+
    ‹°³j‡; ã                  ó4  a € 0 t $ R t^ RIHt ^ RIt^ RIHt ^ RIHtH	t	 ^ RI
Ht ^ RIHt ^ RIHt ^ RIHt ^ R	IHt ^ R
IHtHtHtHtHt ^ RIHt ^ RIHt ^ RIHtH t  ^ RI!H"t"H#t#H$t$ ^ RI%H&t&H't' ^ RI(H)t)H*t*H+t+H,t, ^ RI-H.t. ^ RI/H0t0 ^ RI1H2t2H3t3H4t4H5t5H6t6H7t7H8t8H9t9H:t:H;t;H<t< ^ RI=H>t>H?t?H@t@ ^ RIAHBtB ^ RICHDtDHEtEHFtFHGtG ^ RIHHItI ^ RIJHKtKHLtL ^ RIMHNtNHOtOHPtPHQtQ ^ RIRHStSHTtTHUtUHVtV ^ RIWHXtXHYtY ^ RIZH[t[H\t\ ^ RI]H^t^H_t_H`t`HataHbtbHctcHdtdHeteHftfHgtgHhth ^ RIiHjtj ^ RIkHltlHmtm ^ R InHoto ^R!IpHqtq ^ R"IrHstsHtttHutuHvtvHwtw ^ R#IxHytyHztz ^ R$I{H|t| ^ R%I}H~t ^ R&I}H€t� ])! R'4      t‚R( tƒR) t„^ R*I…H†t† ]†! R+4      t‡R, R- ltˆ ! R. R/]‰4      tŠR0 t‹R1 tŒR2 t�R3 tŽR4 t�R5 t�R6 t‘R7 t’R8 t“R9 t”/ t•R:]–R;&   R< t—R= t˜R> t™RWR? ltšR@ t›RXRA ltœRB t�RXRC ltžRD tŸRXRE lt RF t¡RG t¢RH t£RI t¤RJ t¥Rs¦]]‡RWRK l4       4       t§RWRL lt¨RM t©RN tªRO t«]‡RP 4       t¬RQ t­RR t®RS t¯RT t°]‡RXRU l4       t±RV t²R# )Ya¿  
Integrate functions by rewriting them as Meijer G-functions.

There are three user-visible functions that can be used by other parts of the
sympy library to solve various integration problems:

- meijerint_indefinite
- meijerint_definite
- meijerint_inversion

They can be used to compute, respectively, indefinite integrals, definite
integrals over intervals of the real line, and inverse laplace-type integrals
(from c-I*oo to c+I*oo). See the respective docstrings for details.

The main references for this are:

[L] Luke, Y. L. (1969), The Special Functions and Their Approximations,
    Volume 1

[R] Kelly B. Roach.  Meijer G Function Representations.
    In: Proceedings of the 1997 International Symposium on Symbolic and
    Algebraic Computation, pages 205-211, New York, 1997. ACM.

[P] A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev (1990).
    Integrals and Series: More Special Functions, Vol. 3,.
    Gordon and Breach Science Publisher
)ÚannotationsN)ÚSYMPY_DEBUG)ÚSÚExpr)ÚAdd)ÚBasic)Úcacheit)ÚTuple)Úfactor_terms)ÚexpandÚ
expand_mulÚexpand_power_baseÚexpand_trigÚFunction)ÚMul)Úilcm)ÚRationalÚpi)ÚEqÚNeÚ_canonical_coeff)Údefault_sort_keyÚordered)ÚDummyÚsymbolsÚWildÚSymbol)Úsympify)Ú	factorial)ÚreÚimÚargÚAbsÚsignÚ
unpolarifyÚpolarifyÚ
polar_liftÚprincipal_branchÚunbranched_argumentÚperiodic_argument)ÚexpÚ	exp_polarÚlog)Úceiling)ÚcoshÚsinhÚ_rewrite_hyperbolics_as_expÚHyperbolicFunction©Úsqrt)Ú	PiecewiseÚpiecewise_fold)ÚcosÚsinÚsincÚTrigonometricFunction)ÚbesseljÚbesselyÚbesseliÚbesselk)Ú
DiracDeltaÚ	Heaviside)Ú
elliptic_kÚ
elliptic_e)ÚerfÚerfcÚerfiÚEiÚexpintÚSiÚCiÚShiÚChiÚfresnelsÚfresnelc)Úgamma)ÚhyperÚmeijerg)ÚSingularityFunction)ÚIntegral)ÚAndÚOrÚBooleanAtomÚNotÚBooleanFunction)ÚcancelÚfactor)Úmultiset_partitions)Údebug)ÚdebugfÚzc                óü   a€ \        V 4      p \        V R R4      '       dO   \        ;QJ d)    V3R lV P                   4       F  '       d   K   R# 	  R# ! V3R lV P                   4       4      # V P                  ! S!  # )Úis_PiecewiseFc              3  ó>   <"  € T F  p\        V.SO5!  x € K  	  R # 5i©N)Ú_has)Ú.0ÚiÚfs   & €ÚZ/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/integrals/meijerint.pyÚ	<genexpr>Ú_has.<locals>.<genexpr>T   s   øé € Ð1© 1”4˜�;˜A—;�;«ùs   ƒT)r5   ÚgetattrÚallÚargsÚhas)Úresrd   s   &jre   ra   ra   O   s]   ø€ ô ˜Ó
€CÜˆs�N E×*Ò*ß‹sÔ1¨¯ªÓ1�sŒsÐ1ŠsÐ1ˆsÔ1¨¯ªÓ1Ó1Ð1Ø�7Š7�A‰;Ðó    c                óâ  a aa	a
aaaaaaa€ R p\        \        VR4      4      w  ooo	op\        RR .R7      oS\        S,          ,          oS\        P
                  RR3V 3R llo
RV 3R llpR	 pS	V! S	4      RR3.S R&    ! R
 R\        4      pS
! \        SS,
          4      SS,
          S	^,
          ,          ,          S	.. . ^ .SS,          \        S	4      SS	^,
          ,          ,          \        S^ 8„  4      4       S
! \        SS,
          4      SS,
          S	^,
          ,          ,          . S	.^ .. SS,          \        S	4      SS	^,
          ,          ,          \        S^ 8„  4      4       S
! \        \        SS,          ^S,          ,          ,
          4      SS,
          S	^,
          ,          ,          S	.. . ^ .SS,          \        S	4      SS	^,
          ,          ,          \        S^ 8„  4      4       S
! \        SS,          ^S,          ,          \        ,
          4      SS,
          S	^,
          ,          ,          . S	.^ .. SS,          \        S	4      SS	^,
          ,          ,          \        S^ 8„  4      4       S
! SS,           S	) ,          ^S	,
          .. ^ .. SS,          SS	) ,          \        S	4      ,          \        V! S	4      4      R7       S
! \        SS,
          4      S	) ,          ^S	,
          .^S	,
          ^,          .^ .^S	,
          ^,          .SS,          ^\        \        S	,          ^,          4      ,          \        ^S	,
          4      ,          \        S4      S	) ,          ,          \        S	4      ^8  4       S
! SS	,          SS	,          ,
          SS,
          ,          ^ S	.. ^ S	.. SS,          SS	^,
          ,          \        S	\        ,          4      ,          \        ,          4       R oVV	V
VV3R lpV! ^ ^4       V! ^ R4       V! \        P                  ^4       V! \        P                  R4       VV	V
VVV3R lpV! ^ ^4       V! ^ R4       V! \        P                  ^4       V! \        P                  R4       S
! \!        \#        R4      S,          4      . . ^ .. 4       S
! \%        S4      . ^.\        P                  .^^ .S^,          ^,          \        \'        ^^4      ,          4       S
! \)        S4      . \        P                  .^ .\        P                  \        P                  .S^,          ^,          \        \'        ^^4      ,          4       S
! \        S4      . . \        P                  .^ .S^,          ^,          \+        \        4      4       S
! \-        S4      . . ^ .\        P                  .S^,          ^,          \+        \        4      4       S
! \/        S4      . . ^ .\'        R^4      .S^,          ^,          \+        \        4      ^,          4       VV3R loVV3R loV! \1        S4      S,          \        ^S,
          4      ,          SR4       V! \1        S4      S,          \        S^,
          4      ,          SR4       VV3R lpV! \1        S4      S,          VR4       V! \1        SS	,           4      V! \1        S	4      4      \        P
                  \3        ^^.. ^.^ .SS	,          4      3.,           R4       V! \1        \        SS	,
          4      4      V! \1        \        S	4      4      4      \        \3        ^^.\        P                  .^.^ \        P                  .SS	,          4      3.,           R4       V! \5        S4      V! \        P6                  ) \        ,          4      \        P8                  \3        . ^.^ ^ .. S\#        R4      ,          4      3.,           R4       S
! \;        S4      ^.. \        P                  .^ ^ .S^,          ^,          \+        \        4      ^,          4       S
! \=        S4      . ^.^ ^ .\        P                  .S^,          ^,          \+        \        4      ) ^,          4       S
! \?        S4      \        P                  .. ^ .\'        R^4      \'        R^4      .\#        R4      S^,          ,          ^,          S\+        \        4      ,          ^,          4       S
! \A        S4      . \        P                  ^.^ ^ .\        P                  \        P                  .S^,          ^,          \        \	        R4      ,          ) ^,          4       S
! \C        S	S4      . S	.S	^,
          ^ .. S4       S
! \E        S4      ^.. \        P                  .^ .S^,          ^\+        \        4      ,          4       S
! \G        S4      . ^.^ \        P                  .. S^,          ^\+        \        4      ,          4       S
! \I        S4      \        P                  .. ^ .\'        R^4      .S^,          ) S\+        \        4      ,          4       S
! \K        S4      ^.. \'        ^^4      .^ \'        ^^4      .\        ^,          S^,          ,          ^,          \        P                  4       S
! \M        S4      ^.. \'        ^^4      .^ \'        ^^4      .\        ^,          S^,          ,          ^,          \        P                  4       S
! \O        S	S4      . . S	^,          .S	) ^,          .S^,          ^,          4       S
! \Q        S	S4      . S	^,           ) ^,          .S	^,          S	) ^,          .S	^,           ) ^,          .S^,          ^,          4       S
! \S        S	S4      . ^S	,           ^,          .S	^,          .S	) ^,          ^S	,           ^,          .S^,          ^,          \        4       S
! \U        S	S4      . . S	^,          S	) ^,          .. S^,          ^,          \        P                  4       S
! \W        S4      \        P                  \        P                  .. ^ .^ .S) \        P                  4       S
! \Y        S4      \        P                  ^\        P                  ,          .. ^ .^ .S) \'        R^4      ^,          4       R# )z7Add formulae for the function -> meijerg lookup table. c                ó&   € \        V \        .R 7      # )©Úexclude)r   r\   )Úns   &re   ÚwildÚ"_create_lookup_table.<locals>.wildZ   s   € Ü�A¤˜sÔ#Ð#rm   Úpqabcrr   c                ó4   € V P                   ;'       d    V ^ 8„  # ©é    )Ú
is_Integer©Úxs   &re   Ú<lambda>Ú&_create_lookup_table.<locals>.<lambda>]   s   € ¨¯©×(>Ð(>¸¸Q¹Ð(>rm   )Ú
propertiesTc	                óˆ   <€ S	P                  \        V \        4      . 4      P                  V V\	        WW4V4      3.Wx34       R # r`   )Ú
setdefaultÚ_mytyper\   ÚappendrO   )
ÚformulaÚanÚapÚbmÚbqr!   ÚfacÚcondÚhintÚtables
   &&&&&&&&&€re   ÚaddÚ!_create_lookup_table.<locals>.add`   sD   ø€ Ø×Ñœ ¬!Ó,¨bÓ1×8Ñ8¸'Ø'*¬G°B¸BÀCÓ,HÐ&IÐ%JÈDð:Xö 	Yrm   c                ój   <€ SP                  \        V \        4      . 4      P                  WW#34       R # r`   )r€   r�   r\   r‚   )rƒ   Úinstr‰   rŠ   r‹   s   &&&&€re   ÚaddiÚ"_create_lookup_table.<locals>.addid   s,   ø€ Ø×ÑÜ�GœQÓ ó	%ß%+¡V¨W¸DÐ,GÖ%Hrm   c           	     ó^   € V \        ^.. . ^ .\        4      3V \        . ^.^ .. \        4      3.# ©é   )rO   r\   )Úas   &re   ÚconstantÚ&_create_lookup_table.<locals>.constanth   s>   € Ø”G˜Q˜C  R¨!¨¬aÓ0Ð1Ø”G˜B   a S¨"¬aÓ0Ð1ð3ð 	3rm   c                  ó&   € ] tR t^nt]R 4       tRtR# )Ú2_create_lookup_table.<locals>.IsNonPositiveIntegerc                	óF   € \        V4      pVP                  R J d   V^ 8*  # R# )TN)r$   ry   )Úclsr!   s   &&re   ÚevalÚ7_create_lookup_table.<locals>.IsNonPositiveInteger.evalp   s%   € ä˜S“/ˆCØ�~‰~ Ó%Ø˜a‘x�ñ &rm   © N)Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Úclassmethodrœ   Ú__static_attributes__rž   rm   re   ÚIsNonPositiveIntegerr™   n   s   † à	ñ	 ó 
ô	 rm   r¥   )rŠ   c                ó†   € \         \        R^4      ,          V) V,          ^,          ^^V ,          ,
          ,          ,          # )r”   éÿÿÿÿ)r   r   )Úrr#   Únus   &&&re   ÚA1Ú _create_lookup_table.<locals>.A1ˆ   s/   € Ü”8˜B “?Õ" T E¨"¥H¨Q¥J°!°a¸µcµ'Õ#:Õ:Ð:rm   c                óÆ  <€ S! \        S^,          S,           4      VS,          ,           S,          S^,          S,           V ,          ,          ^S,           ^,          ^^V ,          ,
          S^,          ,           .. SVS,          ,
          ^,          .SVS,          ,           ^,          .SS^,          ,          SS^V ,          ,
          ,          S! WS4      ,          4       R# ©é   Nr2   )r¨   Úsgnrª   r•   rŒ   ÚbÚts   &&€€€€€re   ÚtmpaddÚ$_create_lookup_table.<locals>.tmpadd‹   sŸ   ø€ áŒT�!�Q•$˜•(‹^˜c !�eÕ# aÕ'¨¨A­°­°A­Õ5Ø�!�e�Q�Y˜˜A˜a�C� ! A¥#�Ð&¨Ø�#�a•%�i˜�]ˆO˜q 3 q¥5�y¨!�m˜_¨a°°1µ­fØ��A�a•C•�L™˜A A›Õ&ö	(rm   c                ó0  <€ S! \        SS\        S,          ,          ,           4      V\        S4      ,          \        S^,          ,          ,          ,           S,          SS\        S,          ,          ,           V ,          ,          ^V ,
          VS,          ^,          ,           .^V ,
          VS,          ^,          ,
          .^ \        P                  .. S\        S,          ,          S,          SS^,          V ,
          ,          S! WS4      ,          4       R# r­   )r3   r\   r   ÚHalf)r¨   r¯   rª   r•   rŒ   r°   ÚpÚqs   &&€€€€€€re   r²   r³   —   s±   ø€ ÙŒT�!�aœ˜1�•f•*Ó ¤D¨£G¥¬A°°!µ­HÕ 4Õ4°qÕ8¸!¸aÄÀ1Å½f½*Àq½ÕHØ��U�S˜•U˜1•W�_Ð  A¥¨¨A­¨a­¥Ð0°1´a·f±f°+¸rØŒa��d�F�1�H�a˜!˜A�# �'•l¡2 a¨a£=Õ0ö	2rm   c                óÀ   <€ V S,          p\         P                  V,          \        V4      ,          \        . ^.V^,           ,          ^ .V^,           ,          . S4      3.# r“   )r   ÚNegativeOner   rO   ©ÚsubsÚNrr   r±   s   & €€re   Ú	make_log1Ú'_create_lookup_table.<locals>.make_log1²   sV   ø€ Ø��GˆÜ—‘ Õ!¤)¨A£,Õ.Ü˜˜a˜S ! a¥%�[¨1¨#¨q°1­u­+°r¸1Ó=ð?ð @ð 	@rm   c           	     óˆ   <€ V S,          p\        V4      \        ^.V^,           ,          . . ^ .V^,           ,          S4      3.# r“   )r   rO   rº   s   & €€re   Ú	make_log2Ú'_create_lookup_table.<locals>.make_log2·   sH   ø€ Ø��GˆÜ˜1“Ü˜!˜˜a !�e� b¨"¨q¨c°1°qµ5­k¸1Ó=ð?ð @ð 	@rm   c                ó.   <€ S! V 4      S! V 4      ,           # r`   rž   )r»   r½   rÀ   s   &€€re   Ú	make_log3Ú'_create_lookup_table.<locals>.make_log3Á   s   ø€ Ù˜‹¡¨4£Õ0Ð0rm   z3/2N©Trž   r§   )-ÚlistÚmapr   r\   r   ÚOner   r?   rM   rR   rU   r"   r7   r   r   rµ   r*   r&   r/   r   r.   r3   r6   r8   r,   rO   rE   ÚImaginaryUnitr¹   rG   rH   rI   rJ   rF   rB   rC   rD   rK   rL   r:   r;   r<   r=   r@   rA   )r‹   rs   Úcr�   r–   r¥   r²   rÃ   rª   r•   rŒ   r°   r½   rÀ   rr   r¶   r·   r±   s   f       @@@@@@@@@@re   Ú_create_lookup_tablerË   X   så	  ÿú€ ò$äœ˜T 7Ó+Ó,�M€A€qˆ!ˆQ�ÜˆSÑ>Ð?Ô@€AØ	Œ!ˆQ�$�€Aà)*´·±¸DÀt÷ Y÷Iò3ð ‘X˜a“[ $¨Ð-Ð.€Eˆ"�Iô œxô  ñ Œ	�!�a•%Ó˜!˜a�% 1 q¥5Õ)Õ)¨A¨3°°B¸¸¸Q¸q½SÜˆa‹��Q˜•U•ÕœS  Q¡›Zô)áŒ	�!�a•%Ó˜!˜a�% 1 q¥5Õ)Õ)¨2°¨s°Q°C¸¸Q¸q½SÜˆa‹��Q˜•U•ÕœS  Q¡›Zô)áŒ	”!�q˜•s˜a �c•lÕ"Ó# Q¨¥U¨a°!­eÕ$4Õ4°q°c¸2¸rÀAÀ3ÈÈ!ÍÜˆa‹��Q˜•U•ÕœS  Q¡›Zô)áŒ	�1�Q•3˜!˜A�#•,¤Õ"Ó# Q¨¥U¨a°!­eÕ$4Õ4°b¸1¸#À¸sÀBÈÈ!ÍÜˆa‹��Q˜•U•ÕœS  Q¡›Zô)áˆˆQ��1�"�˜˜A��w  Q C¨¨Q¨q­S°!°q°bµ'¼%À»(Õ2BÜÑ% aÓ(Ó)õ+áŒˆA��E‹
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Œ1�6‰6�2Ô÷2ò 2ñ ˆ1ˆa„LÙ
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Œ1�6‰6�2Ôñ ŒŒJ�r‹N˜1ÕÓ˜r 2¨ s¨BÔ/ñ ŒˆQ‹��a�Sœ1Ÿ6™6˜( Q¨ F¨A¨q­D°­F´B¼ÀÀA»Õ4FÔGÙŒˆQ‹�”a—f‘f�X ˜s¤Q§V¡V¬Q¯V©VÐ$4°a¸µd¸1µf¼bÄ(È1ÈaÃ.Õ>PÔQñ ŒˆA‹��BœŸ™˜ 1 # q¨!¥t¨A¥v¬t´B«xÔ8ÙŒˆA‹��B˜˜œaŸf™f˜X q¨!¥t¨A¥v¬t´B«xÔ8ñ ŒˆQ‹��R˜!˜œx¨¨A›Ð/°°Aµ°aµ¼¼b»À!½ÔDö@ö
@ñ 	ŒˆQ‹��”9˜Q �UÓ#Õ	# Y°Ô5ÙŒˆQ‹��”9˜Q �UÓ#Õ	# Y°Ô5ö1áŒˆQ‹���I˜tÔ$ÙŒˆQ��U‹Ù	”#�a“&Ó	œaŸe™e¤W¨a°¨V°R¸!¸¸q¸cÀ1ÀQÅ3Ó%GÐHÐIÕ	IØ	ôñ 	ŒŒS��Q•‹Z‹™(¤3¤s¨1£v£;Ó/ÜŒw˜˜1�v¤§¡˜x¨!¨¨q´!·&±&¨k¸1¸Q½3Ó?Ð
@Ð	AõBà	ôñ 	ŒˆA‹Ù	”1—?‘?Ð"¤2Õ%Ó	&¬1¯=©=¼'À"ÀqÀcÈAÈqÈ6ÐSUØ”J˜r“NÕ"ó;$ð +%ð *&õ 
&à	ôñ Œˆ1‹�ˆs�BœŸ™˜ 1 a &¨!¨Q­$¨q­&´$´r³(¸1µ*Ô=ÙŒˆ1‹ˆr�A�3˜˜A˜¤§¡ ¨!¨Q­$¨q­&´4¼³8°)¸Aµ+Ô>ñ ŒˆA‹”—‘�˜"˜q˜c¤H¨R°£O´X¸bÀ!³_Ð#EÄzÐRTÃ~ÐVWÐYZÕVZÕGZÐ[\ÕG\Ø	Œ$Œr‹(�
�1�ôáŒˆA‹�”Q—V‘V˜Q�K ! Q ¬!¯&©&´!·&±&Ð)9¸1¸a½4À½6Ü
ŒAˆe‹H�ðDØõDô ñ Œˆq�!‹�b˜1˜#  A¥ q˜z¨2¨qÔ1ñ ŒˆA‹���Rœ!Ÿ&™&˜ A 3¨¨1­¨a´´R³­jÔ9áŒˆQ‹��a�S˜1œaŸf™f˜+ r¨1¨a­4°´4¼³8µÔ<ñ ŒˆQ‹”!—&‘&�˜2 ˜s¤X¨b°!£_Ð$5¸¸1½°u¸aÄÄRÃ½jÔIñ Œ�‹�a�S˜"œx¨¨1›~Ð.°´H¸QÀ³NÐ0CÄRÈÅUÈ1ÈaÍ4ÅZÐPRÅ]ÔTU×TZÑTZÔ[ÙŒ�‹�a�S˜"œx¨¨1›~Ð.°´H¸QÀ³NÐ0CÄRÈÅUÈ1ÈaÍ4ÅZÐPRÅ]ÔTU×TZÑTZÔ[ñ Œ��1‹�r˜2  !¥˜u¨ r¨!¥t f¨a°­d°1­fÔ5ñ Œ��1‹�r˜a !�e˜H Q�J˜<¨!¨A­#°¨r°!­t¨¸¸Q½°xÀµz°lÀAÀqÅDÈÅFÔKñ6 Œ��1‹�r˜Q �U A�I˜;¨¨1­¨°°°1µ°q¸1µu¸aµiÐ/@À!ÀQÅ$ÀqÅ&Ì"ÔMñ Œ��1‹�r˜2  !¥ a R¨¥T˜{¨B°°1µ°Qµ¼¿¹Ô?ñ Œ
�1‹œŸ™¤§¡Ð'¨¨a¨S°1°#¸°r¼1¿6¹6ÔBÙŒ
�1‹œŸ™ ¤!§&¡&¥Ð)¨2°¨s°Q°C¸!¸¼XÀbÈ!»_ÈQÕ=NÖOrm   )ÚtimethisrO   c               ó$   € V ^8„  d   QhRRRRRR/# )r®   rd   r   r{   r   Úreturnztuple[type[Basic], ...]rž   )Úformats   "re   Ú__annotate__rÐ   -  s'   € ÷ 	Nñ 	Nˆuð 	N˜ð 	NÐ$;ñ 	Nrm   c                óÆ   a€ R R lpSV P                   9  d   R# V P                  '       d   \        V 4      3# \        \	        V3R lV P
                   4       VR7      4      # )z3Create a hashable entity describing the type of f. c               ó    € V ^8„  d   QhRRRR/# )r®   r{   ztype[Basic]rÎ   ztuple[int, int, str]rž   )rÏ   s   "re   rÐ   Ú_mytype.<locals>.__annotate__/  s   € ÷ ñ ˆ{ð Ð3ñ rm   c                ó"   € V P                  4       # r`   )Ú	class_keyrz   s   &re   ÚkeyÚ_mytype.<locals>.key/  s   € Ø�{‰{‹}Ðrm   c              3  óL   <"  € T F  p\        VS4       F  q"x € K  	  K  	  R # 5ir`   )r�   )rb   r•   r±   r{   s   &  €re   rf   Ú_mytype.<locals>.<genexpr>6  s   øé € ÐB¡F˜q´G¸A¸q¶M¨qœ±M™£Fùs   ƒ!$©rÖ   rž   )Úfree_symbolsÚis_FunctionÚtypeÚtupleÚsortedrj   )rd   r{   rÖ   s   &f re   r�   r�   -  sK   ø€ õð 	�—‘ÔØˆ	Ø	
��ˆÜ�A‹wˆxˆÜ”ÔB A§F¢FÓBÈÔLÓMÐMrm   c                  ó   € ] tR tRtRtRtR# )Ú_CoeffExpValueErrori9  z<
Exception raised by _get_coeff_exp, for internal use only.
rž   N)rŸ   r    r¡   r¢   Ú__doc__r¤   rž   rm   re   rá   rá   9  s   † ñó 	rm   rá   c                óX  € ^ RI Hp \        V! V 4      4      P                  V4      w  r4V'       g   V\        P
                  3# Vw  pVP                  '       d*   VP                  V8w  d   \        R4      hW4P                  3# WA8X  d   V\        P                  3# \        RV ,          4      h)aP  
When expr is known to be of the form c*x**b, with c and/or b possibly 1,
return c, b.

