolÚWild)
ÚEÚIÚpiÚooÚzooÚnanÚIntegerÚRationalÚFloatÚAlgebraicNumber)ÚEqualityÚGreaterThanÚLessThanÚ
RelationalÚStrictGreaterThanÚStrictLessThanÚ
Unequality)ÚAdd)ÚMul)ÚPow)Ú
DerivativeÚFunctionÚFunctionClassÚLambdaÚWildFunction)ÚInterval)Ú	vectorize)Úgmpy)ÚSymPyDeprecationWarning)ÚS)Úsymbols)Úimport_moduleÚcloudpickleÚ_assumptionsÚ_mhashÚis_EmptySetÚexpr_free_symbolsÚ_sage_T© c                 ó–  ‡ ‡‡	— t        ‰ t        «      rdD ]  Š	t        t        ˆ ˆ	fd„«       Œ dt        j                  t        j
                  ddg}t        r|j                  t        g«       |D ]×  Š	‰	|v rŒt        ‰	«      rt        ‰ t        «      rŒ$ ‰	‰ «      }n_t        j                  ‰	«      r!‰	j                  ‰	j                  ‰ «      «      }n)t        j                  t        j                  ‰ ‰	«      «      }t        ‰ «      }t        |«      }t!        |«      t!        |«      k(  sJ ‚|sŒ¾ˆˆ	fd„} |‰ ||«        ||‰ |«       ŒÙ y)z2 Check that pickling and copying round-trips.
    )r   é   c                  ó0   •— t        j                  ‰ ‰«      S ©N)ÚpickleÚdumps)ÚaÚprotocols   €€úa/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/utilities/tests/test_pickling.pyú<lambda>zcheck.<locals>.<lambda>8   s   ø€ ´·±¸QÀÓ0I€ ó    é   é   é   c                 óÞ  •— |D ]Û  }|t         v rŒ|t        v r!t        | |«      sŒ!t        ||«      rŒ.J |«       ‚|t        v s|‰v r:t	        t
        «      5  t        | |«      t        ||«      k(  sJ |«       ‚	 d d d «       Œ{t        | |«      sŒˆt        | |«      }t        |d«      rŒ¡t        ||«      sJ |«       ‚t        ||«      |k(  rŒÄJ t        ||«      ›d|›d‰›�«       ‚ y # 1 sw Y   ŒèxY w)NÚ__call__z != z, protocol: )Údont_check_attrsÚnot_equal_attrsÚhasattrÚdeprecated_attrsr   r*   Úgetattr)r;   ÚbÚdÚiÚattrÚ
deprecatedr<   s        €€r=   Úczcheck.<locals>.cS   sú   ø€ Øò q�ØÔ(Ñ(ØØœ/Ñ)Ü˜q !•}Ü& q¨!�}Ð/¨aÓ/˜}ØÔ*Ñ*¨a°:©oÜ(Ô)@ÓAñ AÜ& q¨!›}´¸¸1³Ò=Ð@¸qÓ@Ñ=÷Að Aä   AœØä" 1 a›=�DÜ" 4¨Õ4Ü& q¨!œ}Ð/¨aÓ/˜}Ü& q¨!›}°Ó4ÐpÔRYÐZ[Ð]^ÕR_ÒaeÑgoÐ6pÓpÐ4ñq÷Að Aús   Á!C#Ã#C,	N)Ú
isinstancer   r   ÚNotImplementedErrorÚcopyÚdeepcopyr.   ÚextendÚcallableÚtypeÚinspectÚismoduleÚloadsr:   r9   ÚdirÚset)
r;   ÚexcludeÚ
check_attrrN   Ú	protocolsrJ   Úd1Úd2rO   r<   s
   `  `     @r=   Úcheckra   2   s  ú€ ô �!”UÔØò 	KˆHÜÔ&Ô(IÕJð	Kð ”D—I‘IœtŸ}™}¨a°Ð3€IÝØ×Ñœ+˜Ô'àò (ˆØ�wÑØä�HÔÜ˜!œTÔ"àÙ˜“‰AÜ×Ñ˜hÔ'Ø—‘˜xŸ~™~¨aÓ0Ó1‰Aä—‘œVŸ\™\¨!¨XÓ6Ó7ˆAä�‹VˆÜ�‹VˆÜ�2‹wœ#˜b›'Ò!Ð!Ð!áØõ	qñ$ 	
ˆ!ˆQ�ŒÙ	ˆ!ˆQ��ñQ(r?   c                  ót   — t         t        «       t        t        «       t        t        fD ]  } t	        | «       Œ y r8   )r   r   r	   r+   ra   ©rO   s    r=   Útest_core_basicrd   m   s*   € Ü”D“FœE¤5£7Ô,=¼qÐAò ˆÜˆa�ñr?   c                  ó,   — t        t        d«      «       y ©NÚx)ra   r
