
    \hR                     f   S SK Jr  S SKJrJrJrJr  S SKJr  S SK	J
r
  S SKJrJrJrJr  S SKJrJrJr  S SKJrJrJr  S SKJr  S S	KJrJr  S S
KJrJrJ r J!r!  S SK"J#r#J$r$  S SK%J&r&J'r'  S SK(J)r)J*r*  S SK+J,r,J-r-  S SK.J/r/  S SK0J1r1  S SK2J3r3J4r4J5r5J6r6J7r7J8r8J9r9  S SK:J;r;  S SK<J=r=J>r?  S SK@JArAJBrBJCrCJDrDJErEJFrFJGrGJHrHJIrI  S rJS rKS rLS rMS rNS rO\;S 5       rPS rQS rRS rSS rT\;S  5       rUS! rVS" rW\;S# 5       rX\;S$ 5       rYS% rZS& r[S' r\S( r]S) r^S* r_S+ r`S, raS- rbS. rcS/ rdS0 reS1 rfS2 rgS3 rhS4 riS5 rjg6)7    )expand_func)IRationaloopi)S)default_sort_key)Absargre
unpolarify)exp	exp_polarlog)coshacoshsinh)sqrt)	Piecewisepiecewise_fold)cossinsincasin)erferfc)gamma	polygamma)hypermeijerg)Integral	integrate)hyperexpandsimplify)_rewrite_single	_rewrite1meijerint_indefinite
_inflate_g_create_lookup_tablemeijerint_definitemeijerint_inversion)slow)verify_numericallyrandom_complex_number)	xyabcdstzc                     S n S nU " [         S[         5        U " [         S-  S[         S-  5        U " [         S-  [        [         S-  -  -   [        S-   [         S-  5        U" [         S-  [         -   5        U" [         [        -  5        S nU" [        [         * 5      [        [         5      -  [         5        [	        [        [         5      [        [         5      -  [         5      [        S5      * S[        [        5      -  -  S[        [        SS5      S[        SS5      [        R                  [        S	S5      4S
4S[        SS5      S44S[        S[        -  [        -  5      -  [         S-  -  5      4/S4:X  d   eg )Nc           	         [        [        [        /[        /U/[        /U 5      [
        5      nUc   e[        US   S   S   [        5      (       d   eUS   S   S   R                  R                  [
        5      X44:X  d   eg )Nr      )	r&   r    r2   r3   r5   r0   
isinstanceargumentas_coeff_mul)exprr4   mes       \/var/www/auris/envauris/lib/python3.13/site-packages/sympy/integrals/tests/test_meijerint.pyr7   test_rewrite_single.<locals>.t   s{    GQC!qcA3=qA}}!A$q'!*g....tAwqz""//2q$i???    c           	      l    [        [        [        /[        /[        /[
        /U 5      [        5      b   eg N)r&   r    r2   r3   r4   r5   r0   r?   s    rB   tntest_rewrite_single.<locals>.tn!   s*    wsQC!qc4@!DLLLrD      r;   c                     SSK Jn  [        X5      nU" US    Vs/ s H  oDS   US   -  PM     sn6 R                  [        [
        5      n[        XPU5      (       d   eg s  snf )Nr   Addr;   )sympy.core.addrM   r&   replacer   r   r.   )r?   r0   rM   rresrA   s         rB   utest_rewrite_single.<locals>.u*   s^    &D$1Q404Ca&Q-40199s!!1---- 1s   Ar         )rJ    @   T)r0   r1   r   r   r&   r   r   r    r   r   Halfr   r   )r7   rH   rR   s      rB   test_rewrite_singler[      sE   @M aAJadAq!tadQq!tVmQUAqD!q!taxLq!tH. c1"gc!fna 3q6#a&=!,G8QtBxZ !Xb!_a!Q!QPRVW"a!,-r)BqDG2D/DQT/IKL 
MNR	TT T TrD   c                  >   [        [        S-  [        [        /[        /[
        /[        /[        S-  [        [        S-  -  -   5      -  S-  [        5      S[        S-  SS[        [        /[        /[
        /[        /[        S-  [        S-   -  5      4/S4:X  d   eg )NrV   r;      rJ   r   T)r'   r0   r    r2   r3   r4   r5   r1   rW   rD   rB   test_rewrite1r^   C   s    QT'1#sQC!adQq!tVmDDQFJ	