Examples
========

>>> from sympy.abc import x, a, b
>>> from sympy.integrals.meijerint import _get_coeff_exp
>>> _get_coeff_exp(a*x**b, x)
(a, b)
>>> _get_coeff_exp(x, x)
(1, 1)
>>> _get_coeff_exp(2*x, x)
(2, 1)
>>> _get_coeff_exp(x**3, x)
(1, 3)
)Úpowsimpzexpr not of form a*x**bzexpr not of form a*x**b: %s)Úsympy.simplifyrä   r   Úas_coeff_mulr   ÚZeroÚis_PowÚbaserá   r*   rÈ   )Úexprr{   rä   rÊ   Úms   &&   re   Ú_get_coeff_exprì   @  sˆ   € õ& 'Ü™w t›}Ó-×:Ñ:¸1Ó=�F€QßØ”!—&‘&ˆyÐØ
�C€QØ‡x‡x€xØ�6‰6�QŒ;Ü%Ð&?Ó@Ð@Ø—%‘%ˆxˆØ	
ŒØ”!—%‘%ˆxˆä!Ð"?À$Õ"FÓGÐGrm   c                ó:   a€ V3R lo\        4       pS! WV4       V# )aS  
Find the exponents of ``x`` (not including zero) in ``expr``.

Examples
========

>>> from sympy.integrals.meijerint import _exponents
>>> from sympy.abc import x, y
>>> from sympy import sin
>>> _exponents(x, x)
{1}
>>> _exponents(x**2, x)
{2}
>>> _exponents(x**2 + x, x)
{1, 2}
>>> _exponents(x**3*sin(x + x**y) + 1/x, x)
{-1, 1, 3, y}
c                óö   <€ W8X  d   VP                  ^.4       R# V P                  '       d0   V P                  V8X  d   VP                  V P                  .4       R# V P                   F  pS! W1V4       K  	  R# )r”   N)Úupdaterè   ré   r*   rj   )rê   r{   rl   ÚargumentÚ_exponents_s   &&& €re   rñ   Ú_exponents.<locals>._exponents_u  sX   ø€ ØŒ9Ø�J‰J˜�sŒOÙØ�;�;ˆ;˜4Ÿ9™9¨œ>Ø�J‰J˜Ÿ™�zÔ"ÙØŸ	œ	ˆHÙ˜ SÖ)ó "rm   )Úset)rê   r{   rl   rñ   s   && @re   Ú
_exponentsrô   b  s    ø€ õ&*ô ‹%€CÙ�˜ÔØ€Jrm   c                óŽ   € V P                  \        4       Uu0 uF!  q!VP                  9   g   K  VP                  kK#  	  up# u upi )zAFind the types of functions in expr, to estimate the complexity. )Úatomsr   rÛ   Úfunc)rê   r{   Úes   && re   Ú
_functionsrù   ƒ  s4   € à ŸJ™J¤xÔ0ÓHÑ0�q¸¿¹Ñ4GŒFˆA�FŒFÑ0ÑHÐHùÒHs
   ˜A¯Ac                ó�   aaaa€ R Uu. uF  p\        VS.R7      NK  	  upw  ooVVVV3R lo\        4       pS! W4       V# u upi )a8  
Find numbers a such that a linear substitution x -> x + a would
(hopefully) simplify expr.

Examples
========

>>> from sympy.integrals.meijerint import _find_splitting_points as fsp
>>> from sympy import sin
>>> from sympy.abc import x
>>> fsp(x, x)
{0}
>>> fsp((x-1)**3, x)
{1}
>>> fsp(sin(x+3)*x, x)
{-3, 0}
Úpqrp   c                óR  <€ \        V \        4      '       g   R # V P                  SS,          S,           4      pV'       d8   VS,          ^ 8w  d*   VP                  VS,          ) VS,          ,          4       R # V P                  '       d   R # V P
                   F  pS! W14       K  	  R # r`   )Ú
isinstancer   ÚmatchrŒ   Úis_Atomrj   )rê   rl   rë   rð   Úcompute_innermostr¶   r·   r{   s   &&  €€€€re   r   Ú1_find_splitting_points.<locals>.compute_innermostœ  su   ø€ Ü˜$¤×%Ò%ÙØ�J‰J�q˜•s˜Q•wÓˆß��1•˜”Ø�G‰G�Q�q•T�E˜!˜A�$•JÔÙØ�<�<ˆ<ÙØŸ	œ	ˆHÙ˜hÖ,ó "rm   )r   ró   )rê   r{   rr   Ú	innermostr   r¶   r·   s   &f  @@@re   Ú_find_splitting_pointsr  ˆ  sL   û€ ñ$ +/Ó/©$ QŒD�˜Q˜C× ©$Ñ/�D€A€q÷
-ð 
-ô “€IÙ�dÔ&ØÐùò 0s   ‰Ac           	     ó¬  € \         P                  p\         P                  p\         P                  p\        V 4      p \        P                  ! V 4      pV Fú  pWa8X  d   W1,          pK  WP
                  9  d   W&,          pK-  VP                  '       d´   WP                  P
                  9  dš   VP                  P                  V4      w  rxW�38w  d'   \        VP                  4      P                  V4      w  rxW�38X  dI   W1VP                  ,          ,          pV\        \        WvP                  ,          RR7      4      ,          pKò  WF,          pKü  	  W#V3# )aI  
Split expression ``f`` into fac, po, g, where fac is a constant factor,
po = x**s for some s independent of s, and g is "the rest".

Examples
========

>>> from sympy.integrals.meijerint import _split_mul
>>> from sympy import sin
>>> from sympy.abc import s, x
>>> _split_mul((3*x)**s*sin(x**2)*x, x)
(3**s, x*x**s, sin(x**2))
F)r»   )r   rÈ   r   r   Ú	make_argsrÛ   rè   r*   ré   ræ   r   r$   r%   )	rd   r{   rˆ   ÚpoÚgrj   r•   rÊ   r±   s	   &&       re   Ú
_split_mulr  ¬  sö   € ô �%‰%€CÜ	
�‰€BÜ	�‰€AÜ˜!Ó€Aä�=Š=˜Ó€DÛˆØŒ6Ø�GŠBØ—n‘nÔ$Ø�HŠCà�x�xˆx˜A§U¡U×%7Ñ%7Ô7Ø—v‘v×*Ñ*¨1Ó-‘�Ø˜”9Ü% a§f¡fÓ-×:Ñ:¸1Ó=‘D�AØ˜”9Ø˜QŸU™U�(•N�BØœ:¤h¨q·%±%­x¸eÔ&DÓEÕE�CÙØ�FŠAñ ð  �Aˆ:Ðrm   c                ó@  € \         P                  ! V 4      p. pV F  pVP                  '       dZ   VP                  P                  '       d>   VP                  pVP
                  pV^ 8  d   V) p^V,          pW%.V,          ,          pKn  VP                  V4       K�  	  V# )zì
Return a list ``L`` such that ``Mul(*L) == f``.

If ``f`` is not a ``Mul`` or ``Pow``, ``L=[f]``.
If ``f=g**n`` for an integer ``n``, ``L=[g]*n``.
If ``f`` is a ``Mul``, ``L`` comes from applying ``_mul_args`` to all factors of ``f``.
)r   r  rè   r*   ry   ré   r‚   )rd   rj   Úgsr  rr   ré   s   &     re   Ú	_mul_argsr  Ó  s�   € ô �=Š=˜Ó€DØ	€BÛˆØ�8�8ˆ8˜Ÿ™×(×(Ð(Ø—‘ˆAØ—6‘6ˆDØ�1ŒuØ�B�Ø˜•v�Ø�&˜•(�NŠBà�I‰I�aŽLñ ð €Irm   c           	     óà   € \        V 4      p\        V4      ^8  d   R# \        V4      ^8X  d   \        V4      .# \        V^4       UUu. uF  w  r#\	        V!  \	        V!  3NK  	  upp# u uppi )a_  
Find all the ways to split ``f`` into a product of two terms.
Return None on failure.

Explanation
===========

Although the order is canonical from multiset_partitions, this is
not necessarily the best order to process the terms. For example,
if the case of len(gs) == 2 is removed and multiset is allowed to
sort the terms, some tests fail.

Examples
========

>>> from sympy.integrals.meijerint import _mul_as_two_parts
>>> from sympy import sin, exp, ordered
>>> from sympy.abc import x
>>> list(ordered(_mul_as_two_parts(x*sin(x)*exp(x))))
[(x, exp(x)*sin(x)), (x*exp(x), sin(x)), (x*sin(x), exp(x))]
N)r  ÚlenrÞ   rY   r   )rd   r
  r{   Úys   &   re   Ú_mul_as_two_partsr  ê  sb   € ô. 
�1‹€BÜ
ˆ2ƒw�„{ÙÜ
ˆ2ƒw�!„|Ü�b“	ˆ{ÐÜ-@ÀÀQÔ-GÔHÑ-G¡6 AŒS�!‰W”c˜1‘gÓÑ-GÒHÐHùÓHs   Á	A*c                ó"  € R p\        \        V P                  4      \        V P                  4      ,
          4      pV^V P                  ,           V^,          ,           ,          pV^\
        ,          V^,
          V P                  ,          ,          ,          pV\        V! V P                  V4      V! V P                  V4      V! V P                  V4      V! V P                  V4      V P                  V,          WV,          ,          ,          4      3# )zFReturn C, h such that h is a G function of argument z**n and
g = C*h. c                ó�   € \         P                  ! V \        V4      4       UUu. uF  w  r#W#,           V,          NK  	  upp# u uppi )z4(a1, .., ak) -> (a1/n, (a1+1)/n, ..., (ak + n-1)/n) )Ú	itertoolsÚproductÚrange)Úparamsrr   r•   rc   s   &&  re   ÚinflateÚ_inflate_g.<locals>.inflate  s7   € ä&/×&7Ò&7¸ÄÀaÃÔ&IÔJÑ&I™d˜a�•˜—	�	Ñ&IÒJÐJùÓJs   ¤A)r   r  r…   r‡   r©   r   ÚdeltarO   r„   Úaotherr†   Úbotherrð   )r  rr   r  ÚvÚCs   &&   re   Ú
_inflate_gr  	  sÁ   € ò
Kô 	
Œ#ˆa�d‰d‹)”c˜!Ÿ$™$“iÕ
Ó €AØ	ˆA�—‘�H�q˜•s�NÕ€AØˆ!ŒB�$�1�q•5˜!Ÿ'™'•/Õ	"Õ"€AØŒg‘g˜aŸd™d AÓ&©°·±¸!Ó(<Ù˜aŸd™d AÓ&©°·±¸!Ó(<Ø—j‘j !•m a¨A­#¥hÕ.ó0ð 0ð 0rm   c                óÈ   € R p\        V! V P                  4      V! V P                  4      V! V P                  4      V! V P                  4      ^V P
                  ,          4      # )zHTurn the G function into one of inverse argument
(i.e. G(1/x) -> G'(x)) c                ó>   € V  Uu. uF  p^V,
          NK  	  up# u upi r“   rž   )Úlr•   s   & re   ÚtrÚ_flip_g.<locals>.tr  s    € Ù Ó!™q˜!��A—�™qÑ!Ð!ùÒ!ó   …)rO   r†   r  r„   r  rð   )r  r!  s   & re   Ú_flip_gr$    sB   € ò"ä‘2�a—d‘d“8™R §¡›\©2¨a¯d©d«8±R¸¿¹³\À1ÀQÇZÁZÅ<ÓPÐPrm   c           	     óL  € V^ 8  d   \        \        V 4      V) 4      # \        VP                  4      p\        VP                  4      p\        W4      w  r@V P                  pV^\        ,          ^V,
          ^,          ,          V\        R^4      ,          ,          ,          pWRV,          ,          p\        V4       Uu. uF  qf^,           V,          NK  	  ppV\        V P                  V P                  V P                  \        V P                  4      V,           V4      3# u upi )a@  
Let d denote the integrand in the definition of the G function ``g``.
Consider the function H which is defined in the same way, but with
integrand d/Gamma(a*s) (contour conventions as usual).