   r4   r?   r=   Útest_core_Strrh   q   s   € Ü	Œ#ˆc‹(…Or?   c                  óŠ   — t         t        dd¬«      t        t        dd¬«      t        t        d«      fD ]  } t        | «       Œ y )Nrg   F)ÚcommutativeÚ_issue_3130)r   r   r   ra   rc   s    r=   Útest_core_symbolrl   t   s=   € ô ”U˜3¨EÔ2´FÜ�=¨eÔ4´d¼DÀ»IðGò ˆäˆa�ñr?   c                  ó¾   — t        d«      t        dd«      t        d«      fD ]  } t        | «       Œ t        t	        t        d«      «      fD ]  } t        | d¬«       Œ y )Nr@   rA   z1.2F©r]   )r   r   r   ra   r   Úsqrtrc   s    r=   Útest_core_numbersrp   }   sT   € Ü�a‹jœ( 1 a›.¬%°«,Ð7ò ˆÜˆa�ðäœ¬t°A«wÓ7Ð8ò #ˆÜˆa˜EÖ"ñ#r?   c                  ó6   — t        d«      dz   } t        | «       y )Nrg   g      ð?)r   ra   )Úys    r=   Útest_core_float_copyrs   „   s   € äˆs‹�cÑ€AÜ	ˆ!…Hr?   c                  ó4  — t        d«      } t        d«      }t        t        | |«      t        t        | |«      t        t        | |«      t        t	        | |«      t
        t        | |«      t        t        | |«      t        t        | |«      fD ]  }t        |«       Œ y )Nrg   rr   )	r   r   r   r   r   r   r   r   ra   )rg   rr   rO   s      r=   Útest_core_relationalru   Š   s   € Üˆs‹€AÜˆs‹€AÜœ  A›¬´[ÀÀAÓ5FÜœ  A›¬
´J¸qÀ!Ó4DÜÔ!2°1°aÓ!8¼.Ü˜Q Ó"¤J´
¸1¸aÓ0@ðBò ˆô 	ˆa�ñ	r?   c                  ó^   — t        d«      } t        t        | d«      fD ]  }t        |«       Œ y ©Nrg   rB   )r   r   ra   ©rg   rO   s     r=   Útest_core_addry   ”   ó,   € Üˆs‹€AÜ”3�q˜!“9Ðò ˆÜˆa�ñr?   c                  ó^   — t        d«      } t        t        | d«      fD ]  }t        |«       Œ y rw   )r   r    ra   rx   s     r=   Útest_core_mulr|   š   rz   r?   c                  ó^   — t        d«      } t        t        | d«      fD ]  }t        |«       Œ y rw   )r   r!   ra   rx   s     r=   Útest_core_powerr~       rz   r?   c                  ó„   — t        d«      } t        t        | «      t        t        t        t
        fD ]  }t        |«       Œ y rf   )r   r"   r#   r$   r%   r&   ra   ©rg   Úfs     r=   Útest_core_functionr‚   ¦   s5   € Üˆs‹€AÜœ* Q›-¬´=Ä&Üðò ˆäˆa�ñr?   c                  ó0   — t        d«      } t        | «       y )Nr�   )r#   ra   )r�   s    r=   Útest_core_undefinedfunctionsr„   ­   s   € Ü�‹€AÜ	ˆ!…Hr?   c                  óR   — t        d«      } t        d«      }t         || «      «       y )NÚ_long_unique_name_1Ú_long_unique_name_2)r   r#   ra   r€   s     r=   Útest_core_appliedundefrˆ   ²   s#   € ÜÐ$Ó%€AÜÐ&Ó'€AÜ	‰!ˆA‹$…Kr?   c                  óH   — t         t        dd«      fD ]  } t        | «       Œ y )Nr   r@   )r'   ra   rc   s    r=   Útest_core_intervalrŠ   ¸   s#   € Üœ  A›Ð'ò ˆÜˆa�ñr?   c                  óF   — t         t        d«      fD ]  } t        | «       Œ y )Nr   )r(   ra   rc   s    r=   Útest_core_multidimensionalrŒ   ½   s!   € Üœ 1›Ð&ò ˆÜˆa�ñr?   c                  ó"  ‡— g d¢} t         j                   t         j                  g}|| D �‡cg c]  Šˆfd„‘Œ	 c}z  }t        r|d„ gz  }t        d«      t        d«      t        d«      t	        dd«      t