If ``a`` is rational, the function H can be written as C*G, for a constant C
and a G-function G.

This function returns C, G.
r§   )Ú_inflate_fox_hr$  r   r¶   r·   r  rð   r   r   r  rO   r„   r  r†   rÆ   r  )r  r•   r¶   r·   ÚDr\   rr   Úbss   &&      re   r&  r&  "  sÛ   € ð 	ˆ1„uÜœg a›j¨1¨"Ó-Ð-Ü	ˆ!�#‰#‹€AÜ	ˆ!�#‰#‹€Aô �aÓ�D€AØ	�
‰
€AØˆ!ŒB�$�1�q•5˜!•)Õ	˜Q¤¨¨Q£Õ/Õ	/Õ/€AØˆA�…I€AÜ" 1œXÓ	&™X˜ˆq�5�!�)ˆ)™X€BÐ	&ØŒg�a—d‘d˜AŸH™H a§d¡d¬D°·±«N¸RÕ,?ÀÓCÐCÐCùò 
's   Â>D!zdict[tuple[str, str], Dummy]Ú_dummiesc                óV   € \        W3/ VB pWBP                  9   d   \        V 3/ VB # V# )z¦
Return a dummy. This will return the same dummy if the same token+name is
requested more than once, and it is not already in expr.
This is for being cache-friendly.
)Ú_dummy_rÛ   r   )ÚnameÚtokenrê   ÚkwargsÚds   &&&, re   Ú_dummyr0  ?  s4   € ô 	�Ñ&˜vÑ&€AØ×ÑÔÜ�TÑ$˜VÑ$Ð$Ø€Hrm   c                ó^   € W3\         9   g   \        V 3/ VB \         W3&   \         W3,          # )zT
Return a dummy associated to name and token. Same effect as declaring
it globally.
)r)  r   )r,  r-  r.  s   &&,re   r+  r+  K  s1   € ð
 ˆ=œHÔ$Ü"'¨Ñ"7°Ñ"7Œ�$�ÑÜ�T�MÕ"Ð"rm   c                óö   a€ \         ;QJ dA    V3R lV P                  \        \        4       4       F  '       g   K   R'       * # 	  R'       * # ! V3R lV P                  \        \        4       4       4      '       * # )z�Check if f(x), when expressed using G functions on the positive reals,
will in fact agree with the G functions almost everywhere c              3  óB   <"  € T F  pSVP                   9   x € K  	  R # 5ir`   )rÛ   ©rb   rê   r{   s   & €re   rf   Ú_is_analytic.<locals>.<genexpr>X  s   øé € ÐNÑ6M¨d�1˜×)Ñ)Ö)Ó6Mùó   ƒTF)Úanyrö   r?   r"   )rd   r{   s   &fre   Ú_is_analyticr8  U  sM   ø€ ÷ ‹sÔN°a·g±g¼iÌÔ6MÓN�sŒsÔNÐNŠsÔNÐNˆsÔN°a·g±g¼iÌÔ6MÓNÓNÔNÐNrm   c                óâ  aa€ V'       d   V P                  R \        4      p Rp\        V \        4      '       g   V # \	        R\
        R7      w  oop\        SS8  \        SS4      4      SS8*  3\        \        \        S4      4      \        8*  \        \        S4      ^\        ,          ,
          4      \        8*  4      \        \        S4      \        ,
          ^ 4      3\        \        ^\        S4      ,          \        ,           4      \        8*  \        ^\        S4      ,          \        ,
          4      \        8*  4      \        \        S4      ^ 4      3\        \        ^\        S4      ,          \        ,           4      \        8  \        ^\        S4      ,          \        ,
          4      \        8*  4      \        P                  3\        \        \        S4      \        ^,          ,
          4      \        ^,          8*  \        \        S4      \        ^,          ,           4      \        ^,          8*  4      \        \        S4      ^ 4      3\        \        \        S4      \        ^,          ,
          4      \        ^,          8*  \        \        S4      \        ^,          ,           4      \        ^,          8  4      \        P                  3\        \        \        S^,          ^,          ^,           4      4      \        8  \        \        \        S^,          ^,          ^,           4      4      \        4      4      \        P                  3\        \        \        S^,          ^,          ^,           4      4      \        8  \        ^S^,          ^,          ^,           ,          ^ 4      4      \        P                  3\        \        \!        S4      4      \        8*  \        \!        \#        R\        ,          \        P$                  ,          4      S,          4      4      \        8*  4      \        \!        \#        \        P$                  ) \        ,          4      S,          4      ^ 4      3\        \        \!        S4      4      \        ^,          8*  \        \!        \#        \        ) \        P$                  ,          4      S,          4      4      \        ^,          8*  4      \        \!        \#        \        P$                  ) \        ,          ^,          4      S,          4      ^ 4      3\        SS8*  \        SS8  V4      4      SS8*  3\        S^,          ^4      S^,          ^8„  ,          S^,          ^8„  3\        ^S,          ^4      \'        \        \        S4      4      4      \        S4      ,          ^8„  ,          \        S4      ^8„  3\        S^4      \'        \        \        S4      4      4      \        S4      ,          ^8„  ,          \        S4      ^8„  3\        \        S4      4      \        ^,          8  \'        \        \        S4      4      4      \)        \        S^,          4      4      ,          ^8„  ,          S^,          ^8„  3.pV P*                  ! V P,                   Uu. uF  p\/        WA4      NK  	  up!  p RpV'       Edï   Rp\1        V4       EFÙ  w  pw  rxVP*                  V P*                  8w  d   K&  \1        V P,                  4       EF™  w  ršW'P,                  ^ ,          P2                  9   d&   V
P5                  VP,                  ^,          4      p^pM$^ pV
P5                  VP,                  ^ ,          4      pV'       g   Kz  VP,                  RV VP,                  V^,           R ,            Uu. uF  qÝP7                  V4      NK  	  ppV	.pV EF/  p\1        V P,                  4       EF  w  ppVV9   d   K  VV8X  d   VV.,          p K=  \        V\        4      '       d^   VP,                  ^,          V8X  dF   \        V\        4      '       d0   VP,                  ^ ,          VP,                  9   d   VV.,          p K°  \        V\        4      '       g   K¯  VP,                  ^ ,          V8X  g   KÉ  \        V\        4      '       g   Ká  VP,                  ^,          VP,                  9   g   EK  VV.,          p EK-  	  EK2  	  \9        V4      \9        V4      ^,           8w  d   EK  \1        V P,                  4       UUu. uF  w  ppVV9  g   K  VNK  	  uppVP7                  V4      .,           p\:        '       d   VR9  d   \=        RV4       V P*                  ! V!  p Rp EK×  	  EKÜ  	  EK÷  VV3R lpV P                  R	 V4      p \:        '       d   \=        R
V 4       V # u upi u upi u uppi )az  
Do naive simplifications on ``cond``.

Explanation
===========

Note that this routine is completely ad-hoc, simplification rules being
added as need arises rather than following any logical pattern.

Examples
========

>>> from sympy.integrals.meijerint import _condsimp as simp
>>> from sympy import Or, Eq
>>> from sympy.abc import x, y
>>> simp(Or(x < y, Eq(x, y)))
x <= y
c                ó   € V P                   # r`   ©Úis_Relational©Ú_s   &re   r|   Ú_condsimp.<locals>.<lambda>o  s   €  a§o¢orm   Fzp q r)r›   TNzused new rule:c                ó  <€ V P                   R 8w  g   V P                  ^ 8w  d   V # V P                  pVP                  \	        S4      S,          4      pV'       g+   VP                  \        \        S4      S,          4      4      pV'       gw   \        V\        4      '       d_   VP                  ^ ,          P                  '       g<   VP                  ^,          \        P                  J d   VP                  ^ ,          ^ 8„  # V # VS,          ^ 8„  # )z==)Úrel_opÚrhsÚlhsrþ   r!   r(   r&   rý   r)   rj   Úis_polarr   ÚInfinity)ÚrelÚLHSrë   r¶   r·   s   &  €€re   Úrel_touchupÚ_condsimp.<locals>.rel_touchupÂ  s¼   ø€ Ø�:‰:˜Ô §¡¨A¤ØˆJð �g‰gˆØ�I‰I”c˜!“f˜a•iÓ ˆßØ—	‘	Ô-¬j¸«m¸QÕ.>Ó?Ó@ˆAßÜ˜#Ô0×1Ò1¸#¿(¹(À1½+×:N×:NÐ:NØŸ™ �¤q§z¡zÓ1ØŸ™ � a™Ð(ØˆJØ�!•�q‘Ðrm   c                ó   € V P                   # r`   r;  r=  s   &re   r|   r?  Ñ  s   €  !§/¢/rm   z_condsimp: éþÿÿÿ)
rx   r®   é   é   é   é   é   é   é   é   )Úreplacer   rý   rV   r   r   rS   r   rR   r"   r!   r   r   Úfalser   Útruer(   r+   rÉ   r6   r3   r÷   rj   Ú	_condsimpÚ	enumeraterÛ   rþ   r»   r  r   Úprint)r‰   Úfirstr¨   Úrulesr>  ÚchangeÚiruleÚfroÚtorr   Úarg1rë   Únumr{   Ú	otherargsÚ	otherlistÚarg2ÚkÚarg3Úarg_ÚnewargsrH  r¶   r·   s   &&                    @@re   rW  rW  [  s  ù€ ÷& Ø�|‰|Ñ5Ô7GÓHˆØˆÜ�dœO×,Ò,ØˆÜ�g¤4Ô(�G€A€qˆ!ô
 
ˆA�‰E”2�a˜“8Ó	˜a 1™fÐ%ô 
ŒS”�Q“‹[œBÑ¤¤C¨£F¨Q¬r­T¥MÓ 2´bÑ 8Ó	9Ü	ŒC�‹F”R�K˜Ó	ð	ä	ŒS�”3�q“6•œB•Ó¤2Ñ%¤s¨1¬S°«V­8´b­=Ó'9¼RÑ'?Ó	@Ü	ŒC�‹F�A‹ð	ä	ŒS�”3�q“6•œB•Ó¤"Ñ$¤c¨!¬C°«F­(´R­-Ó&8¼BÑ&>Ó	?Ü	
�‰ð	ä	ŒS”�Q“œ"˜Q�$•Ó¤2 a¥4Ñ'¬¬S°«V´b¸µd­]Ó);¼rÀ!½tÑ)CÓ	DÜ	ŒC�‹F�A‹ð	ä	ŒS”�Q“œ"˜Q�$•Ó¤2 a¥4Ñ'¬¬S°«V´b¸µd­]Ó);¼bÀ½dÑ)BÓ	CÜ	
�‰ð	ä	ŒS”�Q˜•T˜!•V˜a•Z“Ó!¤BÑ&¬¬3¬s°1°aµ4¸µ6¸Aµ:«Ó+?ÄÓ(DÓ	EÜ	
�‰ð	ä	ŒC”�A�q•D˜•F˜Q•J“Ó ¤2Ñ%¤r¨!¨Q°­T°!­V°a­Z­.¸!Ó'<Ó	=Ü	
�‰ð	ä	ŒSÔ$ QÓ'Ó(¬BÑ.ÜÔ"¤9¨R´­U´1·?±?Õ-BÓ#CÀAÕ#EÓFÓGÌ2ÑMó
Oä	Ô¤	¬1¯?©?Ð*:¼2Õ*=Ó >¸qÕ @ÓAÀ1Ó	Eð	Gô 
ŒSÔ$ QÓ'Ó(¬B¨q­DÑ0ÜÔ"¤9¬b¨S´·±Õ-@Ó#AÀ!Õ#CÓDÓEÌÈAÍÑMó
Oä	Ô¤	¬1¯?©?Ð*:¼2Õ*=¸aÕ*?Ó @ÀÕ BÓCÀQÓ	Gð	Iô 
ˆA�‰F”C˜˜A™˜q“MÓ	" A¨¡FÐ+Ü	ˆAˆq�D�!‹˜˜1�˜q™Õ	! 1 a¥4¨!¡8Ð,Ü	ˆAˆa�C�‹”sœ3œs 1›v›;Ó'¬¨A«Õ.°Ñ2Õ	3´S¸³V¸a±ZÐ@Ü	ˆAˆq‹”SœœS ›V›Ó%¤c¨!£fÕ,¨qÑ0Õ	1´3°q³6¸A±:Ð>Ü
Œc�!‹f‹+œ˜1�Ñ
¤¤S¬¨Q«£[Ó!1´$´s¸1¸a½4³y³/Õ!AÀAÑ!EÕ	FÈÈ1ÍÈqÉÐQð9€Eð< �9Š9°D·I²IÓ>±I¨q”y Ö*±IÑ>Ñ?€DØ€Fß
ˆ&ØˆÜ )¨%× 0ÑˆE‘9�CØ�x‰x˜4Ÿ9™9Ô$ÙÜ$ T§Y¡Y×/‘�ØŸ™ �×0Ñ0Ô0ØŸ
™
 3§8¡8¨A¥;Ó/�AØ‘Cà�CØŸ
™
 3§8¡8¨A¥;Ó/�AßÙØ03·±¸¸#°ÀÇÁÈ#ÐPQÍ'È(ÐASÖ0SÓTÑ0S¨1ŸV™V AžYÑ0S�	ÐTØ˜C�	Ü%�DÜ#,¨T¯Y©Y×#7™˜˜4Ø 	œ>Ù$Ø 4œ<Ø%¨!¨Õ,˜IÚ!Ü% d¬C×0Ò0°T·Y±Y¸qµ\ÀQÔ5FÜ *¨4´× 5Ò 5¸$¿)¹)ÀA½,È$Ï)É)Ô:SØ%¨!¨Õ,˜IÚ!Ü% d¬C×0Ô0°T·Y±Y¸qµ\ÀQÖ5FÜ *¨4´× 5Ô 5¸$¿)¹)ÀA½,È$Ï)É)×:SØ%¨!¨Õ,˜IÛ!ô $8ñ &ô �y“>¤S¨£^°aÕ%7Ô7ÚÜ1:¸4¿9¹9Ô1Eô 2Ñ1E¡I Q¨Ø yÑ0÷  ˜4Ñ1Eò 2Ø57·W±W¸Q³Z°LõA�ç“;ØÐ$FÔFÜÐ.°Ô6Ø—y’y 'Ñ*�Ø�ÛôG 0ô !1öRð �<‰<Ñ1°;Ó?€Dßƒ{Üˆm˜TÔ"Ø€Kùò ?ùò  Uùó&2s   Úg!Þ-g&ä<g+
åg+
c                ód   € \        V \        4      '       d   V # \        V P                  4       4      # )zRe-evaluate the conditions. )rý   ÚboolrW  Údoit)r‰   s   &re   Ú
_eval_condrl  Ö  s%   € ä�$œ×ÒØˆÜ�T—Y‘Y“[Ó!Ð!rm   c                óZ   € \        W4      pV'       g   VP                  \         R 4      pV# )zÚBring expr nearer to its principal branch by removing superfluous
factors.
This function does *not* guarantee to yield the principal branch,
to avoid introducing opaque principal_branch() objects,
unless full_pb=True. c                ó   € V # r`   rž   )r{   r  s   &&re   r|   Ú&_my_principal_branch.<locals>.<lambda>é  s   € ¹rm   )r'   rT  )rê   ÚperiodÚfull_pbrl   s   &&& re   Ú_my_principal_branchrr  á  s'   € ô ˜4Ó
(€CßØ�k‰kÔ*©NÓ;ˆØ€Jrm   c           	     ó°  a	a
€ \        W4      w  po
\        VP                  V4      w  po	VP                  4       p\        WV4      pV \	        S	4      VS
^,           S	,          ^,
          ,          ,          ,          pV	V
3R lpV\        V! VP                  4      V! VP                  4      V! VP                  4      V! VP                  4      WS,          4      3# )z„
Rewrite the integral fac*po*g dx, from zero to infinity, as
integral fac*G, where G has argument a*x. Note po=x**s.
Return fac, G.
c                óh   <€ V  Uu. uF   q^S,           S,          ,           ^,
          NK"  	  up# u upi r“   rž   )r   r•   r°   Úss   & €€re   r!  Ú_rewrite_saxena_1.<locals>.trü  s-   ø€ Ù+,Ó-©1 a�Q˜•U˜A•I• ×!Ð!©1Ñ-Ð-ùÒ-s   †&/)
rì   rð   Ú
get_periodrr  r"   rO   r„   r  r†   r  )rˆ   r  r  r{   r>  r•   rp  r  r!  r°   ru  s   &&&&     @@re   Ú_rewrite_saxena_1rx  í  s¨   ù€ ô ˜"Ó �D€A€qÜ˜!Ÿ*™* aÓ(�D€A€qØ�\‰\‹^€FÜ˜QÓ'€Að 	ŒS�‹V�A˜˜Q� �	 A�Õ&Õ&Õ'€Aö.àŒg‘b˜Ÿ™“h¡ 1§8¡8£©b°·±«h¹¸1¿8¹8»Ø•cóð ð rm   c                ó8  € V P                   p\        V P                  V4      w  rE\        \	        V P
                  4      \	        V P                  4      \	        V P                  4      \	        V P                  4      .4      w  rgr‰W‰8”  dc   R p
\        \        V
! V P
                  4      V
! V P                  4      V
! V P                  4      V
! V P                  4      W,          4      V4      # V P
                   Uu. uF  p\        V4      ) ^8  NK  	  upV P                   Uu. uF  p^^\        V4      ,
          8  NK  	  up,           p\        V!  pYÐP                   Uu. uF  p\        V4      ) ^8  NK  	  up,          pYÐP                   Uu. uF  p^^\        V4      ,
          8  NK  	  up,          p\        V!  p\        V P                  4      ) V	^,           V,
          ^,          ,           W˜,
          8„  pR pR pV! R4       V! RW4WgW‰34       V! R\!        V P                  4      \!        V P                  4      34       V! R\!        V P
                  4      \!        V P                  4      34       V! RWïV34       . p. p^V8*  W‰8  ^V8*  .p^V8*  ^V8*  \#        W˜^,           4      \%        \        \#        V^ 4      \#        Wh^,           4      4      4      .p^V8*  \#        W˜4      .p\'        \)        V^,          4      ^,           4       FB  pV\+        \-        \/        V4      4      V^V,          ,
          \0        ,          4      .,          pKD  	  V^ 8„  \-        \/        V4      4      V\0        ,          8  .p\+        V^ 4      V.pV'       d   . pVVV3 F"  pV\        VV,           V,           !  .,          pK$  	  VV,          pV! R	V4       V.pV'       d   . p\        \#        V^ 4      V^,           V8*  Wi8*  \-        \/        V4      4      V\0        ,          8  .VO5!  .pVV,          pV! R
V4       VV.pV'       d   . p\        W‰8  ^V8*  V^ 8„  \#        \-        \/        V4      4      V\0        ,          4      .VO5!  .pV\        W‰^,
          8*  \#        V^ 4      \#        \-        \/        V4      4      ^ 4      .VO5!  .,          pVV,          pV! RV4       . pV\#        W‰4      \#        V^ 4      \#        \/        V4      ^ 4      \+        V^ 4      .,          pV'       g   VV.,          p. p\3        V P                  V P                  4       F  w  rËVW¼,
          .,          pK  	  V\        \5        V!  4      ^ 8  .,          p\        V!  pVV.,          pV! RV.4       \        V^ 8„  \-        \/        V4      4      V\0        ,          8  4      .pV'       g   VV.,          p\        V!  pVV.,          pV! RV.4       \7        V!  # u upi u upi u upi u upi )a:  
Return a condition under which the mellin transform of g exists.
Any power of x has already been absorbed into the G function,
so this is just $\int_0^\infty g\, dx$.