        t        t        t        t         t        t        t        j                  t        j                  t        j                  t        j                  t        j                   t        j"                  fD ]  }|D ]  } ||«      |u rŒJ ‚ Œ y c c}w )N)r   r6   r@   rA   rB   c                 óV   •— t        j                  t        j                  | ‰«      «      S r8   )r9   rY   r:   )rg   Úprotos    €r=   r>   z!test_Singletons.<locals>.<lambda>Å   s   ø€ œ&Ÿ,™,¤v§|¡|°A°uÓ'=Ó>€ r?   c                 óR   — t         j                  t         j                  | «      «      S r8   )r.   rY   r:   )rg   s    r=   r>   z!test_Singletons.<locals>.<lambda>È   s   € œk×/Ñ/´×0AÑ0AÀ!Ó0DÓE€ r?   éÿÿÿÿr   r6   r@   )rR   rS   r.   r   r   r   r   r   r   r   r   r+   ÚGoldenRatioÚTribonacciConstantÚ
EulerGammaÚCatalanÚEmptySetÚIdentityFunction)r^   Úcopiersr�   ÚobjÚfuncs     `  r=   Útest_Singletonsr›   Â   sÚ   ø€ Ú€IÜ�y‰yœ$Ÿ-™-Ð(€GØØ"÷$Øõ ?ò $ñ $€GåØÑEÐFÑFˆä˜“œW Q›Z¬°«´X¸aÀ³^ÄRÌÌAÜ”�”Sœ#œqŸ}™}¬a×.BÑ.BÜ�L‰Lœ!Ÿ)™)¤Q§Z¡Z´×1CÑ1CðEò $ˆð ò 	$ˆDÙ˜“9 Ò#Ð#Ð#ñ	$ñ$ùò$s   ¬D)Ú	FreeGroupc                  ó0   — t        t        d«      d¬«       y )Nzx, y, zFrn   )ra   rœ   r4   r?   r=   Útest_free_grouprž   Ó   s   € Ü	Œ)�IÓ
¨5Ö1r?   );Ú	PiecewiseÚ
lowergammaÚacoshÚ
chebyshevuÚ
chebyshevtÚlnÚchebyshevt_rootÚlegendreÚ	HeavisideÚ	bernoulliÚcothÚtanhÚassoc_legendreÚsignÚargÚasinÚ
DiracDeltaÚreÚrfÚAbsÚ
uppergammaÚbinomialÚsinhÚcosÚcotÚacosÚacotÚgammaÚbellÚhermiteÚharmonicÚLambertWÚzetaÚlogÚ	factorialÚasinhÚacothÚcoshÚdirichlet_etaÚEijkÚloggammaÚerfÚceilingÚimÚ	fibonacciÚ
tribonacciÚ	conjugateÚtanÚchebyshevu_rootÚfloorÚatanhro   ÚsinÚatanÚffÚlucasÚatan2Ú	polygammaÚexpc                  óÎ  — g t         ‘t        ‘t        ‘t        ‘t        ‘t
        ‘t        ‘t        ‘t        ‘t        ‘t        ‘t        ‘t        ‘t        ‘t        ‘t        ‘t         ‘t"        ‘t$        ‘t&        ‘t(        ‘t*        ‘t,        ‘t.        ‘t        ‘t0        ‘t2        ‘t4        ‘t6        ‘t8        ‘t:        ‘t<        ‘t>        ‘t@        ‘tB        ‘tD        ‘tF        ‘tH        ‘tJ        ‘tL        ‘tN        ‘tP        ‘tR        ‘­} tT        tV        tX        tZ        t\        t^        t`        tb        td        tf        th        f}tk        d«      \  }}}tl        tn        tq        |||«      ts        d|dk  f|dz  |dk  f|dz  df«      tt        f}| D ]   }tw        |«        ||«      }tw        |«       Œ" |D ]!  }tw        |«        |||«      }tw        |«       Œ# |D ]  }tw        |«       Œ y )Núx,y,zr   r‘   r@   r6   rA   T)<r¡   r¤   r§   rÁ   r¨   r©   rª   r¬   r­   r®   r¯   r°   r²   rµ   r¶   r·   r¸   r¹   rº   r»   r½   r¾   r¿   rÀ   rÂ   rÃ   rÄ   rÅ   rÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÐ   rÑ   rÒ   rÓ   rÕ   rØ   r±   rÔ   r    r¢   r£   r´   rÖ   r×   r¼   r¦   r³   r,   r¥   rÏ   rÆ   rŸ   r«   ra   )Úone_varÚtwo_varrg   rr   ÚzÚothersÚclsrO   s           r=   Útest_functionsrà   á   s�  € ðMŒuð M”bð Mœ)ð M¤Yð M´	ð M¼4ð MÄð MÜðMÜðMÜðMÜ'ðMÜ)+ðMÜ-0ðMÜ26ðMÜ8;ðMÜ=@ðMÜBFðMÜHLðMäðMäðMä!ðMä#+ðMä-1ðMä36ðMä8AðMäCHðMô ðMô ðMô 'ðMô )1ðMô 36ðMô 8?ðMô ACðMô ENðMô ð	Mô "ð	Mô $'ð	Mô ).ð	Mô 05ð	Mô 7:ð	Mô <@ð	Mô BGð	Mô ILñ	M€Gô
 ”2”z¤:¬z¼8Ü”9œg¤x´ð=€Gä�gÓ�G€A€qˆ!Üœ´°Q¸¸1³Ü˜˜1˜r™6�{ Q¨¡T¨1°©6 N°Q¸±T¸4°LÓAÜð€Fð ò ˆÜˆcŒ
Ù�‹FˆÜˆa�ðð ò ˆÜˆcŒ
Ù��1‹IˆÜˆa�ðð ò ˆÜˆc�
ñr?   )ÚGeometryEntity)ÚPoint)ÚCircleÚEllipse)ÚLineÚLinearEntityÚRayÚSegment)ÚPolygonÚRegularPolygonÚTrianglec                  óÞ  — t        dd«      } t        dd«      }t        dd«      }t        dd«      }t        t        «       t         | t        t        | d«      t        t        | dd«      t        t	        | |«      t
        t        | |«      t        t        | |«      t        t        | |«      t        t        | |||«      t        t        | dd«      t        t        | ||«      fD ]  }t        |d¬«       Œ y )	Nr6   r@   rA   r   rB   é   Frn   )râ   rá   rã   rä   rå   ræ   rç   rè   ré   rê   rë   ra   )Úp1Úp2Úp3Úp4rO   s        r=   Útest_geometryrò      sÅ   € Ü	ˆq�!‹€BÜ	ˆq�!‹€BÜ	ˆq�!‹€BÜ	ˆq�!‹€BäœÓ(¬%°´V¼VÀBÈ»]Ü”˜˜Q Ó"¤D¬$¨r°2«,¼Ü�R˜Óœc¤3 r¨2£;´¼ÀÀR»Ü”˜˜R  RÓ(¬.Ü˜2˜q !Ó$¤h´¸¸RÀÓ0DðFò #ˆô 	ˆa˜EÖ"ñ#r?   )ÚIntegralc                  ó\   — t        d«      } t        t        | «      fD ]  }t        |«       Œ y rf   )r   ró   ra   rx   s     r=   Útest_integralsrõ     s*   € Üˆs‹€AÜœ ›Ð$ò ˆÜˆa�ñr?   )ÚLogicc                  óF   — t         t        d«      fD ]  } t        | «       Œ y ©Nr6   )rö   ra   rc   s    r=   Ú
test_logicrù     s!   € Ü”U˜1“XÐò ˆÜˆa�ñr?   )ÚMatrixÚSparseMatrixc                  ó|   — t         t        g d¢«      t        t        ddgddgg«      fD ]  } t        | ddg¬«       Œ y )	N©r6   r@   rA   r6   r@   rA   rB   Ú_smatÚ_mat©rN   )rú   rû   ra   rc   s    r=   Útest_matricesr  "  sA   € Ü”fšYÓ'¬´|ÀaÈÀVÈaÐQRÈVÐDTÓ7UÐVò /ˆÜˆa˜W fÐ-Ö.ñ/r?   )ÚSievec                  óD   — t         t        «       fD ]  } t        | «       Œ y r8   )r  ra   rc   s    r=   Útest_ntheoryr  *  s   € Ü”U“WÐò ˆÜˆa�ñr?   )ÚPauli)ÚUnitc                  óZ   — t         t        t        t        d«      fD ]  } t        | «       Œ y rø   )r  r   r  ra   rc   s    r=   Útest_physicsr  3  s%   € Ü”Eœ5¤%¨£(Ð+ò ˆÜˆa�ñr?   c                  ó8  — ddl m} m} ddlm} ddlm}m} ddlm	}m