See [L, section 5.6.1]. (Note that s=1.)

If ``helper`` is True, only check if the MT exists at infinity, i.e. if
$\int_1^\infty g\, dx$ exists.
c                ó>   € V  Uu. uF  p^V,
          NK  	  up# u upi r“   rž   ©r   r{   s   & re   r!  Ú _check_antecedents_1.<locals>.tr  s    € Ù#$Ó%¡1˜a�A˜—E�E¡1Ñ%Ð%ùÒ%r#  c                 ó   € \        V !   R # r`   )Ú_debug)Úmsgs   *re   rZ   Ú#_check_antecedents_1.<locals>.debug"  s	   € Ü�Œrm   c                ó   € \        W4       R # r`   ©Ú_debugf)Ústringr!   s   &&re   r[   Ú$_check_antecedents_1.<locals>.debugf%  s
   € Ü�Örm   z$Checking antecedents for 1 function:z*  delta=%s, eta=%s, m=%s, n=%s, p=%s, q=%sz  ap = %s, %sz  bq = %s, %sz"  cond_3=%s, cond_3*=%s, cond_4=%sz	  case 1:z	  case 2:z	  case 3:z  extra case:z  second extra case:)r  rì   rð   r   r  r†   r„   r…   r‡   Ú_check_antecedents_1rO   r  r  r   rR   r©   rÆ   r   rU   r  r-   r   r"   r(   r   Úzipr   rS   ) r  r{   Úhelperr  Úetar>  rë   rr   r¶   r·   r!  r°   r•   ÚtmpÚcond_3Úcond_3_starÚcond_4rZ   r[   ÚcondsÚcase1Útmp1Útmp2Útmp3re  Úextrar±   Úcase2Úcase3Ú
case_extraru  Úcase_extra_2s    &&&                             re   r†  r†    sG  € ð �G‰G€EÜ˜AŸJ™J¨Ó*�F€CÜ”C˜Ÿ™“Iœs 1§4¡4›y¬#¨a¯d©d«)´S¸¿¹³YÐ?Ó@�J€Aˆ!à„uò	&ä#¤G©B¨q¯t©t«H±b¸¿¹³lÙ,.¨q¯t©t«H±b¸¿¹³lÀAÅEó%Kà$%ó'ð 	'ð  !ŸtštÓ
$™t˜!ŒBˆq‹Eˆ6�AŒ:™tÑ
$¸q¿tºtÓ'D¹t¸!¨¨A´°1³­I¬¹tÑ'DÕ
D€CÜ�#‰Y€Fà§¢Ó)¡˜1ŒR�‹UˆF�QŒJ¡Ñ)Õ)€CØ§8¢8Ó,¡8˜aˆA�”B�q“E•	ŒM¡8Ñ,Õ,€CÜ�s‘)€Kä�!—$‘$‹xˆi˜1˜q�5 1�9 a�-Õ'¨!­%Ñ/€Fòòñ 
Ð
0Ô1Ù
Ð7Ø˜˜aÐ#ô%á
ˆ?œT !§$¡$›Z¬¨a¯h©h«Ð8Ô9Ù
ˆ?œT !§$¡$›Z¬¨a¯h©h«Ð8Ô9Ù
Ð/°&ÀvÐ1NÔOà€Eð €EØ�‰F�A‘E˜1 ™6Ð"€DØ�‰F�A˜‘FœB˜q a¥%›L¬#¬c´"°Q¸³(¼B¸qÀaÅ%»LÓ.IÓ*JÐK€DØ�‰F”B�q“HÐ€DÜ”7˜5 �7Ó# aÕ'Ö(ˆØ””CÔ+¨CÓ0Ó1°E¸A¸a½CµKÄÕ3CÓDÐEÕEŠñ )à�1‰9”cÔ-¨cÓ2Ó3°e¼BµhÑ>Ð
?€CÜ��Q‹Z˜Ð €EßØˆØ�D˜$ÓˆØ”#˜˜C� %�Ñ)Ð*Õ*Šñ  à	ˆU…N€EÙ	ˆ+�uÔð ˆH€EßØˆÜ”�A�q“˜1˜q�5 A™: q¡vÜÔ(¨Ó-Ó.°´rµÑ9ðCØ<AóCð D€Eà	ˆU…N€EÙ	ˆ+�uÔð �VÐ€EßØˆÜ�‘˜˜Q™ ¨¡	¬2¬cÔ2EÀcÓ2JÓ.KÈUÔSUÍXÓ+Vð Øóð €Eà	Œc�!˜1•u‘*œb ¨›l¬B¬sÔ3FÀsÓ3KÓ/LÈaÓ,PÐYÐSXÓYÐZÕZ€EØ	ˆU…N€EÙ	ˆ+�uÔð €JØ”2�a“8œR  q›\¬2Ô.AÀ#Ó.FÈÓ+JÌBÈsÐTUËJÐWÕW€JßØ�v�hÕˆ
Ø
€AÜ�A—D‘D˜!Ÿ$™$–‰ˆØ	ˆa�eˆW�Šñ  à”2”c˜1‘g“; ‘?Ð#Õ#€JÜ�jÑ!€JØ	ˆjˆ\Õ€EÙ	ˆ/˜J˜<Ô(ä˜ ™	¤3Ô':¸3Ó'?Ó#@À5ÌÅ8Ñ#KÓLÐM€LßØ˜˜Õ ˆÜ˜Ñ%€LØ	ˆlˆ^Õ€EÙ	Ð
  < .Ô1ô
 ˆu‰:Ðùòm %ùÒ'Dùò *ùÚ,s   Ã9XÄ!XÅXÆXc                óî  € ^ RI Hp \        V P                  V4      w  r4^V,          pV P                   F  pV\        V^,           4      ,          pK  	  V P                   F#  pV\        ^V,
          ^,
          4      ,          pK%  	  V P                   F#  pV\        ^V,
          ^,
          4      ,          pK%  	  V P                   F  pV\        V^,           4      ,          pK  	  V! \        V4      4      # )a[  
Evaluate $\int_0^\infty g\, dx$ using G functions,
assuming the necessary conditions are fulfilled.

Examples
========

>>> from sympy.abc import a, b, c, d, x, y
>>> from sympy import meijerg
>>> from sympy.integrals.meijerint import _int0oo_1
>>> _int0oo_1(meijerg([a], [b], [c], [d], x*y), x)
gamma(-a)*gamma(c + 1)/(y*gamma(-d)*gamma(b + 1))
)Ú	gammasimp)
rå   r™  rì   rð   r†   rM   r„   r  r  r$   )r  r{   r™  r‰  r>  rl   r°   r•   s   &&      re   Ú	_int0oo_1rš  r  s»   € õ )ä˜AŸJ™J¨Ó*�F€CØ
ˆC�%€Cà�TŒTˆØŒu�Q˜•U‹|ÕŠñ à�TŒTˆØŒu�Q˜•U˜Q•YÓÕŠñ à�XŒXˆØŒu�Q˜•U˜Q•YÓÕŠñ à�XŒXˆØŒu�Q˜•U‹|ÕŠñ á”Z “_Ó%Ð%rm   c                ó¬  aaa€ VV3R lp\        VS4      w  rx\        VP                  S4      w  ry\        VP                  S4      w  rzV	^ 8  R8X  d   V	) p	\        V4      pV
^ 8  R8X  d   V
) p
\        V4      pV	P                  '       d   V
P                  '       g   R# T	P                  V	P
                  rËV
P                  V
P
                  rí\        W¾,          WÜ,          4      pWûV,          ,          pWýV,          ,          p\        VV4      w  pp\        VV4      w  ppV! V4      pV! V4      pV VV,          ,          p \        VP                  S4      w  pp\        VP                  S4      w  ppV^,           V,          ^,
          oV \        V4      VS,          ,          ,          p V3R lp\        V! VP                  4      V! VP                  4      V! VP                  4      V! VP                  4      VS,          4      p\        VP                  VP                  VP                  VP                  VS,          4      p^ RIHp V! V RR7      W#3# )a�  
Rewrite the integral ``fac*po*g1*g2`` from 0 to oo in terms of G
functions with argument ``c*x``.

Explanation
===========

Return C, f1, f2 such that integral C f1 f2 from 0 to infinity equals
integral fac ``po``, ``g1``, ``g2`` from 0 to infinity.

Examples
========

>>> from sympy.integrals.meijerint import _rewrite_saxena
>>> from sympy.abc import s, t, m
>>> from sympy import meijerg
>>> g1 = meijerg([], [], [0], [], s*t)
>>> g2 = meijerg([], [], [m/2], [-m/2], t**2/4)
>>> r = _rewrite_saxena(1, t**0, g1, g2, t)
>>> r[0]
s/(4*sqrt(pi))
>>> r[1]
meijerg(((), ()), ((-1/2, 0), ()), s**2*t/4)
>>> r[2]
meijerg(((), ()), ((m/2,), (-m/2,)), t/4)
c                óò   <€ \        V P                  S4      w  rV P                  4       p\        V P                  V P
                  V P                  V P                  \        WS4      SV,          ,          4      # r`   )	rì   rð   rw  rO   r„   r  r†   r  rr  )r  r•   r°   Úperrq  r{   s   &   €€re   ÚpbÚ_rewrite_saxena.<locals>.pb«  sZ   ø€ Ü˜aŸj™j¨!Ó,‰ˆØ�l‰l‹nˆÜ�q—t‘t˜QŸX™X q§t¡t¨Q¯X©XÜ+¨A°GÓ<¸QÀ½TÕAóCð 	Crm   TNc                ó>   <€ V  Uu. uF  qS,           NK  	  up# u upi r`   rž   )r   r•   r*   s   & €re   r!  Ú_rewrite_saxena.<locals>.trÐ  s   ø€ Ù!"Ó#¡˜A�C—�¡Ñ#Ð#ùÒ#ó   †©Ú	powdenest©Úpolar)rì   rð   r$  Úis_Rationalr¶   r·   r   r  r"   rO   r„   r  r†   r  rå   r¤  )rˆ   r  Úg1Úg2r{   rq  rž  r>  ru  Úb1Úb2Úm1Ún1Úm2Ún2ÚtauÚr1Úr2ÚC1ÚC2Úa1r°   Úa2r!  r¤  r*   s   &&&&ff                   @re   Ú_rewrite_saxenar·  �  sÔ  ú€ ö6Cô ˜"˜aÓ �D€AÜ˜2Ÿ;™;¨Ó*�E€AÜ˜2Ÿ;™;¨Ó*�E€AØ
ˆQ‰�4ÔØˆSˆÜ�R‹[ˆØ
ˆQ‰�4ÔØˆSˆÜ�R‹[ˆØ�>�>ˆ> §§ ÙØ�T‰T�2—4‘4ˆØ�T‰T�2—4‘4ˆÜ
ˆr�u�b•eÓ
€CØ	�"�u�€BØ	�"�u�€Bä˜˜BÓ�F€BˆÜ˜˜BÓ�F€BˆÙ	ˆB‹€BÙ	ˆB‹€Bàˆ2ˆb�5…L€CÜ˜2Ÿ;™;¨Ó*�E€BˆÜ˜2Ÿ;™;¨Ó*�E€Bˆð ˆq�5�!�)�a�-€CØ
Œs�1‹v˜˜C�ÕÕ
 €Cõ$ä	‘�B—E‘E“™B˜rŸy™y›M©2¨b¯e©e«9±b¸¿¹³mÀRÈÅTÓ	J€BÜ	�—‘˜Ÿ	™	 2§5¡5¨"¯)©)°R¸µTÓ	:€Bå(Ù�S Ô% rÐ-Ð-rm   c                óÜ5  a aa.a/a0a1a2a3a4a5a6€ \        S P                  V4      w  o3p\        SP                  V4      w  o/p\        \        S P                  4      \        S P
                  4      \        S P                  4      \        S P                  4      .4      w  rEo5o6\        \        SP                  4      \        SP
                  4      \        SP                  4      \        SP                  4      .4      w  rgo0o2WE,           S5S6,           ^,          ,
          pWg,           S0S2,           ^,          ,
          p	S P                  S5S6,
          ^,          ,           ^,           p
SP                  S0S2,
          ^,          ,           ^,           pS2S0,
          S6S5,
          ,
          p^S6S5,
          ,
          V,
          V
,
          p\        S2V,
          V,
          ,          \        \        S/4      4      ,           S2S0,
          ,          o1\        S6V,
          V,
          ,          \        \        S34      4      ,           S6S5,
          ,          o4\        R4       \        RS3WES5S6WŠ34       \        RS/WgS0S2W›34       \        RWÍS1S434       V V3R lpV! 4       p\        S P                   UUu. uF2  pSP                   F  p\        ^V,           V,           4      ^ 8„  NK!  	  K4  	  upp!  p\        S P
                   UUu. uF2  pSP
                   F  p\        ^V,           V,           4      ^8  NK!  	  K4  	  upp!  p\        S P
                   Uu. uFG  pS0S2,
          \        ^V,           ^,
          4      ,          \        V4      ,
          \!        R^4      8„  NKI  	  up!  p\        S P                   Uu. uF@  pS0S2,
          \        ^V,           4      ,          \        V4      ,
          \!        R^4      8„  NKB  	  up!  p\        SP
                   Uu. uFG  pS5S6,
          \        ^V,           ^,
          4      ,          \        V
4      ,
          \!        R^4      8„  NKI  	  up!  p\        SP                   Uu. uF@  pS5S6,
          \        ^V,           4      ,          \        V
4      ,
          \!        R^4      8„  NKB  	  up!  p\        V4      ^\        V
^,
          S2S0,
          ,          S6S5,
          S2S0,
          ,          ,           V^,
          S6S5,
          ,          ,           4      ,          ,           ^ 8„  p\        V4      ^\        V
^,
          S2S0,
          ,          S6S5,
          S2S0,
          ,          ,           V^,
          S6S5,
          ,          ,           4      ,          ,
          ^ 8„  p\        \        S34      4      V\        ,          8  p\#        \        \        S34      4      V\        ,          4      p\        \        S/4      4      V	\        ,          8  p\#        \        \        S/4      4      V	\        ,          4      p\%        W‰,           ) \        ,          \        P&                  ,          4      p\)        VS/,          S3,          4      p\)        VS3,          S/,          4      p V^V ,          8X  dx   \        \#        V^ 4      W‰,           ^8*  \+        \-        V^4      \        Wº,           S6,           S5,
          4      ^8  \        Wº,           S2,           S0,
          4      ^8  4      4      p!EMR p"\        \#        V^ 4      V^,
          V	,           ^ 8*  \+        \        \-        V^4      V"! V4      4      \        \        Wº,           S6,           S5,
          4      ^8  \#        V^4      4      4      4      p!\        \#        V^ 4      V	^,
          V,           ^ 8*  \+        \        \-        V ^4      V"! V 4      4      \        \        Wº,           S2,           S0,
          4      ^8  \#        V ^4      4      4      4      p#\+        V!V#4      p!  S2S0,
          \        S/4      ^S2S0,
          ,          ,          ,          \/        S14      ,          S6S5,
          \        S34      ^S6S5,
          ,          ,          ,          \/        S44      ,          ,           p$\1        V$^ 8„  4      R8w  d   V$^ 8„  p%EMÍV/V0V1V2V3V4V5V63R lp&\3        V&! ^^4      V&! RR4      ,          \        \#        \        S34      ^ 4      \#        \        S/4      ^ 4      4      3V&! \5        \        S/4      4      ^4      V&! \5        \        S/4      4      R4      ,          \        \#        \        S34      ^ 4      \-        \        S/4      ^ 4      4      3V&! ^\5        \        S34      4      4      V&! R\5        \        S34      4      4      ,          \        \-        \        S34      ^ 4      \#        \        S/4      ^ 4      4      3V&! \5        \        S/4      4      \5        \        S34      4      4      R	34      p'V$^ 8„  \        \#        V$^ 4      \-        V'^ 4      \        V4      R8„  4      \        \#        V$^ 4      \#        V'^ 4      \        V4      ^ 8„  4      .p(\+        V(!  p% V^3V^3V^3V^3V^3V^3V^3V^3V^	3V^
3V^3V^3V^3V!^3V%^33 F  w  p)p\        R
VV)34       K  	  . o.V.3R lp*S.\        Wg,          V,          V,          ^ 8g  VP8                  R	J V	P8                  R	J VVVVV4      .,          o.V*! ^4       S.\        \#        S5S64      \#        V^ 4      V	P8                  R	J S3P8                  R	J \        V
4      ^8  VVVV4	      .,          o.V*! ^4       S.\        \#        S0S24      \#        V	^ 4      VP8                  R	J S/P8                  R	J \        V4      ^8  VVVV4	      .,          o.V*! ^4       S.\        \#        S0S24      \#        S5S64      \#        V^ 4      \#        V	^ 4      S3P8                  R	J S/P8                  R	J \        V4      ^8  \        V
4      ^8  \-        S3S/4      VVV4      .,          o.V*! ^4       S.\        \#        S0S24      \#        S5S64      \#        V^ 4      \#        V	^ 4      S3P8                  R	J S/P8                  R	J \        Wº,           4      ^8  \-        S/S34      VVV4      .,          o.V*! ^4       S.\        S0S28„  VP8                  R	J VP8                  R	J V	^ 8¬  VVVVVV4
      .,          o.V*! ^4       S.\        S0S28  VP8                  R	J VP8                  R	J V	^ 8¬  VVVVVV4
      .,          o.V*! ^4       S.\        S5S68„  VP8                  R	J V	P8                  R	J V^ 8¬  VVVVVV4
      .,          o.V*! ^4       S.\        S5S68  VP8                  R	J V	P8                  R	J V^ 8¬  VVVVVV4
      .,          o.V*! ^	4       S.\        S0S28„  \#        S5S64      \#        V^ 4      V	^ 8¬  S3P8                  R	J \        V
4      ^8  VVVVV4      .,          o.V*! ^
4       S.\        S0S28  \#        S5S64      \#        V^ 4      V	^ 8¬  S3P8                  R	J \        V
4      ^8  VVVVV4      .,          o.V*! ^4       S.\        \#        S0S24      S5S68„  V^ 8¬  \#        V	^ 4      S/P8                  R	J \        V4      ^8  VVVVV4      .,          o.V*! ^4       S.\        \#        S0S24      S5S68  V^ 8¬  \#        V	^ 4      S/P8                  R	J \        V4      ^8  VVVVV4      .,          o.V*! ^4       S.\        S0S28  S5S68„  V^ 8¬  V	^ 8¬  VVVVVVV4      .,          o.V*! ^4       S.\        S0S28„  S5S68  V^ 8¬  V	^ 8¬  VVVVVVV4      .,          o.V*! ^4       S.\        S0S28„  S5S68„  V^ 8¬  V	^ 8¬  VVVVVVVVV!4      .,          o.V*! ^4       S.\        S0S28  S5S68  V^ 8¬  V	^ 8¬  VVVVVVVVV!4      .,          o.V*! ^4       S.\        \#        V^ 4      VP8                  R	J VP8                  R	J VP8                  R	J VVV4      .,          o.V*! ^4       S.\        \#        V^ 4      VP8                  R	J VP8                  R	J VP:                  R	J VVV4      .,          o.V*! ^4       S.\        \#        V^ 4      VP8                  R	J V	P8                  R	J VP:                  R	J VVV4      .,          o.V*! ^4       S.\        \#        V^ 4      VP8                  R	J V	P8                  R	J VP8                  R	J VVV4      .,          o.V*! ^4       S.\        \#        WE,          ^ 4      VP8                  R	J V	P8                  R	J VVVVV4      .,          o.V*! ^4       S.\        \#        Wg,          ^ 4      VP8                  R	J V	P8                  R	J VVVVV4      .,          o.V*! ^4       \=        S VR	R7      p+\=        SVR	R7      p,S.\        V,\#        V^ 4      S5V8  VP8                  R	J VVVV4      .,          o.V*! R4       S.\        V,\#        V^ 4      S6V8  VP8                  R	J VVVV4      .,          o.V*! R4       S.\        V+\#        V^ 4      S0V8  V	P8                  R	J VVVV4      .,          o.V*! R4       S.\        V+\#        V^ 4      S2V8  V	P8                  R	J VVVV4      .,          o.V*! R4       \+        S.!  p-\1        V-4      R8w  d   V-# S.\        Wg,           S08„  \#        V^ 4      \#        V^ 4      VP8                  R	J VP8                  R	J V	P:                  R	J \        \        S/4      4      Wg,           S0,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^4       S.\        Wg,           S28„  \#        V^ 4      \#        V^ 4      VP8                  R	J VP8                  R	J V	P:                  R	J \        \        S/4      4      Wg,           S2,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^4       S.\        \#        S0S2^,
          4      \#        V^ 4      \#        V^ 4      VP8                  R	J VP8                  R	J V	^ 8¬  V	\        ,          \        \        S/4      4      8  VVVV!V%4      .,          o.V*! ^4       S.\        \#        S0S2^,           4      \#        V^ 4      \#        V^ 4      VP8                  R	J VP8                  R	J V	^ 8¬  V	\        ,          \        \        S/4      4      8  VVVV!V%4      .,          o.V*! ^4       S.\        S0S2^,
          8  \#        V^ 4      \#        V^ 4      VP8                  R	J VP8                  R	J V	^ 8¬  V	\        ,          \        \        S/4      4      8  \        \        S/4      4      Wg,           S0,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^4       S.\        S0S2^,           8„  \#        V^ 4      \#        V^ 4      VP8                  R	J VP8                  R	J V	^ 8¬  V	\        ,          \        \        S/4      4      8  \        \        S/4      4      Wg,           S2,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^4       S.\        \#        V^ 4      \#        V^ 4      WE,           ^ 8„  VP8                  R	J V	P8                  R	J VP:                  R	J \        \        S34      4      WE,           S5,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^4       S.\        \#        V^ 4      \#        V^ 4      WE,           S68„  VP8                  R	J V	P8                  R	J VP:                  R	J \        \        S34      4      WE,           S6,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^4       S.\        \#        V^ 4      \#        V^ 4      \#        S5S6^,
          4      VP8                  R	J V	P8                  R	J V^ 8¬  V\        ,          \        \        S34      4      8  \        \        S34      4      V^,           \        ,          8  VVVV!V%4      .,          o.V*! ^ 4       S.\        \#        V^ 4      \#        V^ 4      \#        S5S6^,           4      VP8                  R	J V	P8                  R	J V^ 8¬  V\        ,          \        \        S34      4      8  \        \        S34      4      V^,           \        ,          8  VVVV!V%4      .,          o.V*! ^!4       S.\        \#        V^ 4      \#        V^ 4      S5S6^,
          8  VP8                  R	J V	P8                  R	J V^ 8¬  V\        ,          \        \        S34      4      8  \        \        S34      4      WE,           S5,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^"4       S.\        \#        V^ 4      \#        V^ 4      S5S6^,           8„  VP8                  R	J V	P8                  R	J V^ 8¬  V\        ,          \        \        S34      4      8  \        \        S34      4      WE,           S6,
          ^,           \        ,          8  VVVV!V%4      .,          o.V*! ^#4       \+        S.!  # u uppi u uppi u upi u upi u upi u upi   \6         d    Rp% EL[i ; i)z=Return a condition under which the integral theorem applies. zChecking antecedents:z1  sigma=%s, s=%s, t=%s, u=%s, v=%s, b*=%s, rho=%sz1  omega=%s, m=%s, n=%s, p=%s, q=%s, c*=%s, mu=%s,z"  phi=%s, eta=%s, psi=%s, theta=%sc                 óê   <€ SS3 Fi  p \         P                  ! V P                  V P                  4       F7  w  rW,
          pVP                  '       g   K!  VP
                  '       g   K5    R # 	  Kk  	  R# ©FT)r  r  r„   r†   Ú
is_integerÚis_positive)r  rc   ÚjÚdiffr¨  r©  s       €€re   Ú_c1Ú_check_antecedents.<locals>._c1ú  sU   ø€ Ø�b“ˆAÜ!×)Ò)¨!¯$©$°·±Ö5‘�Ø•u�Ø—?—?’? t×'7×'7Ò'7Û ó 6ñ ñ
 rm   c                ó`   € V ^8g  ;'       d#    \        \        ^V ,
          4      4      \        8  # )aw  Returns True if abs(arg(1-z)) < pi, avoiding arg(0).