}m}m} ddlm}	 ddlm}
 ddlm} dd	lm} dd
lm} ddlm}m}m}m}m}m}m}m} ddl m!} ddl"m#} ddl$m%} |  | dd«      ||||||||||	|
||||||||||||||fD ]  }tM        |«       Œ y )Nr   )ÚColorGradientÚColorScheme)ÚManagedWindow)ÚPlotÚ
ScreenShot)ÚPlotAxesÚPlotAxesBaseÚPlotAxesFrameÚPlotAxesOrdinate)Ú
PlotCamera)ÚPlotController)Ú	PlotCurve)ÚPlotInterval)ÚPlotMode)ÚCartesian2DÚCartesian3DÚCylindricalÚParametricCurve2DÚParametricCurve3DÚParametricSurfaceÚPolarÚ	Spherical)Ú
PlotObject)ÚPlotSurface)Ú
PlotWindowgš™™™™™É?gš™™™™™Ù?)'Ú&sympy.plotting.pygletplot.color_schemer
  r  Ú(sympy.plotting.pygletplot.managed_windowr  Úsympy.plotting.plotr  r  Ú#sympy.plotting.pygletplot.plot_axesr  r  r  r  Ú%sympy.plotting.pygletplot.plot_camerar  Ú)sympy.plotting.pygletplot.plot_controllerr  Ú$sympy.plotting.pygletplot.plot_curver  Ú'sympy.plotting.pygletplot.plot_intervalr  Ú#sympy.plotting.pygletplot.plot_moder  Ú$sympy.plotting.pygletplot.plot_modesr  r  r  r  r  r  r  r  Ú%sympy.plotting.pygletplot.plot_objectr   Ú&sympy.plotting.pygletplot.plot_surfacer!  Ú%sympy.plotting.pygletplot.plot_windowr"  ra   )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"  rO   s                             r=   Útest_plottingr0  ;  sœ   € çQÝFß4ßkÓkÝ@ÝHÝ>ÝDÝ<÷R÷ Ró Rå@ÝBÝ@à‘} S¨#Ó.°¸]Ø�t˜Z¨°<ØÐ'¨°^Ø�< ¨;¸ØÐ&Ð(9Ø˜5 )¨Z¸Øðò ˆô 	ˆa�ñr?   c                  ó�   — ddl m}  ddlm} ddlm} t         | d«      «       t         |dd¬«      «       t         |«       «       y )	Nr   )r  )r  )r  Úrainbowr6   F)Úvisible)r#  r  r%  r  r&  r  ra   )r  r  r  s      r=   Útest_plotting2r4  V  s6   € õ Cå(å<ô 
‰+�iÓ
 Ô!Ü	‰$ˆq˜%Ô
 Ô!Ü	‰(‹*Õr?   )ÚZZ)ÚQQ)Úlex)ÚPolyc                  óž   — ddl m}  t        d«      }t        t        ||«      fD ]  }t	        |«       Œ |  | |«      fD ]  }t	        |«       Œ y )Nr   )ÚPurePolyrg   )Úsympy.polys.polytoolsr:  r   r8  ra   )r:  rg   rO   s      r=   Útest_pickling_polys_polytoolsr<  s  sP   € Ý.äˆs‹€Aä”D˜˜A“JÐò ˆÜˆa�ðð ™ ›Ð$ò ˆÜˆa�ñr?   c            	      óÔ  — ddl m} m}m} |  | t	        d«      gt	        d«      gt	        d«      ggt        «      fD ]  }t        |dg¬«       Œ | |t	        d«      t	        d«      gt	        d«      t	        d«      gft        «      fD ]  }t        |«       Œ | |t        d«      t        d«      gt        d«      t        d«      t        d«      gt        «      fD ]  }t        |«       Œ y )Nr   )ÚDMPÚDMFÚANPr6   r@   rA   Úrepr   )Úsympy.polys.polyclassesr>  r?  r@  r5  ra   r6  )r>  r?  r@  rO   s       r=   Útest_pickling_polys_polyclassesrC  ‚  sÊ   € ß5Ñ5à‘3œ˜A›˜¤" Q£% ¬2¨a«5¨'Ð2´BÓ7Ð8ò %ˆÜˆa˜U˜GÖ$ð%à‘3œ˜A›¤ 1£˜¬¨A«´°1³¨Ð7¼Ó<Ð=ò ˆÜˆa�ðà‘3œ˜1›œr !›u�~¬¨1«¬r°!«u´b¸³eÐ'<¼bÓAÐBò ˆÜˆa�ñr?   c                  ó¾   — ddl m}   | dt        t        «      }| |fD ]  }t	        |ddg¬«       Œ |j