Explanation
===========

If ``z`` is 1 then arg is NaN. This raises a
TypeError on `NaN < pi`. Previously this gave `False` so
this behavior has been hardcoded here but someone should
check if this NaN is more serious! This NaN is triggered by
test_meijerint() in test_meijerint.py:
`meijerint_definite(exp(x), x, 0, I)`
)r"   r!   r   )r\   s   &re   Ú_condÚ!_check_antecedents.<locals>._cond$  s'   € ð ˜‘6×2Ð2œc¤# a¨!¥e£*›o´Ñ2Ð2rm   Fc                ó"  <€ V SS,
          ,          \        S4      ^SS,
          ,          ,          ,          \        S4      ,          VS	S,
          ,          \        S4      ^S	S,
          ,          ,          ,          \        S4      ,          ,           # r“   )r"   r7   )
Úc1Úc2Úomegar¶   Úpsir·   ÚsigmaÚthetaÚur  s
   &&€€€€€€€€re   Ú	lambda_s0Ú%_check_antecedents.<locals>.lambda_s0S  sc   ø€ Ø˜1˜q�5•z¤# e£*¨q°!°aµ%­yÕ"9Õ9¼#¸c»(ÕBØ˜!˜a�%•j¤ U£¨a°°Qµ­iÕ!8Õ8¼¸U»ÕCõDð Drm   Tz	  c%s: %sc                ó2   <€ \        R V SR,          34       R# )z  case %s: %sNr§   r‚  )ÚcountrŽ  s   &€re   ÚprÚ_check_antecedents.<locals>.prl  s   ø€ Ü� %¨¨r­Ð!3Ö4rm   )rˆ  ÚE1ÚE2ÚE3ÚE4éýÿÿÿr§   )rì   rð   r   r  r†   r„   r…   r‡   r©   r   r"   r(   r~  rƒ  rR   r   r   r   r*   rÉ   r$   rS   r   r6   rl  r4   r#   Ú	TypeErrorr¼  Úis_negativer†  )7r¨  r©  r{   r>  ru  r±   rë   rr   ÚbstarÚcstarÚrhoÚmuÚphir‰  r¿  rÅ  rc   r½  rÆ  Úc3Úc4Úc5Úc6Úc7Úc8Úc9Úc10Úc11Úc12Úc13Úz0ÚzosÚzsoÚc14rÂ  Úc14_altÚlambda_cÚc15rÌ  Úlambda_srŠ  r‰   rÐ  Ú
mt1_existsÚ
mt2_existsr¨   rŽ  rÇ  r¶   rÈ  r·   rÉ  rÊ  rË  r  s7   ff&                                           @@@@@@@@@re   Ú_check_antecedentsró  Ù  sz  ÿú€ ô ˜bŸk™k¨1Ó-�H€Eˆ1Ü˜bŸk™k¨1Ó-�H€Eˆ1Ü”C˜Ÿ™“J¤ B§E¡E£
¬C°·±«J¼¸B¿E¹E»
ÐCÓD�J€Aˆ!ˆQÜ”C˜Ÿ™“J¤ B§E¡E£
¬C°·±«J¼¸B¿E¹E»
ÐCÓD�J€Aˆ!ˆQØ�E�Q˜•U˜A•IÕ€EØ�E�Q˜•U˜A•IÕ€EØ
�%‰%�1�q•5˜!•)Õ
˜aÕ
€CØ	�‰�!�a•%˜•Õ	˜QÕ	€BØ
ˆa�%�1�q•5�/€CØ
ˆq�1�u�+˜Õ
˜SÕ
 €CÜˆq�1�u�q�y�>œCÔ 3°EÓ :Ó;Õ;¸aÀ!½eÕ
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õBØ�!�eõAõ ó õ õ Øñ€BäÔ" 5Ó)Ó*¨U´2­XÑ5€CÜ
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�R˜•X˜e•^Ó
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�R˜•X˜e•^Ó
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¨E°Q©JØ�b˜"˜b " c¨3ó0ð 1õ 1€Eá€r„FØ	Œc�!�a‘%˜˜Q™ ¨¡
¨E°Q©JØ�b˜"˜b " c¨3ó0ð 1õ 1€Eá€r„FØ	Œc�!�a‘%˜˜Q™ ¨¡
¨E°Q©JØ�b˜"˜b " b¨#¨s°Có9ð :õ :€Eá€r„FØ	Œc�!�a‘%˜˜Q™ ¨¡
¨E°Q©JØ�b˜"˜b " b¨#¨s°Có9ð :õ :€Eá€r„FØ	Œc”"�Q˜“(˜AŸM™M¨TÐ1°5×3DÑ3DÈÐ3LÈcÏoÉoÐaeÐNeÐgiÐkmÐorÓsÐtÕt€EÙ€r„FØ	Œc”"�Q˜“(˜AŸM™M¨TÐ1°5×3DÑ3DÈÐ3LÈcÏoÉoÐaeÐNeÐgiÐkmÐorÓsÐtÕt€EÙ€r„FØ	Œc”"�Q˜“(˜AŸM™M¨TÐ1°5×3DÑ3DÈÐ3LÈcÏoÉoÐaeÐNeÐgiÐkmÐorÓsÐtÕt€EÙ€r„FØ	Œc”"�Q˜“(˜AŸM™M¨TÐ1°5×3DÑ3DÈÐ3LÈcÏoÉoÐaeÐNeÐgiÐkmÐorÓsÐtÕt€EÙ€r„FØ	Œc”"�Q•S˜!“*˜e×/Ñ/°4Ð7¸×9JÑ9JÈdÐ9RØ�b˜"˜c 3ó(ð )õ )€Eá€r„FØ	Œc”"�Q•S˜!“*˜e×/Ñ/°4Ð7¸×9JÑ9JÈdÐ9RØ�b˜"˜c 3ó(ð )õ )€Eá€r„Fô & b¨!°DÔ9€JÜ% b¨!°DÔ9€JØ	Œc�*œb  A›h¨¨A©¨u×/@Ñ/@ÀDÐ/HÈ#ÈrÐSUÐWYÓZÐ[Õ[€EÙ€t„HØ	Œc�*œb  A›h¨¨A©¨u×/@Ñ/@ÀDÐ/HÈ#ÈrÐSUÐWYÓZÐ[Õ[€EÙ€t„HØ	Œc�*œb  A›h¨¨A©¨u×/@Ñ/@ÀDÐ/HÈ#ÈrÐSUÐWYÓZÐ[Õ[€EÙ€t„HØ	Œc�*œb  A›h¨¨A©¨u×/@Ñ/@ÀDÐ/HÈ#ÈrÐSUÐWYÓZÐ[Õ[€EÙ€t„Hô 	ˆE‰
€AÜ�!ƒ}˜ÔØˆà	Œc�!•%˜!‘)œR  1›X¤r¨#¨q£z°1·=±=ÀDÐ3HÈ%×J[ÑJ[Ð_cÐJcÐej×evÑevÐz~Ðe~ÜÔ)¨%Ó0Ó1°QµU¸QµYÀµ]ÄBÕ4FÑFØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	Œc�!•%˜!‘)œR  1›X¤r¨#¨q£z°1·=±=ÀDÐ3HÈ%×J[ÑJ[Ð_cÐJcÐej×evÑevÐz~Ðe~ÜÔ)¨%Ó0Ó1°QµU¸QµYÀµ]ÄBÕ4FÑFØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	Œc”"�Q˜˜A�“,¤ 1 a£¬"¨S°!«*°a·m±mÀtÐ6KÈU×M^ÑM^ÐbfÐMfØ˜1‘*˜e¤B�h¬Ô-@ÀÓ-GÓ)HÑHØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	Œc”"�Q˜˜A�“,¤ 1 a£¬"¨S°!«*°a·m±mÀtÐ6KÈU×M^ÑM^ÐbfÐMfØ˜1‘*˜e¤B�h¬Ô-@ÀÓ-GÓ)HÑHØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	Œc�!�a˜!•e‘)œR  1›X¤r¨#¨q£z°1·=±=ÀDÐ3HÈ%×J[ÑJ[Ð_cÐJcØ˜1‘*˜e¤B�h¬Ô-@ÀÓ-GÓ)HÑHÜÔ)¨%Ó0Ó1°QµU¸QµYÀµ]ÄBÕ4FÑFØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	ŒcØ	ˆA��E‰	”2�a˜“8œR  Q›Z¨¯©¸$Ð)>À×@QÑ@QÐUYÐ@YÐ[`ÐdeÑ[eØœ•(œSÔ!4°UÓ!;Ó<Ñ<ÜÔ)¨%Ó0Ó1°QµU¸QµYÀµ]ÄBÕ4FÑFØ�b˜#˜s Có	)ð *õ *€Eñ
 €r„FØ	Œc”"�Q˜“(œB˜s A›J¨­°©	°1·=±=ÀDÐ3HÈ%×J[ÑJ[Ð_cÐJcÐej×evÑevÐz~Ðe~ÜÔ)¨%Ó0Ó1°QµU¸QµYÀµ]ÄBÕ4FÑFØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	Œc”"�Q˜“(œB˜s A›J¨­°©	°1·=±=ÀDÐ3HÈ%×J[ÑJ[Ð_cÐJcÐej×evÑevÐz~Ðe~ÜÔ)¨%Ó0Ó1°QµU¸QµYÀµ]ÄBÕ4FÑFØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	Œc”"�Q˜“(œB˜s A›J¬¨1¨a°!­e«°a·m±mÀtÐ6KÈU×M^ÑM^ÐbfÐMfØ˜1‘*˜e¤B�h¬Ô-@ÀÓ-GÓ)HÑHÜÔ)¨%Ó0Ó1°U¸QµYÄµNÑBØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	Œc”"�Q˜“(œB˜s A›J¬¨1¨a°!­e«°a·m±mÀtÐ6KÈU×M^ÑM^ÐbfÐMfØ˜1‘*˜e¤B�h¬Ô-@ÀÓ-GÓ)HÑHÜÔ)¨%Ó0Ó1°U¸QµYÄµNÑBØ�b˜#˜s Có)ð *õ *€Eñ €r„FØ	ŒcÜ
ˆ1ˆa‹”"�S˜!“*˜a ! a¥%™i¨¯©¸$Ð)>À×@QÑ@QÐUYÐ@YÐ[`ÐdeÑ[eØŒb�”3Ô*¨5Ó1Ó2Ñ2ÜÔ Ó&Ó'¨1­5°1­9°q­=¼"Õ*<Ñ<Ø
ˆB��S˜#ó	ð  õ  €Eñ
 €r„FØ	ŒcÜ
ˆ1ˆa‹”"�S˜!“*˜a ! a¥%™i¨¯©¸$Ð)>À×@QÑ@QÐUYÐ@YÐ[`ÐdeÑ[eØŒb�”3Ô*¨5Ó1Ó2Ñ2ÜÔ Ó&Ó'¨1­5°1­9°q­=¼"Õ*<Ñ<Ø
ˆB��S˜#ó	ð  õ  €Eñ
 €r„Fäˆu‰:ÐùóC @ùÛCùÚOùÚKùÚPùÚLøôv ô Ø‹ðúsN   Ê8Aj:
Ë/8Ak 
Í AAkÎ%AAkÐAAkÑ(AAkà'BAk ãGAk ÁkAk+Ák*Ak+c                óü  € \        V P                  V4      w  r4\        VP                  V4      w  rTR pV! V P                  4      \        VP                  4      ,           p\        VP
                  4      V! V P                  4      ,           pV! V P                  4      \        VP                  4      ,           p	\        VP                  4      V! V P
                  4      ,           p
\        WxWšWS,          4      V,          # )a°  
Express integral from zero to infinity g1*g2 using a G function,
assuming the necessary conditions are fulfilled.