                  |j                  fD ]  }t	        |ddgd¬«       Œ y )Nr   )ÚPolyRingrÚ   r6   )r\   F)r\   r]   )Úsympy.polys.ringsrE  r5  r7  ra   ÚdtypeÚone)rE  ÚringrO   s      r=   Útest_pickling_polys_ringsrJ  Œ  se   € õ
 +á�GœR¤Ó%€Dà˜Ðò !ˆÜˆa˜!˜Q˜Ö ð!ð �j‰j˜$Ÿ(™(Ð#ò 3ˆÜˆa˜!˜Q˜¨EÖ2ñ3r?   c                   ó   — y r8   r4   r4   r?   r=   Útest_pickling_polys_fieldsrL  ›  s   € Ør?   c                  óF   — ddl m}  |  | dd«      fD ]  }t        |«       Œ y )Nr   )ÚPythonRationalr6   é   )Ú"sympy.polys.domains.pythonrationalrN  ra   )rN  rO   s     r=   Útest_pickling_polys_elementsrQ  ¬  s)   € ÝAð ™n¨Q°Ó2Ð3ò ˆÜˆa�ñr?   c                  óº  — ddl m}  ddlm} |  | «       fD ]  }t	        |d¬«       Œ | |«       fD ]  }t	        |d¬«       Œ t
        �Bddlm} ddlm	} | |«       fD ]  }t	        |d¬«       Œ | |«       fD ]  }t	        |d¬«       Œ ddl
m} dd	lm} | |t        t        d
«      «      fD ]  }t	        |d¬«       Œ | |«       fD ]  }t	        |d¬«       Œ y )Nr   )ÚPythonIntegerRing)ÚPythonRationalFieldFrn   )ÚGMPYIntegerRing)ÚGMPYRationalField)ÚAlgebraicField)ÚExpressionDomainrA   )Ú%sympy.polys.domains.pythonintegerringrS  Ú'sympy.polys.domains.pythonrationalfieldrT  ra   Ú_gmpyÚ#sympy.polys.domains.gmpyintegerringrU  Ú%sympy.polys.domains.gmpyrationalfieldrV  Ú"sympy.polys.domains.algebraicfieldrW  Ú$sympy.polys.domains.expressiondomainrX  r6  ro   )rS  rT  rO   rU  rV  rW  rX  s          r=   Útest_pickling_polys_domainsr`  Ä  s   € åGÝKð  Ñ!2Ó!4Ð5ò #ˆÜˆa˜EÖ"ð#ð "Ñ#6Ó#8Ð9ò #ˆÜˆa˜EÖ"ð#ô ÐåGÝKð "¡?Ó#4Ð5ò 	'ˆAÜ�! Ö&ð	'ð $Ñ%6Ó%8Ð9ò 	'ˆAÜ�! Ö&ð	'õ
 Bõ Fð ™n¬R´°a³Ó9Ð:ò #ˆÜˆa˜EÖ"ð#ð Ñ 0Ó 2Ð3ò #ˆÜˆa˜EÖ"ñ#r?   c                  óð   — ddl m} m}m}m} |  | «       fD ]  }t        |«       Œ | |«       fD ]  }t        |«       Œ | |«       fD ]  }t        |«       Œ | | | «       «      fD ]  }t        |«       Œ y )Nr   )ÚLexOrderÚGradedLexOrderÚReversedGradedLexOrderÚInverseOrder)Úsympy.polys.orderingsrb  rc  rd  re  ra   )rb  rc  rd  re  rO   s        r=   Útest_pickling_polys_orderingsrg     s�   € ÷.ó .ð ™›
Ð#ò ˆÜˆa�ðð ™nÓ.Ð/ò ˆÜˆa�ðð %Ñ&<Ó&>Ð?ò ˆÜˆa�ðð ™L©«Ó4Ð5ò ˆÜˆa�ñr?   c                  ó¢   — ddl m} m} t        d«      \  }}}|  | d«      fD ]  }t	        |«       Œ | |d|||f«      fD ]  }t	        |«       Œ y )Nr   )ÚMonomialOpsÚMonomialrÚ   rA   rý   )Úsympy.polys.monomialsri  rj  r,   ra   )ri  rj  rg   rr   rÝ   rO   s         r=   Útest_pickling_polys_monomialsrl    s^   € ß;Ü�gÓ�G€A€qˆ!à™; q›>Ð*ò ˆÜˆa�ðð ™ ¨Q°°1¨IÓ6Ð7ò ˆÜˆa�ñr?   c                  ó  — ddl m} m}m}m}m}m}m}m}m	}m
}	m}
m}m}m}m}m}m}m}m} |  | «       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ |	 |	«       fD ]  }t)        |«       Œ |
 |