Examples
========

>>> from sympy.integrals.meijerint import _int0oo
>>> from sympy.abc import s, t, m
>>> from sympy import meijerg, S
>>> g1 = meijerg([], [], [-S(1)/2, 0], [], s**2*t/4)
>>> g2 = meijerg([], [], [m/2], [-m/2], t/4)
>>> _int0oo(g1, g2, t)
4*meijerg(((0, 1/2), ()), ((m/2,), (-m/2,)), s**(-2))/s**2
c                ó0   € V  Uu. uF  q) NK  	  up# u upi r`   rž   r{  s   & re   ÚnegÚ_int0oo.<locals>.neg  s   € Ù‹™A�q“™A‰ÐùŠs   …)rì   rð   r†   rÆ   r„   r  r  rO   )r¨  r©  r{   r‰  r>  rÇ  rö  rµ  r¶  rª  r«  s   &&&        re   Ú_int0oorø  	  s«   € ô" ˜BŸK™K¨Ó+�F€CÜ˜bŸk™k¨1Ó-�H€Eòá	ˆR�U‰U‹”d˜2Ÿ5™5“kÕ	!€BÜ	ˆb�i‰i‹™3˜rŸy™y›>Õ	)€BÙ	ˆR�U‰U‹”d˜2Ÿ5™5“kÕ	!€BÜ	ˆb�i‰i‹™3˜rŸy™y›>Õ	)€BÜ�2˜2 5¥9Ó-¨cÕ1Ð1rm   c           	     ó\  aa	€ \        W4      w  po	\        VP                  V4      w  poVV	3R lp^ RIHp V! WS	S,          ,          ,          RR7      \	        V! VP
                  4      V! VP                  4      V! VP                  4      V! VP                  4      VP                  4      3# )zAbsorb ``po`` == x**s into g. c                óL   <€ V  Uu. uF  qSS,          ,           NK  	  up# u upi r`   rž   )r   r±   r°   ru  s   & €€re   r!  Ú_rewrite_inversion.<locals>.tr+  s#   ø€ Ù!"Ó#¡˜A�A�a•C—�¡Ñ#Ð#ùÒ#s   †!r£  Tr¥  )	rì   rð   rå   r¤  rO   r„   r  r†   r  )
rˆ   r  r  r{   r>  r•   r!  r¤  r°   ru  s
   &&&&    @@re   Ú_rewrite_inversionrü  &  s�   ù€ ä˜"Ó �D€A€qÜ˜!Ÿ*™* aÓ(�D€A€qö$å(Ù�c˜a �c�(•l¨$Ô/Ü‘B�q—t‘t“H™b §¡›l©B¨q¯t©t«H±b¸¿¹³lÀAÇJÁJÓOðQð Qrm   c                ó�  a aaaaa€ \        R4       S P                  p\        VS4      w  r4V^ 8  d!   \        R4       \        \	        S 4      S4      # V3R loV3R lo\        \        S P                  4      \        S P                  4      \        S P                  4      \        S P                  4      .4      w  rVrxWV,           V,
          p	W…,
          V,
          p
Wš,
          ^,          pW‡,
          oS^8X  d   \
        P                  pMS^8”  d   ^pM\
        P                  p^S,
          ^,          \        S P                  !  ,           \        S P                  !  ,
          S,          oS P                  p\        RWVWxWšVS34       \        RVSV34       S P                  V^,          8¼  g   V^8¼  d   Wx8¼  g   \        R4       R# \         P"                  ! S P                  S P                  4       F3  w  rïWï,
          P$                  '       g   K  Wï8”  g   K'  \        R	4        R# 	  Wx8¼  d?   \        R
4       \'        S P                   Uu. uF  pS! V^,
          ^ ^ V4      NK  	  up!  # V V3R lpVVV3R lpVVV3R lpVVV3R lp. pV\'        ^V8*  ^V8*  V\(        ,          V,
          \(        ^,          8¬  V^ 8„  V! V\+        \
        P,                  \(        ,          V
^,           ,          4      ,          4      4      .,          pV\'        V^,           V8*  V^,           V8*  V^ 8„  V\(        ^,          8  V^ 8H  WW,
          ^,           \(        ,          V,
          \(        ^,          8¬  V! V\+        \
        P,                  \(        ,          W…,
          ,          4      ,          4      V! V\+        \
        P,                  ) \(        ,          W…,
          ,          4      ,          4      4      .,          pV\'        WX8H  V^ 8H  V^ 8„  SV,           \(        ,          V,
          \(        ^,          8¬  V! V4      4      .,          pV\'        \/        \'        Wx^,
          8*  ^V	8*  V	S^,          8*  4      \'        V^,           WV,           8*  WV,           Wx,           ^,          8*  4      4      V^ 8„  V\(        ^,          8  V	^,           \(        ,          V,
          \(        ^,          8¬  V! V\+        \
        P,                  \(        ,          V
,          4      ,          4      V! V\+        \
        P,                  ) \(        ,          V
,          4      ,          4      4      .,          pV\'        ^V8*  V^ 8„  V^ 8„  WÛ\(        ,          ,           \(        ^,          8  Wœ,           \(        ,          V,
          \(        ^,          8¬  V! V\+        \
        P,                  \(        ,          V
,          4      ,          4      V! V\+        \
        P,                  ) \(        ,          V
,          4      ,          4      4      .,          pVV^ 8H  .,          p\/        V!  # u upi )z6Check antecedents for the laplace inversion integral. z#Checking antecedents for inversion:z  Flipping G.c           
     ó^  <€ \        VS4      w  rVW,          p WV,          ,          pW&,          p. pV\        \        P                  \	        V4      ,          \
        ,          ^,          4      ,          pV\        \        P                  ) \	        V4      ,          \
        ,          ^,          4      ,          p	V'       d   Tp
MT	p
V\        \        \        V^ 4      \	        V4      ^ 8*  4      \	        V 4      R8*  4      .,          pV\        \        V^ 4      \        \        V4      ^ 4      \	        V4      ^ 8„  \	        V
4      ^ 8  4      .,          pV\        \        V^ 4      \        \        V4      ^ 4      \	        V4      ^ 8„  \	        V
4      ^ 8*  \	        V 4      R8*  4      .,          p\        V!  # )r®   r§   )rì   r*   r   rÉ   r   r   rR   rS   r   r   r    )r•   r°   rÊ   r\   ÚplusÚcoeffÚexponentrŽ  ÚwpÚwmÚwr{   s   &&&&&      €re   Ústatement_halfÚ4_check_antecedents_inversion.<locals>.statement_half<  sG  ø€ Ü(¨¨AÓ.‰ˆØ	�ˆØ	�A�X�ˆØ	�ˆØˆØŒs”1—?‘?¤2 a£5Õ(¬Õ+¨AÕ-Ó.Õ.ˆØŒs”A—O‘OÐ#¤B q£EÕ)¬"Õ,¨QÕ.Ó/Õ/ˆßØ‰AàˆAØ”#”bœ˜A˜q›¤2 a£5¨A¡:Ó.´°1³¸±Ó<Ð=Õ=ˆØ”#”b˜˜A“h¤¤2 a£5¨!£¬b°«e°a©i¼¸A»À¹ÓCÐDÕDˆØ”#”b˜˜A“h¤¤2 a£5¨!£¬b°«e°a©i¼¸A»À!¹Ü˜“e˜r‘kó#ð $õ 	$ˆä�5‰zÐrm   c           
     ó<   <€ \        S! WW#R4      S! WW#R4      4      # )zIProvide a convergence statement for z**a * exp(b*z**c),
c/f sphinx docs. TF)rR   )r•   r°   rÊ   r\   r  s   &&&&€re   Ú	statementÚ/_check_antecedents_inversion.<locals>.statementN  s)   ø€ ô ‘> !¨¨dÓ3Ù! !¨¨eÓ4ó6ð 	6rm   z9  m=%s, n=%s, p=%s, q=%s, tau=%s, nu=%s, rho=%s, sigma=%sz   epsilon=%s, theta=%s, delta=%sz-  Computation not valid for these parameters.Fz  Not a valid G function.z$  Using asymptotic Slater expansion.c                ót   <€ \        SP                   Uu. uF  pS! V^,
          ^ ^ V 4      NK  	  up!  # u upi r“   )rR   r„   )r\   r•   r  r  s   & €€re   ÚEÚ'_check_antecedents_inversion.<locals>.E~  s3   ø€ Ü¸¿ºÓ=¹°1‘Y˜q 1�u a¨¨AÖ.¹Ñ=Ñ>Ð>ùÒ=s   •5c                ó*   <€ S! SS) ^S,          V 4      # r“   rž   )r\   rÉ  r  rÊ  s   &€€€re   ÚHÚ'_check_antecedents_inversion.<locals>.H�  s   ø€ Ù˜  ¨¨%­°Ó3Ð3rm   c                ó,   <€ S! SS) ^S,          V R4      # )r”   Trž   ©r\   rÉ  r  rÊ  s   &€€€re   ÚHpÚ(_check_antecedents_inversion.<locals>.Hp„  s   ø€ Ù˜e e V¨Q¨u­W°a¸Ó>Ð>rm   c                ó,   <€ S! SS) ^S,          V R4      # )r”   Frž   r  s   &€€€re   ÚHmÚ(_check_antecedents_inversion.<locals>.Hm‡  s   ø€ Ù˜e e V¨Q¨u­W°a¸Ó?Ð?rm   )r~  rð   rì   Ú_check_antecedents_inversionr$  r   r  r†   r„   r…   r‡   rµ   ÚNaNr   r  rƒ  r  r  r»  rR   r   r*   rÉ   rS   )r  r{   r\   r>  rø   rë   rr   r¶   r·   r°  r©   rÛ  Úepsilonr  r•   r°   r  r  r  r  rŽ  rÉ  r  r  rÊ  s   ff                   @@@@re   r  r  2  sÂ  ý€ ä
Ð0Ô1Ø	�
‰
€AÜ˜!˜QÓ�D€AØˆ1„uÜˆÔä+¬G°A«J¸Ó:Ð:õõ$6ô ”C˜Ÿ™“Iœs 1§4¡4›y¬#¨a¯d©d«)´S¸¿¹³YÐ?Ó@�J€Aˆ!Ø
�%�!�)€CØ	
���€BØ�8�Q�,€CØ�E€EØ�„zÜ—&‘&‰Ø	�ŒØ‰ä—%‘%ˆØ�%�i˜�]œS !§$¡$™ZÕ'¬#¨q¯t©t©*Õ4°eÕ;€EØ�G‰G€EÜÐGØ�1˜ # uÐ-ô/äÐ.°¸%ÀÐ0GÔHð �G‰G�q˜•sŒN˜q Aœv¨!¬&ÜÐ>Ô?Ùô
 ×!Ò! !§$¡$¨¯©Ö-‰ˆØ�E××Ò !¦%ÜÐ.Ô/Úñ .ð 	„vÜÐ5Ô6Ü¸¿ºÓ=¹°1‘Y˜q 1�u a¨¨AÖ.¹Ñ=Ñ>Ð>ö?÷4÷?÷@ð €Eà	Œc�!�q‘&˜!˜q™& #¤b¥&¨5¥.´B°qµDÑ"8¸%À!¹)Ù�A”cœ!Ÿ/™/¬"Õ,¨b°1­fÕ5Ó6Õ6Ó7ó9ð :õ :€Eð 
Œc�!�a•%˜1‘*˜a !�e q™j¨%°!©)°U¼RÀ½T±\À1ÈÁ6Ø•5˜1•9œb•. 5Õ(¬B¨q­DÑ0Ù�Q”sœ1Ÿ?™?¬2Õ-¨q­uÕ5Ó6Õ6Ó7Ù�Q”sœAŸO™OÐ+¬BÕ.°µÕ6Ó7Õ7Ó8ó:ð ;õ ;€Eð
 
Œc�!‘&˜!˜q™& %¨!¡)Ø˜7•?¤BÕ&¨Õ.´"°Qµ$Ñ6¹¸!»ó>ð ?õ ?€Eð 
Œc”"”S˜ !�e™ Q¨#¡X¨s°e¸Aµg©~Ó>Ü˜˜Q� !¥%™¨­°1µ5¸!µ)Ñ);Ó<ó>à˜!‘)˜U¤R¨¥T™\¨C°!­G´R­<¸%Õ+?Ä2ÀaÅ4Ñ+GÙ�Q”sœ1Ÿ?™?¬2Õ-¨bÕ0Ó1Õ1Ó2Ù�Q”sœAŸO™OÐ+¬BÕ.¨rÕ1Ó2Õ2Ó3ó	5ð 6õ 6€Eð 
Œc�!�q‘&˜# ™' 5¨1¡9¨e¼"µf­n¼rÀ!½tÑ.CØ•=¤"Õ$ uÕ,´°1µÑ4Ù�Q”sœ1Ÿ?™?¬2Õ-¨bÕ0Ó1Õ1Ó2Ù�Q”sœAŸO™OÐ+¬BÕ.¨rÕ1Ó2Õ2Ó3ó5ð 6õ 6€Eð
 