«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ | |«       fD ]  }t)        |«       Œ y )Nr   )ÚHeuristicGCDFailedÚHomomorphismFailedÚIsomorphismFailedÚExtraneousFactorsÚEvaluationFailedÚRefinementFailedÚCoercionFailedÚNotInvertibleÚNotReversibleÚNotAlgebraicÚDomainErrorÚPolynomialErrorÚUnificationFailedÚGeneratorsErrorÚGeneratorsNeededÚUnivariatePolynomialErrorÚMultivariatePolynomialErrorÚOptionErrorÚ	FlagError)Úsympy.polys.polyerrorsrn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  ra   )rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  rO   s                       r=   Útest_pickling_polys_errorsr‚  "  s„  € ÷÷ ÷ ÷ ÷ ñ ð( !Ñ"4Ó"6Ð7ò ˆÜˆa�ðð !Ñ"4Ó"6Ð7ò ˆÜˆa�ðð  Ñ!2Ó!4Ð5ò ˆÜˆa�ðð  Ñ!2Ó!4Ð5ò ˆÜˆa�ðð Ñ 0Ó 2Ð3ò ˆÜˆa�ðð Ñ 0Ó 2Ð3ò ˆÜˆa�ðð ™nÓ.Ð/ò ˆÜˆa�ðð ™]›_Ð-ò ˆÜˆa�ðð ™]›_Ð-ò ˆÜˆa�ðð ™L›NÐ+ò ˆÜˆa�ðð ™;›=Ð)ò ˆÜˆa�ðð ™Ó0Ð1ò ˆÜˆa�ðð  Ñ!2Ó!4Ð5ò ˆÜˆa�ðð ™Ó0Ð1ò ˆÜˆa�ðð Ñ 0Ó 2Ð3ò ˆÜˆa�ðð (Ñ)BÓ)DÐEò ˆÜˆa�ðð *Ñ+FÓ+HÐIò ˆÜˆa�ðð ™;›=Ð)ò ˆÜˆa�ðð ™›Ð%ò ˆÜˆa�ñr?   c                  ó´   — ddl m} m} t        d«      }|dz  |z   dz   }|  | |d«      fD ]  }t	        |«       Œ | ||t
        «      fD ]  }t	        |«       Œ y )Nr   )ÚCRootOfÚRootSumrg   rA   )Úsympy.polys.rootoftoolsr„  r…  r   ra   rØ   )r„  r…  rg   r�   rO   s        r=   Útest_pickling_polys_rootoftoolsr‡  ƒ  sc   € ß8äˆs‹€AØ	ˆ1‰ˆq‰�1‰€Aà‘w˜q !“}Ð%ò ˆÜˆa�ðð ‘w˜q¤#“Ð'ò ˆÜˆa�ñr?   )ÚLatexPrinter)ÚMathMLContentPrinterÚMathMLPresentationPrinter)ÚPrettyPrinter)Ú
prettyFormÚ
stringPict)ÚPrinter)ÚPythonPrinterc                  óÂ   — t         t        «       t        t        t        t        t
        t        d«      t        t        «       t        t        «       fD ]  } t        | «       Œ y )Nr;   )	rˆ  r‰  rŠ  r‹  rŒ  r�  rŽ  r�  ra   rc   s    r=   Útest_printingr‘  ˜  sC   € ÜœL›NÔ,@Ü'¬¼
ÄJÜ˜‹oœw¬«	´=Ü‹oðò ˆô 	ˆa�ñ	r?   c                  ó*   — t        t        «       «       y r8   )ra   r‰  r4   r?   r=   Útest_printing1r“     s   € ä	Ô
Ó
 Õ!r?   c                  ó*   — t        t        «       «       y r8   )ra   rŠ  r4   r?   r=   Útest_printing2r•  ¥  s   € ä	Ô
#Ó
%Õ&r?   c                  ó*   — t        t        «       «       y r8   )ra   r‹  r4   r?   r=   Útest_printing3r—  ª  s   € ä	Œ-‹/Õr?   )ÚLimit)ÚOrderc                  ó”   — t        d«      } t        d«      }t        t        | |d«      t        t        | «      fD ]  }t        |«       Œ y )NÚerg   r6   )r   r˜  r™  ra   )r›  rg   rO   s      r=   Útest_seriesrœ  ³  s?   € Üˆs‹€AÜˆs‹€AÜ”U˜1˜a “^¤U¬E°!«HÐ5ò ˆÜˆa�ñr?   )ÚProduct)ÚSumc            	      óŠ   — t        d«      } t        t        | | ddf«      t        t        | | ddf«      fD ]  }t        |«       Œ y )Nrg   r@   rB   )r   r�  rž  ra   rx   s     r=   Útest_concreter   ¾  sD   € Üˆs‹€AÜ”w˜q 1 a¨ )Ó,¬c´3°q¸1¸aÀ¸)Ó3DÐEò ˆÜˆa�ñr?   c                  ó6   — t        ddd¬«      } t        | «       y )NÚmessagez1.0zactive-deprecations)Údeprecated_since_versionÚactive_deprecations_target)r*   ra   )Úws    r=   Útest_deprecation_warningr¦  Ã  s   € Ü 	ÀEÐf{Ô|€AÜ	ˆ!…Hr?   c                  ó–   — t        j                  t        j                  t        j                  «      «      t        j                  k(  sJ ‚y r8   )r9   rY   r:   r+   ÚHalfr4   r?   r=   Útest_issue_18438r©  Ç  s*   € Ü�<‰<œŸ™¤Q§V¡VÓ,Ó-´·±Ò7Ð7Ñ7r?   c                  óN   — d} t        j                  | «      t        d«      k(  sJ ‚y )Nsi   €•^       Œsympy.core.power”ŒPow”“”Œsympy.core.numbers”ŒInteger”“”K…”R”}”bhŒHalf”“”)R”}”b†”R”}”b.r@   )r9   rY   ro   )Údatas    r=   Ú!test_unpickle_from_older_versionsr¬  Ì  s)   € ð	8ð 	ô �<‰<˜Ó¤ a£Ò(Ð(Ñ(r?   )èrW   rR   r9   Úsympy.physics.unitsr   Úsympy.testing.pytestr   r   r   Úsympy.core.basicr   r   Úsympy.core.singletonr	   Úsympy.core.symbolr
   r   r   r   Úsympy.core.numbersr   r   r   r   r   r   r   r   r   r   Úsympy.core.relationalr   r   r   r   r   r   r   Úsympy.core.addr   Úsympy.core.mulr    Úsympy.core.powerr!   Úsympy.core.functionr"   r#   r$   r%   r&   Úsympy.sets.setsr'   Úsympy.core.multidimensionalr(   Úsympy.external.gmpyr)   r[  Úsympy.utilities.exceptionsr*   r+   r,   Úsympy.externalr-   r.   rF   rH   rE   ra   rd   rh   rl   rp   rs   ru   ry   r|   r~   r‚   r„   rˆ   rŠ   rŒ   r›   Úsympy.combinatorics.free_groupsrœ   rž   Úsympy.functionsrŸ   r    r¡   r¢   r£   r¤   r¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r¯   r°   r±   r²   r³   r´   rµ   r¶   r·   r¸   r¹   rº   r»   r¼   r½   r¾   r¿   rÀ   rÁ   rÂ   rÃ   rÄ   rÅ   rÆ   rÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   ro   rÒ   rÓ   rÔ   rÕ   rÖ   r×   rØ   rà   Úsympy.geometry.entityrá   Úsympy.geometry.pointrâ   Úsympy.geometry.ellipserã   rä   Úsympy.geometry.linerå   ræ   rç   rè   Úsympy.geometry.polygonré   rê   rë   rò   Úsympy.integrals.integralsró   rõ   Úsympy.core.logicrö   rù   Úsympy.matricesrú   rû   r  Úsympy.ntheory.generater  r  Úsympy.physics.paulialgebrar  r  r  r0  r4  Úsympy.polys.domains.integerringr5  Ú!sympy.polys.domains.rationalfieldr6  rf  r7  r;  r8  r<  rC  rJ  rL  rQ  r`  rg  rl  r‚  r‡  Úsympy.printing.latexrˆ  Úsympy.printing.mathmlr‰  rŠ  Úsympy.printing.pretty.prettyr‹  Ú sympy.printing.pretty.stringpictrŒ  r�  Úsympy.printing.printerrŽ  Úsympy.printing.pythonr�  r‘  r“  r•  r—  Úsympy.series.limitsr˜  Úsympy.series.orderr™  rœ  Úsympy.concrete.productsr�  Úsympy.concrete.summationsrž  r   r¦  r©  r¬  r4   r?   r=   ú<module>rÕ     s¡  ðÛ Û Û å %ç ?Ñ ?ç (Ý 2ß 6Ó 6÷*÷ *÷ *÷7÷ 7ñ 7å Ý Ý  ÷õ å $Ý 1å -Ý >å "Ý %å (Ù˜MÓ*€ð Øð€ð ØðÐ ð ðÐ ð
  D°Ró 4òvòòò#òòòòòòòò
òò
ò
$õ 6ò2÷0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0÷ 0ñ 0òõ0 1Ý &ß 2ß @Ó @ß DÑ Dò#õ /òõ #ò÷
 0ò/õ
 )òõ
 -Ý $òð ñó ðð4 ñó ðõ. /Ý 0Ý %Ý &ò	òð ñ3ó ð3ò	ò"ò09#òxò0òTòB
õ .ß QÝ 6ß CÝ *Ý /òð ñ"ó ð"ð ñ'ó ð'ð ñó ðõ &Ý $òõ ,Ý )òò
ò8ó
)r?   