ˆa�1‰fˆXÕ€Eô ˆu‰:Ðùò[ >s   ÉYc                óò   € \        V P                  V4      w  r4\        \        V P                  V P
                  V P                  V P                  W2V,          ,          4      V) 4      w  rPWR,          V ,          # )zG
Compute the laplace inversion integral, assuming the formula applies.
)rì   rð   r&  rO   r„   r  r†   r  )r  r{   r±   r°   r•   r  s   &&&   re   Ú_int_inversionr  ¬  sT   € ô ˜!Ÿ*™* aÓ(�D€AÜœ' !§$¡$¨¯©°!·$±$¸¿¹À!ÀqÅDÅ&ÓIÈAÈ2ÓN�D€AØ�3ˆq�5€Lrm   c                óh  a a!€ ^RI HpHo!HpHo  \
        '       g   / s\        \
        4       \        V \        4      '       dÐ   \        V P                  V4      P                  V4      w  rV\        V4      ^8”  d   R# V^ ,          pVP                  '       d1   VP                  V8w  g   VP                  P                   '       g   R# MWa8w  d   R# ^^ \        V P"                  V P$                  V P&                  V P(                  WV,          4      3.R3# T pV P+                  V\,        4      p \/        V \,        4      pV\
        9   Ed?   \
        V,          p	V	 EF*  w  r«rÍV P1                  V
RR7      pV'       g   K$  / pVP3                  4        F!  w  pp\5        \7        VRR7      RR7      VV&   K#  	  Tp\        V\8        4      '       g   VP+                  V4      pVR8X  d   K�  \        V\8        \:        34      '       g   \5        VP+                  V4      4      p\=        V4      R8X  d   KÕ  \        V\>        4      '       g	   V! V4      p. pV EF   w  pp\A        \5        VP+                  V4      P+                  \,        V4      RR7      V4      p VP+                  V4      P+                  \,        V4      p\E        TT3,           !  PG                  \H        PJ                  \H        PL                  \H        PN                  4      '       d   K»  \        TP"                  TP$                  TP&                  TP(                  \5        TP                  RR7      4      pTPQ                  TT3,           4       EK#  	  V'       g   EK'  VV3u # 	  V'       g   R# \S        R4       V V!3R	 lpTp \U        R
RV 4      pR p V! WVVRRR7      w  pppV! VVVV4      pVft   \W        RR4      pVV PX                  9  dW   \[        W4      '       dF    V! V P+                  VVV,          4      VVVRRR7      w  pppV! VVVV4      P+                  V^4      pVeD   VPG                  \H        PJ                  \H        P\                  \H        PL                  4      '       d   \S        R4       R# \^        P`                  ! V4      p. pV Fº  p V P                  V4      w  pp\        V4      ^8”  d   \c        R4      hV^ ,          p\A        VP                  V4      w  ppVV^ \        VP"                  VP$                  VP&                  VP(                  \5        \7        VRR7      RR7      VV,          ,          4      3.,          pK¼  	  \S        RV4       VR3#   \B         d     EKE  i ; i  T d    Rp ELÒi ; i  T d    Rp ELki ; i)a,  
Try to rewrite f as a sum of single G functions of the form
C*x**s*G(a*x**b), where b is a rational number and C is independent of x.
We guarantee that result.argument.as_coeff_mul(x) returns (a, (x**b,))
or (a, ()).
Returns a list of tuples (C, s, G) and a condition cond.
Returns None on failure.
)Úmellin_transformÚinverse_mellin_transformÚIntegralTransformErrorÚMellinTransformStripErrorNT)Úold)Úlift)Úexponents_onlyFz)Trying recursive Mellin transform method.c           
     óŽ   <€  S! WW#RRR7      #   S d/    ^ RI Hp S! T! \        \        T 4      4      4      YTRRR7      u # i ; i)z»Calling simplify() all the time is slow and not helpful, since
most of the time it only factors things in a way that has to be
un-done anyway. But sometimes it can remove apparent poles. T)Ú
as_meijergÚneedeval)Úsimplify)rå   r'  rW   r   )ÚFru  r{   Ústripr'  r   r  s   &&&& €€re   Úmy_imtÚ_rewrite_single.<locals>.my_imt
  sY   ø€ ð
	0Ù+¨A°!Ø7;ÀdôLð Løà(ô 	0Ý/Ù+Ùœ¤ q£	Ó*Ó+¨Q°5Ø¨$ô0ò 0ð	0ús   ƒ �2AÁAru  zrewrite-singlec           	     ó   € \        WR R7      pVeU   ^ RIHp Vw  rE\        V! VRR7      4      p\	        WE3\        W\        P                  \        P                  34      R 34      # \        W\        P                  \        P                  34      # )T)Úonly_double©ÚhyperexpandÚnonrepsmall)Úrewrite)	Ú_meijerint_definite_4rå   r/  Ú_my_unpolarifyr4   rQ   r   rç   rE  )rd   r{   r¨   r/  rl   r‰   s   &&    re   Úmy_integratorÚ&_rewrite_single.<locals>.my_integrator  sw   € Ü! !°DÔ9ˆØŠ=Ý2Ø‰IˆCÜ ¡¨S¸-Ô!HÓIˆCÜ˜c˜[Ü& q¬a¯f©f´a·j±jÐ*AÓBÀDÐIóKð Kä˜œqŸv™v¤q§z¡zÐ2Ó3Ð3rm   )Ú
integratorr'  r&  r•   )r6  r&  r'  z"Recursive Mellin transform failed.zUnexpected form...z"Recursive Mellin transform worked:)2Ú
transformsr  r  r  r   Ú_lookup_tablerË   rý   rO   rX   rð   ræ   r  rè   ré   r*   r§  r„   r  r†   r  r»   r\   r�   rþ   Úitemsr$   r%   rj  rT   rl  rÆ   rì   Ú
ValueErrorr	   rk   r   rE  ÚComplexInfinityÚNegativeInfinityr‚   r~  r0  r+  rÛ   r8  r  r   r  ÚNotImplementedError)"rd   r{   Ú	recursiver  r  r   rë   Úf_r±   r   rƒ   Útermsr‰   rŠ   r»   Úsubs_r^  r_  rl   rˆ   r  r±  r*  ru  r4  r(  r)  r>  r•   rj   rÊ   r°   r   r  s"   &&&                             @@re   Ú_rewrite_singlerB  ¼  sÝ  ù€ ÷;ó ;÷ ‹=ØˆÜœ]Ô+ä�!”W×ÒÜ˜!Ÿ*™* aÓ(×5Ñ5°aÓ8‰ˆÜˆq‹6�AŒ:ÙØˆa�DˆØ�8�8ˆ8Ø�v‰v˜Œ{ !§%¡%×"3×"3Ð"3Ùð #4àŒVÙØ�A”w˜qŸt™t Q§X¡X¨q¯t©t°Q·X±X¸u½wÓGÐHÐIÈ4ÐOÐOà	
€BØ	�‰ˆq”!‹€AÜ�”1‹€AØŒMÕÜ˜!ÕˆÜ*+Ñ&ˆG˜DØ—7‘7˜7¨�7Ó-ˆDß‰tØ�Ø#Ÿz™zž|‘G�C˜Ü!+¬H°R¸dÔ,CØ;?ô"A�E˜#“Jñ  ,ð �Ü! $¬×-Ò-ØŸ9™9 T›?�DØ˜5”=ÙÜ! $¬¬{Ð(;×<Ò<Ü% d§i¡i°£oÓ6�DÜ˜dÓ# uÔ,ÙÜ! %¬×.Ò.Ù! $›K�EØ�Ü#‘F�C˜Ü'¬
°3·8±8¸D³>×3FÑ3FÄqÈ!Ó3LØBFô)HØIJóL�Bð!ØŸF™F 4›L×-Ñ-¬a°Ó3˜ô ˜r Q D�yÑ*×.Ñ.¬q¯z©z¼1×;LÑ;LÌa×N`ÑN`×aÒaÙ Ü §¡ a§h¡h°·±°a·h±hÜ *¨1¯:©:ÀdÔ KóM�Aà—J‘J˜r Q D�y×)ñ $÷ ’3Ø ˜9Ò$ñG +,÷L ÙÜ
Ð6Ô7ö0ð 	€AÜˆsÐ$ aÓ(€Aò4ðÙ& q¨Q¸=Ø05ÀôF‰ˆˆ5�!á�1�a˜˜EÓ"ˆð 	‚yô �CÐ)Ó*ˆØ�A—N‘NÔ"¤|°A×'9Ò'9ðÙ.¨q¯v©v°a¸¸1½«~¸qÀ!Ø:GØ8<ÀuôN‘��5˜!ñ ˜1˜a  EÓ*×/Ñ/°°1Ó5�ð 	‚y�A—E‘Eœ!Ÿ*™*¤a§e¡e¬Q×->Ñ->×?Ò?ÜÐ3Ô4ÙÜ�=Š=˜Ó€DØ
€CÛˆØ�~‰~˜aÓ ‰ˆˆ1Üˆq‹6�AŒ:Ü%Ð&:Ó;Ð;Øˆa�DˆÜ˜aŸj™j¨!Ó,‰ˆˆ1Ø��A”w˜qŸt™t Q§X¡X¨q¯t©t°Q·X±XÜ)¬(Ø#$¨4ô+1ØAEô Gà ! 1¥õ %ó&ð 'ð (õ 	(Šñ ô Ð/°Ô3Ø�ˆ9Ðøô_ &ô !Û ð!ûð` "ô Ø‹ðûð *ô Ø“ðús7   Ê%VÎ2V ÐAV$ ÖVÖVÖ	V!Ö V!Ö$	V1Ö0V1c                óp   € \        W4      w  r4p\        WQV4      pV'       d   W4V^ ,          V^,          3# R# )zç
Try to rewrite ``f`` using a (sum of) single G functions with argument a*x**b.
Return fac, po, g such that f = fac*po*g, fac is independent of ``x``.
and po = x**s.
Here g is a result from _rewrite_single.
Return None on failure.
N)r  rB  )rd   r{   r>  rˆ   r  r  s   &&&   re   Ú	_rewrite1rD  J  s;   € ô ˜AÓ!�J€CˆQÜ˜˜iÓ(€AßØ˜˜!�˜a �dÐ"Ð"ñ 	rm   c           	     óP  a€ \        V S4      w  r#p\        ;QJ d(    V3R l\        V4       4       F  '       g   K   RM	  RM! V3R l\        V4       4       4      '       d   R# \        V4      pV'       g   R# \	        \        VV3R lV3R lV3R l.4      4      p\        P                  ! RV4       Fm  w  pw  rx\        VSV4      p	\        VSV4      p
V	'       g   K,  V
'       g   K6  \        V	^,          V
^,          4      pVR8w  g   KY  W#V	^ ,          V
^ ,          V3u # 	  R# )	zô
Try to rewrite ``f`` as a product of two G functions of arguments a*x**b.
Return fac, po, g1, g2 such that f = fac*po*g1*g2, where fac is
independent of x and po is x**s.
Here g1 and g2 are results of _rewrite_single.
Returns None on failure.
c              3  óB   <"  € T F  p\        VSR 4      RJ x € K  	  R# 5i)FN)rB  r4  s   & €re   rf   Ú_rewrite2.<locals>.<genexpr>a  s   øé € Ð
L¹|°tŒ?˜4  EÓ*¨dÕ2»|ùr6  TFNc           	     ó„   <€ \        \        \        V ^ ,          S4      4      \        \        V ^,          S4      4      4      # rw   )Úmaxr  rô   ©r¶   r{   s   &€re   r|   Ú_rewrite2.<locals>.<lambda>g  ó,   ø€ ”#”cœ* Q q¥T¨1Ó-Ó.´´J¸qÀ½tÀQÓ4GÓ0HÔIrm   c           	     ó„   <€ \        \        \        V ^ ,          S4      4      \        \        V ^,          S4      4      4      # rw   )rI  r  rù   rJ  s   &€re   r|   rK  h  rL  rm   c           	     ó„   <€ \        \        \        V ^ ,          S4      4      \        \        V ^,          S4      4      4      # rw   )rI  r  r  rJ  s   &€re   r|   rK  i  s1   ø€ ”#”cÔ0°°1µ°qÓ9Ó:ÜÔ0°°1µ°qÓ9Ó:ô<rm   rº  )
r  r7  r  r  rÆ   r   r  r  rB  rR   )rd   r{   rˆ   r  r  r   r>  Úfac1Úfac2r¨  r©  r‰   s   &f          re   Ú	_rewrite2rQ  X  sì   ø€ ô ˜A˜qÓ!�J€CˆQß
ƒsÔ
L¼yÈ¼|Ó
L‡s‡s‚sÔ
L¼yÈ¼|Ó
L×LÒLÙÜ˜!Ó€AßÙÜŒW�QÜIÜIô	<ð=ó >ó 	?€Aô $-×#4Ò#4°]ÀAÖ#FÑˆ	‘<�DÜ˜T 1 iÓ0ˆÜ˜T 1 iÓ0ˆß‰2—"‘"Ü�r˜!•u˜b �eÓ$ˆDØ�uŽ}Ø  1¥ r¨!¥u¨dÐ2Ò2ó $Grm   c                óØ  € \        V 4      p . p\        \        W4      \        P                  0,          \
        R7       Fw  p\        V P                  WV,           4      V4      pV'       g   K/  VP                  WV,
          4      p\        V\        \        4      '       d   VP                  V4       Ku  Vu # 	  V P                  \        4      '       d{   \        R4       \        \!        V 4      V4      pV'       dS   \#        V\$        4      '       g,   ^ RIHp V! \+        V4      VP-                  \.        4      4      # VP1                  V4       V'       d   \3        \5        V4      4      # R# )zÿ
Compute an indefinite integral of ``f`` by rewriting it as a G function.

Examples
========

>>> from sympy.integrals.meijerint import meijerint_indefinite
>>> from sympy import sin
>>> from sympy.abc import x
>>> meijerint_indefinite(sin(x), x)
-cos(x)
rÚ   ú*Try rewriting hyperbolics in terms of exp.©ÚcollectN)r   rß   r  r   rç   r   Ú_meijerint_indefinite_1r»   ra   rN   rO   r‚   rk   r1   r~  Úmeijerint_indefiniter0   rý   rÆ   Úsympy.simplify.radsimprU  r
   rö   r*   ÚextendÚnextr   )rd   r{   Úresultsr•   rl   ÚrvrU  s   &&     re   rW  rW  u  s  € ô 	�‹
€AØ€GÜÔ*¨1Ó0´A·F±F°8Õ;ÔAQ×RˆÜ% a§f¡f¨Q°AµÓ&6¸Ó:ˆßÙØ�h‰h�q˜a�%Ó ˆÜ�”UœG×$Ò$Ø�N‰N˜3ÖàŠJñ Sð 	‡u�uÔ× Ò ÜÐ;Ô<Ü!Ü'¨Ó*¨Aó/ˆçÜ˜b¤$×'Ò'Ý:Ùœ|¨BÓ/°·±¼#³Ó?Ð?Ø�N‰N˜2ÔßÜ”G˜GÓ$Ó%Ð%ñ rm   c           	     óª  aa€ \        RV RS4       ^ RIHpHp \	        V S4      pVf   R# Vw  rVrx\        RV4       \
        P                  p	V EFh  w  r«p\        VP                  S4      w  rÞ\        VS4      w  ppVV,          pWZ,          S^V,           ,          ,          V,          pV^,           V,          o\        RR\
        P                  4      pV3R lp\        ;QJ d,    R	 V! VP                  4       4       F  '       g   K   R
M!	  RM! R	 V! VP                  4       4       4      '       dv   \        \        VP                  4      \        VP                   4      ^S,
          .,           \        VP                  4      S) .,           \        VP"                  4      V4      ) pMs\        \        VP                  4      ^S,
          .,           \        VP                   4      \        VP                  4      \        VP"                  4      S) .,           V4      pVP$                  '       dH   V P'                  S^ 4      P)                  \
        P*                  \
        P,                  4      '       g   ^ pMRpV! VP'                  VVSV,          ,          4      VR7      pW“! VV,          R
R7      ,          p	EKk  	  V3R lp\/        V	RR7      p	V	P0                  '       dB   . pV	P2                   F#  w  pp\5        V! V4      4      pVVV3.,          pK%  	  \7        VRR/ p	M\5        V! V	4      4      p	\7        V	\5        V4      3\9        V S4      R
34      # )z/Helper that does not attempt any substitution. z,Trying to compute the indefinite integral ofÚwrt)r/  r¤  Nz could rewrite:r±   zmeijerint-indefinitec                ó>   <€ V  Uu. uF  qS,           NK  	  up# u upi r`   rž   )r¶   r•   rÛ  s   & €re   r!  Ú#_meijerint_indefinite_1.<locals>.trº  s   ø€ Ù%&Ó'¡Q ˜—G�G¡QÑ'Ð'ùÒ'r¢  c              3  óX   "  € T F   qP                   ;'       d	    V^ 8*  R8H  x € K"  	  R# 5i)rx   TN)r»  )rb   r°   s   & re   rf   Ú*_meijerint_indefinite_1.<locals>.<genexpr>¼  s&   é € ÐC¹(°Q�|‰|×0Ð0  a¡¨DÑ 0Ô0»(ùs   ‚*™*TF)Úplacer¥  c                óˆ   <€ \        \        V 4      RR7      p \        P                  ! V P	                  S4      ^,          4      # )a9  This multiplies out superfluous powers of x we created, and chops off
constants:

    >> _clean(x*(exp(x)/x - 1/x) + 3)
    exp(x)

cancel is used before mul_expand since it is possible for an
expression to have an additive constant that does not become isolated
with simple expansion. Such a situation was identified in issue 6369:

Examples
========

>>> from sympy import sqrt, cancel
>>> from sympy.abc import x
>>> a = sqrt(2*x + 1)
>>> bad = (3*x*a**5 + 2*x - a**5 + 1)/a**2
>>> bad.expand().as_independent(x)[0]
0
>>> cancel(bad).expand().as_independent(x)[0]
1
F)Údeep)r   rW   r   Ú
_from_argsÚas_coeff_add)rl   r{   s   &€re   Ú_cleanÚ'_meijerint_indefinite_1.<locals>._cleanÎ  s4   ø€ ô. œ ›¨5Ô1ˆÜ�~Š~˜c×.Ñ.¨qÓ1°!Õ4Ó5Ð5rm   )Úevaluaterj  )r~  rå   r/  r¤  rD  r   rç   rì   rð   r0  rÈ   r7  r†   rO   rÆ   r„   r  r  Úis_extended_nonnegativer»   rk   r  r;  r5   r^   rj   r3  r4   rQ   )rd   r{   r/  r¤  r
  rˆ   r  Úglr‰   rl   r  ru  r  r•   r°   r>  rÊ   Úfac_r±   r!  r¨   rc  rh  rh  rø   rÛ  s   &f                       @re   rV  rV  š  s¡  ù€ ä
Ð9¸1¸eÀQÔGß5ä	�1�a‹€BØ	‚záàÑ€CˆRÜ
Ð˜bÔ!Ü
�&‰&€CÜ‰ˆˆaÜ˜aŸj™j¨!Ó,‰ˆÜ˜b !Ó$‰ˆˆ1Ø	ˆQ�ˆð �w˜˜Q �U�Õ# aÕ'ˆØ�1�u�a�iˆô �3Ð.´·±Ó6ˆõ	(ç‹3ÑC¹"¸Q¿T¹T¼(ÓC�3�3Š3ÑC¹"¸Q¿T¹T¼(ÓC×CÒCÜÜ�Q—T‘T“
œD §¡›N¨a°­e¨WÕ4´d¸1¿4¹4³jÀSÀDÀ6Õ6IÌ4ÐPQ×PXÑPXË>Ð[\ó^ð ^‰Aô Ü�Q—T‘T“
˜a �e˜WÕ$¤d¨1¯8©8£n´d¸1¿4¹4³jÄ$ÀqÇxÁxÃ.ÐUXÐTXÐSYÕBYÐ[\ó^ˆAð ×$×$Ð$¨Q¯V©V°A°q«\×-=Ñ-=¼a¿e¹eÄQ×EVÑEV×-WÒ-WØ‰EàˆEÙ˜Ÿ™˜q ! A q¥D¥&Ó)°Ô7ˆð 	ˆy˜˜a� tÔ,Õ,‹ñK õN6ô4 ˜ tÔ
,€CØ
××ÐØˆØ—H”H‰DˆAˆqÜ™v a›yÓ)ˆAØ˜˜A˜�xÕŠGñ ô ˜Ð1¨5Ñ1‰ä™V C›[Ó)ˆÜ�cœ>¨$Ó/Ð0´8¸A¸q³>À4Ð2HÓIÐIrm   c                óì
  € \        RWW#34       \        V 4      p V P                  \        4      '       d   \	        R4       R# V P                  \
        4      '       d   \	        R4       R# WW#3w  rErg\        R4      pV P                  W4      p TpW#8X  d   \        P                  R3# . p	V\        P                  J d4   V\        P                  Jd    \        V P                  W) 4      W) V) 4      # V\        P                  J Ed!   \	        R4       \        W4      p
\	        RV
4       \        V
\        RR	7      \        P                  .,            FÐ  p\	        R
V4       VP                   '       g   \	        R4       K.  \#        V P                  WV,           4      V4      pVf   \	        R4       Ka  \#        V P                  WV,
          4      V4      pVf   \	        R4       K”  Vw  rÎVw  rß\%        \'        Wï4      4      pVR8X  d   \	        R4       KÄ  WÍ,           pVV3u # 	  EM~V\        P                  J d/   \        WV\        P                  4      pV^ ,          ) V^,          3# W#3\        P                  \        P                  38X  dH   \#        W4      pV'       d3   \)        V^ ,          \*        4      '       d   V	P-                  V4       EMÓV# EMÏV\        P                  J d®   \        W4       Fž  pVV,
          ^ 8¬  R8X  g   K  \        RV4       \#        V P                  WV,           4      \/        VV,           V,
          4      ,          V4      pV'       g   Kl  \)        V^ ,          \*        4      '       d   V	P-                  V4       Kœ  Vu # 	  V P                  WV,           4      p W2,
          p^ pV\        P                  Jd}   \1        \        P2                  \5        V4      ,          4      p\7        V4      pV P                  VVV,          4      p V \/        W1,
          4      V,          ,          p \        P                  p\	        RW#4       \	        RV 4       \#        W4      pV'       d2   \)        V^ ,          \*        4      '       d   V	P-                  V4       MV# VP                  \8        4      '       d›   \	        R4       \        \;        V4      WVV4      pV'       dr   \=        V\>        4      '       gK   ^ RI H!p V! \E        V^ ,          4      V^ ,          PG                  \0        4      4      3VR,          ,           pV# V	PI                  V4       V	'       d   \K        \M        V	4      4      # R# )a   
Integrate ``f`` over the interval [``a``, ``b``], by rewriting it as a product
of two G functions, or as a single G function.

Return res, cond, where cond are convergence conditions.

Examples
========

>>> from sympy.integrals.meijerint import meijerint_definite
>>> from sympy import exp, oo
>>> from sympy.abc import x
>>> meijerint_definite(exp(-x**2), x, -oo, oo)
(sqrt(pi), True)

This function is implemented as a succession of functions
meijerint_definite, _meijerint_definite_2, _meijerint_definite_3,
_meijerint_definite_4. Each function in the list calls the next one
(presumably) several times. This means that calling meijerint_definite
can be very costly.
z$Integrating %s wrt %s from %s to %s.z+Integrand has DiracDelta terms - giving up.Nz5Integrand has Singularity Function terms - giving up.r{   Tz  Integrating -oo to +oo.z  Sensible splitting points:)rÖ   Úreversez  Trying to split atz  Non-real splitting point.z'  But could not compute first integral.z(  But could not compute second integral.Fz)  But combined condition is always false.zTrying x -> x + %szChanged limits tozChanged function torS  rT  :r”   NN)'rƒ  r   rk   r>   r~  rP   r   r»   r   rç   r<  rE  Úmeijerint_definiter  rß   r   Úis_extended_realÚ_meijerint_definite_2rW  rR   ra   rO   r‚   r?   r*   rÉ   r!   r"   r1   r0   rý   rÆ   rX  rU  r
   rö   rY  rZ  r   )rd   r{   r•   r°   r?  Úx_Úa_Úb_r/  r[  r  rÊ   Úres1Úres2Úcond1Úcond2r‰   rl   ÚsplitrÝ  r\  rU  s   &&&&                  re   rp  rp  ô  s>  € ô< Ð2°Q¸1°LÔAÜ�‹
€AØ‡u�uŒZ×ÒÜÐ<Ô=Ùà‡u�uÔ ×!Ò!ÜÐFÔGÙà˜1�Z�N€BˆBô 	ˆc‹
€AØ	�‰ˆq‹€AØ	€Aà„vÜ—‘˜ˆ~Ðà€GØŒA×ÑÓ 1¬A¯J©JÓ#6Ü! !§&¡&¨¨B£-°°B¸¸Ó;Ð;à	
Œa× Ñ Ô	 äÐ*Ô+Ü*¨1Ó0ˆ	ÜÐ-¨yÔ9Ü˜	Ô'7ÀÔFÌ!Ï&É&È×QÐQˆAÜÐ)¨1Ô-Ø×%×%Ð%ÜÐ4Ô5ÙÜ(¨¯©°°qµ5Ó)9¸1Ó=ˆDØŠ|ÜÐ@ÔAÙÜ(¨¯©°°qµ5Ó)9¸1Ó=ˆDØŠ|ÜÐAÔBÙØ‰KˆDØ‰KˆDÜœS Ó.Ó/ˆDØ�uŒ}ÜÐBÔCÙØ•+ˆCØ˜�9Òó) Rð, 
Œa�j‰j‹Ü   q¬!¯*©*Ó5ˆØ�A•ˆw˜˜A�ˆÐà
ˆ”A—F‘FœAŸJ™JÐ'Ô	'ä# AÓ)ˆßÜ�C˜•FœG×$Ò$Ø—‘˜sÖ#à�
ñ	 ð ”—
‘
‹?Ü/°Ö5�Ø˜•I ‘N tÖ+ÜÐ0°%Ô8Ü/°·±°q¸e½)Ó0DÜ1:¸1¸u½9Àq½=Ó1Iõ1JØKLóN�Cç‘sÜ  A¥¬×0Ò0Ø#ŸN™N¨3Ö/à#&šJñ 6ð �F‰F�1˜!•eÓˆØ�EˆØˆØ”A—J‘JÓÜ”a—o‘o¤c¨!£fÕ,Ó-ˆCÜ�A“ˆAØ—‘�q˜#˜a�%Ó ˆAØ”˜1�5Ó! #Õ%Õ%ˆAÜ—
‘
ˆAäÐ" AÔ)ÜÐ$ aÔ(Ü# AÓ)ˆßÜ�C˜•FœG×$Ò$Ø—‘˜sÕ#à�
Ø	‡v�vÔ ×!Ò!ÜÐ;Ô<ÜÜ'¨Ó+¨R°Ró9ˆçÜ˜b¤$×'Ò'Ý:Ùœl¨2¨a­5Ó1°2°aµ5·;±;¼sÓ3CÓDÐFÈÈBÍÕO�Ø�	Ø�N‰N˜2ÔßÜ”G˜GÓ$Ó%Ð%ñ rm   c                ó6  € V R3.pVR,          ^ ,          pV0p\        V4      pWT9  d   W%R3.,          pVP                  V4       \        V4      pWT9  d   W%R3.,          pVP                  V4       VP                  \        \
        4      '       d7   \        \        V4      4      pWT9  d   W%R3.,          pVP                  V4       VP                  \        \        4      '       d1   ^ RI	H
p V! V4      pWt9  d   W'R3.,          pVP                  V4       V# )z5Try to guess sensible rewritings for integrand f(x). zoriginal integrandr   r   zexpand_trig, expand_mul)Úsincos_to_sumztrig power reductionr§   )r   rŒ   r   rk   r9   r1   r   r6   r7   Úsympy.simplify.fur|  )rd   r{   rl   ÚorigÚsawÚexpandedr|  Úreduceds   &&      re   Ú_guess_expansionr‚    s  € àÐ#Ð$Ð
%€Càˆr�7�1�:€DØˆ&€CÜ˜$Ó€HØÔØ˜<Ð(Ð)Õ)ˆØ�‰�Ôä�d‹|€HØÔØ˜8Ð$Ð%Õ%ˆØ�‰�Ôà‡x�xÔ%Ô'9×:Ò:Üœk¨$Ó/Ó0ˆØÔØÐ8Ð9Ð:Õ:ˆCØ�G‰G�HÔà‡x�x””S×ÒÝ3Ù Ó%ˆØÔØÐ4Ð5Ð6Õ6ˆCØ�G‰G�GÔà€Jrm   c                óê   € \        RRV RR7      pV P                  W4      p TpV ^ 8X  d   \        P                  R3# \	        W4       F(  w  r4\        RV4       \        W14      pV'       g   K&  Vu # 	  R# )a`  
Try to integrate f dx from zero to infinity.

The body of this function computes various 'simplifications'
f1, f2, ... of f (e.g. by calling expand_mul(), trigexpand()
- see _guess_expansion) and calls _meijerint_definite_3 with each of
these in succession.
If _meijerint_definite_3 succeeds with any of the simplified functions,
returns this result.
r{   zmeijerint-definite2T)ÚpositiveÚTryingN)r0  r»   r   rç   r‚  r~  Ú_meijerint_definite_3)rd   r{   Údummyr  Úexplanationrl   s   &&    re   rr  rr  Ÿ  sl   € ô  �3Ð-¨q¸4Ô@€EØ	�‰ˆqÓ€AØ€AàˆA„vÜ�v‰v�tˆ|Ðä*¨1Ö0‰ˆÜˆx˜Ô%Ü# AÓ)ˆß‰3ØŠJó	 1rm   c                óÖ  € \        W4      pV'       d   V^,          R8w  d   V# V P                  '       d¯   \        R4       V P                   Uu. uF  p\        W14      NK  	  pp\        ;QJ d    R V 4       F  '       d   K   RM	  RM! R V 4       4      '       dD   . p\
        P                  pV F  w  rgW&,          pWW.,          pK  	  \        V!  pVR8w  d   W'3# R# R# R# u upi )z¢
Try to integrate f dx from zero to infinity.

This function calls _meijerint_definite_4 to try to compute the
integral. If this fails, it tries using linearity.
Fz#Expanding and evaluating all terms.c              3  ó(   "  € T F  qR Jx € K
  	  R # 5ir`   rž   )rb   r¨   s   & re   rf   Ú(_meijerint_definite_3.<locals>.<genexpr>Ê  s   é € Ð+¡d ˜�}£dùs   ‚TN)r2  Úis_Addr~  rj   ri   r   rç   rR   )rd   r{   rl   r  ÚressrŽ  r¨   rÊ   s   &&      re   r†  r†  ½  sÆ   € ô   Ó
%€Cß
ˆs�1�v˜ŒØˆ
Ø‡x‡x€xÜÐ4Ô5Ø56·V²VÓ<±V°Ô% aÖ+±VˆÐ<ß‹3Ñ+¡dÓ+�3�3Š3Ñ+¡dÓ+×+Ò+ØˆEÜ—&‘&ˆCÛ‘�Ø•�Ø˜•’ñ ô �U‘ˆAØ�EŒzØ�v�ñ ñ ,ñ ùâ<s   ÁC&c                ó*   € \        \        V 4      4      # r`   )rl  r$   )rd   s   &re   r3  r3  Õ  s   € Ü”j “mÓ$Ð$rm   c                óh  € ^ RI Hp \        RV 4       V'       gÞ   \        WRR7      pVeÍ   Vw  rVrx\        RWVV4       \        P
                  p	V Fg  w  r«p V
^ 8X  d   K  \        WZ,          WaV,          ,          W4      w  r Wš\        W4      ,          ,          p	\        V\        W4      4      pVR8X  g   Kg   M	  \        V4      pVR8X  d   \        R4       M\        RV	4       \        V! V	4      4      V3# \        W4      pVEe+   R EF!  pVw  rVrÞp\        R	WVWÞ4       \        P
                  p	V F¨  w  pppV F™  w  ppp\        W_,          V,          WaVV,           ,          ,          VVW4      pVf   \        R
4          R# Vw  p
pp\        RV
VV4       \        V\        VVV4      4      pVR8X  d    M Wš\        VVV4      ,          ,          p	K›  	  K¨   M	  \        V4      pVR8X  d   \        RV4       Kõ  \        RV	34       V'       d   W˜3u # \        V! V	4      4      V3u # 	  R# R# )aa  
Try to integrate f dx from zero to infinity.

Explanation
===========

This function tries to apply the integration theorems found in literature,
i.e. it tries to rewrite f as either one or a product of two G-functions.

The parameter ``only_double`` is used internally in the recursive algorithm
to disable trying to rewrite f as a single G-function.
r.  ÚIntegratingF)r>  Nú#Could rewrite as single G function:úBut cond is always False.z&Result before branch substitutions is:z!Could rewrite as two G functions:zNon-rational exponents.zSaxena subst for yielded:z&But cond is always False (full_pb=%s).z)Result before branch substitutions is: %srº  )rå   r/  r~  rD  r   rç   rx  rš  rR   r†  r3  rQ  r·  ró  rø  rƒ  )rd   r{   r-  r/  r
  rˆ   r  r  r‰   rl   r  ru  rq  r¨  r©  r³  Ús1Úf1r´  Ús2Úf2r¨   Úf1_Úf2_s   &&&                     re   r2  r2  Ù  s  € õ +ä
ˆ=˜!ÔçÜ�q uÔ-ˆØŠ>Ø!ÑˆC�QÜÐ8¸#À1ÔEÜ—&‘&ˆCÛ‘��aØ˜”6ÙÜ(¨­°°aµ4µ¸Ó>‘�Øœ 1›Õ(Õ(�Ü˜4Ô!5°aÓ!;Ó<�Ø˜5–=Ùñ ô " $Ó'ˆDØ�uŒ}ÜÐ2Õ3äÐ?ÀÔEÜ%¡k°#Ó&6Ó7¸Ð=Ð=ô 
�1‹€BØ	ƒ~Ü$ˆGØ$&Ñ!ˆC�R˜TÜÐ6¸ÀÔHÜ—&‘&ˆCÛ ‘
��B˜Û"$‘J�B˜˜BÜ'¨­¨r­	°2¸"¸r½'µlµ?Ø(*¨B°ó<�Aà’yÜÐ8Ô9ÜØ"#‘K�A�s˜CÜÐ6¸¸3ÀÔDÜ˜tÔ%7¸¸SÀ!Ó%DÓE�DØ˜u”}ÙØœW S¨#¨qÓ1Õ1Õ1’Cñ #%ñ Ùñ !ô  " $Ó'ˆDØ�uŒ}ÜÐ@À'ÖJäÐCÀcÀWÔMßØ˜9Ò$Ü%¡k°#Ó&6Ó7¸Ð=Ò=ó7 %ñ rm   c           	     óø  € T pTp\        RRR7      pV P                  WB4      p \        RV 4       \        W4      '       g   \        R4       R# \        P
                  pV P                  '       d   \        V P                  4      pM\        V \        4      '       d   V .pMRpV'       Ed”   . p. pV'       Edu   VP                  4       p	\        V	\        4      '       d   \        V	4      p
V
P                  '       d   WjP                  ,          pK`   \        V	P                  ^ ,          V4      w  r¼V^8X  d   VP                  X4       Kš  VP                  V	4       K­  V	P                   '       d«   \        V	4      p
V
P                  '       d   WjP                  ,          pKð  WP"                  P$                  9  dL    \        V	P                  V4      w  r¼V^8X  d,   VP                  X\'        V	P"                  4      ,          4       VP                  V	4       EKi  VP                  V	4       EK}  \)        V!  p\+        V!  p WP$                  9  dv   \        RW4       \-        \/        V4      ^ 4      pVR8X  d   \        R	4       R# V \1        W%,           4      ,          p\        R
Wí4       \3        VP                  W$4      V34      # \5        W4      pVEe�   Vw  pppp\        RVVV4       \        P
                  pV Fd  w  ppp \7        VV,          VVV,          ,          W4      w  pp VV\9        WV4      ,          ,          p\;        V\=        W4      4      pVR8X  g   Kd   M	  \?        V4      pVR8X  d   \        R4       R# \        RV4       ^ RI H!p \?        V! V4      4      pVPE                  \F        4      '       g   V\G        V4      ,          pVP                  W"V,           4      p\        V\H        4      '       g   VP                  W"V,           4      p^RI%H&p \3        VP                  W$4      V3V! VP                  W$4      WR4      R34      # R#   \         d    ^ p EL6i ; i  \         d    ^ p EL§i ; i)aº  
Compute the inverse laplace transform
$\int_{c+i\infty}^{c-i\infty} f(x) e^{tx}\, dx$,
for real c larger than the real part of all singularities of ``f``.

Note that ``t`` is always assumed real and positive.

Return None if the integral does not exist or could not be evaluated.

Examples
========

>>> from sympy.abc import x, t
>>> from sympy.integrals.meijerint import meijerint_inversion
>>> meijerint_inversion(1/x, x, t)
Heaviside(t)
r±   Tr¥  zLaplace-invertingzBut expression is not analytic.Nz.Expression consists of constant and exp shift:Fz3but shift is nonreal, cannot be a Laplace transformz1Result is a delta function, possibly conditional:r‘  r’  z"Result before branch substitution:r.  )ÚInverseLaplaceTransform)'r   r»   r~  r8  r   rç   Úis_MulrÆ   rj   rý   r*   Úpopr   rì   rá   r‚   rè   ré   rÛ   r,   r   r   r   r    r>   r4   rD  rü  r  rR   r  r3  rå   r/  rk   r?   rj  r7  rš  )rd   r{   r±   r?  Út_Úshiftrj   rh  Úexponentialsr!   rd  r•   r°   r‰   rl   r
  rˆ   r  r  r  ru  r/  rš  s   &&&                    re   Úmeijerint_inversionr   !  s   € ð$ 
€BØ	
€BÜˆc˜Ô€AØ	�‰ˆr‹€AÜ
Ð Ô"Ü˜×ÒÜÐ0Ô1Ùô �F‰F€Eà‡x‡x€xÜ�A—F‘F‹|‰Ü	�A”s×	Ò	Øˆs‰àˆç€tØˆØˆßˆdØ—(‘(“*ˆCÜ˜#œs×#Ò#Ü˜c“{�Ø—;—;�;ØŸI™IÕ%�DÙðÜ)¨#¯(©(°1­+°qÓ9‘D�Að ˜”6Ø ×'Ñ'¨Ö*à—N‘N 3Ö'Ø——�Ü˜c“{�Ø—;—;�;ØŸI™IÕ%�DÙØŸH™H×1Ñ1Ô1ðÜ-¨c¯g©g°qÓ9™˜ð ˜A”vØ$×+Ñ+¨A¬c°#·(±(«m­OÔ<Ø—‘˜s×#à—‘˜s×#Ü�\Ñ"ˆÜ�‰Mˆà—‘ÔÜÐ?ÀÔJÜ”"�U“)˜QÓˆØ�5Œ=ÜÐHÔIÙØ”
˜1�9Ó%Õ%ˆÜÐBÀCÔNä˜#Ÿ(™( 1›/¨4Ð0Ó1Ð1ä	�1‹€BØ	ƒ~ØÑˆˆR��DÜÐ4°c¸2¸qÔAÜ�f‰fˆÛ‰GˆAˆq�!Ü% c¨!¥e¨R°°1µ­W°aÓ;‰DˆAˆqØ�1”^ A¨!Ó,Õ,Õ,ˆCÜ�tÔ9¸!Ó?Ó@ˆDØ�uŽ}Ùñ ô ˜dÓ#ˆØ�5Œ=ÜÐ.Ö/äÐ7¸Ô=Ý2Ü ¡¨SÓ!1Ó2ˆCØ—7‘7œ9×%Ò%Ø”y “|Õ#�Ø—(‘(˜1 %�iÓ(ˆCÜ˜d¤D×)Ò)Ø—y‘y ¨¥IÓ.�Ý;Ü˜cŸh™h q›o¨tÐ4Ù5°b·g±g¸a³nÀaÈTÓRÐTXÐYó[ð [ñ/ øôI +ô Ø“Aðûô /ô Ø›ðús$   ÄQ Æ9Q( ÑQ%Ñ$Q%Ñ(Q9Ñ8Q9rÅ   )F)³Ú__conditional_annotations__râ   Ú
__future__r   r  Úsympyr   Ú
sympy.corer   r   Úsympy.core.addr   Úsympy.core.basicr   Úsympy.core.cacher   Úsympy.core.containersr	   Úsympy.core.exprtoolsr
   Úsympy.core.functionr   r   r   r   r   Úsympy.core.mulr   Úsympy.core.intfuncr   Úsympy.core.numbersr   r   Úsympy.core.relationalr   r   r   Úsympy.core.sortingr   r   Úsympy.core.symbolr   r   r   r   Úsympy.core.sympifyr   Ú(sympy.functions.combinatorial.factorialsr   Ú$sympy.functions.elementary.complexesr   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   Ú&sympy.functions.elementary.exponentialr*   r+   r,   Ú#sympy.functions.elementary.integersr-   Ú%sympy.functions.elementary.hyperbolicr.   r/   r0   r1   Ú(sympy.functions.elementary.miscellaneousr3   Ú$sympy.functions.elementary.piecewiser4   r5   Ú(sympy.functions.elementary.trigonometricr6   r7   r8   r9   Úsympy.functions.special.besselr:   r;   r<   r=   Ú'sympy.functions.special.delta_functionsr>   r?   Ú*sympy.functions.special.elliptic_integralsr@   rA   Ú'sympy.functions.special.error_functionsrB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   Ú'sympy.functions.special.gamma_functionsrM   Úsympy.functions.special.hyperrN   rO   Ú-sympy.functions.special.singularity_functionsrP   Ú	integralsrQ   Úsympy.logic.boolalgrR   rS   rT   rU   rV   Úsympy.polysrW   rX   Úsympy.utilities.iterablesrY   Úsympy.utilities.miscrZ   r~  r[   rƒ  r\   ra   rË   Úsympy.utilities.timeutilsrÌ   Útimeitr�   r:  rá   rì   rô   rù   r  r  r  r  r  r$  r&  r)  Ú__annotations__r0  r+  r8  rW  rl  rr  rx  r†  rš  r·  ró  rø  rü  r  r  r8  rB  rD  rQ  rW  rV  rp  r‚  rr  r†  r3  r2  r   )r¡  s   @re   Ú<module>rÉ     s(  øðôõ8 #Û å ß Ý Ý "Ý $Ý 'Ý -÷8õ 8å Ý #ß +ß :Ñ :ß 8ß :Ó :Ý &Ý >÷÷ ÷ ñ ÷ GÑ FÝ 7÷9ó 9å 9ß J÷ó ç MÓ Mß Iß M÷6÷ 6÷ 6ñ 6å 9ß 8Ý MÝ ß JÕ Jß &Ý 9Ý 0Ý 2ñ 
ˆ#ƒJ€òòJPõb /Ù	�)Ó	€õ	Nô	˜*ô 	òHòDòBIò
!òH$òNò.Iò>0ò QòDð4 +-€Ð
&Ó ,ò	ò#òOôyòv"ô	òô*mò`&ô<F.òRjò`	2ò:	Qòwòtð €ð 	ØóIó ó 	ðIôX#ò3ò:"&òJWJðt ñG&ó ðG&òTò@ò<ò0%ð óD>ó ðD>ôNn[rm   