AqDAq'1#sQC!adAElCDEtLM M MrD   c                  6   S n U " S[         5        U " S[         5        U " SS[         -  5        U " S[         S-  5        U " S[         [        S5      -  5        U " [         S-  [         5        U " S[         [        S5      -  -  S[         [        S5      -  -  5        g )	Nc           	         [        [        /[        /[        /[        /U5      U -  n[        [        5       S-  [        [        5       S-  [        -   [        [        5       [        [        5       0n[        U[        5      nUc   e[        UR                  U5      UR                  [        5      R                  U5      [        5      (       d   eg )N
   )r    r2   r3   r4   r5   randcplxr   r(   r0   r.   subsdiff)facr   grc   integrals        rB   r7   0test_meijerint_indefinite_numerically.<locals>.tI   s    QC!qcA3,S08:b=!XZ]Q%68:q(*.'1-###!!&&,a0@0E0Ed0KQOOOOrD   rJ   r;   r]   3/2rV   rU   z7/3)r0   r   )r7   s    rB   %test_meijerint_indefinite_numericallyrj   H   sw    P aGaGa1IaAJaAeHadAJa1U8mQq!E({]#rD   c                      [        [        [        SS5      u  pU R                  (       a  USL d   e[        [        [        [        [        5      u  pU R                  (       a  USL d   eg )Nr   T)r+   r0   is_zeror   )vr3   s     rB   test_meijerint_definitern   Y   sN    aAq)DA99d""aB+DA99d""rD   c                    ^ [         [        5       S-  [        [        5       S-  [        -   [        [        5       [
        [        5       [        [        5       S-  0mU4S jn U " [         /[        //[        /[
        //[        S5      (       d   eU " [         [        /[        //[        /[
        //[        S5      (       d   eU " [         /[        //[        [        /[
        //S[        S-  -  S5      (       d   eg )Nra   c                    > SSK Jn  [        XU5      nU" [        XS5      6 n[	        UR                  T5      UR                  T5      [        SSS9$ )Nr   )Mulg?g)r3   r5   )sympy.core.mulrq   r    r)   r.   rc   r0   )r2   r3   r   nrq   m1m2rc   s          rB   r7   test_inflate.<locals>.td   sF    &Q3*R#$ ""''$-SDQQrD   rV   r;   )r2   rb   r3   r   r4   r5   r1   r0   )r7   rc   s    @rB   test_inflaterw   `   s    xz"}aB!2Axzxz1hjm-DR qcA3Z1#sQ****q!fqc]aS1#J1----qcA3Z1a&1#!Q$2222rD   c                     SSK Jn   U " SSS9u  pn[        [        U-
  S-  * 5      [        [        U-
  S-  * 5      -  n[	        U[        S[
        4SS9n[        UR                  5       5      [        S5      [        [        5      -  [        [        S5      X-   -  S-  5      S-   [        US-  * S-  X-  -   US-  S-  -
  5      -  -  S	-  :X  d   e[	        [        [        U-
  S-  * 5      [        [        U-
  S-  * 5      -  [        U[        -  5      -  [        S[
        4SS9n[        U5      [        S5      [        [        5      -  [        [        S5      SU-  SU-  -   U-   -  S	-  5      S-   -  [        US-  * US-  -
  SU-  SU-  -   U-   S-  S
-  -   5      -  S	-  :X  d   e[        [	        [        [        U-
  U-
  U-
  S-  * 5      [        S[
        4SS95      [        [        5      S-  S[        X-   U-   5      -   -  :X  d   e[        [	        [        [        U-   U-   U-   S-  * 5      [        S[
        4SS95      [        [        5      S-  S[        X-   U-   5      -
  -  :X  d   eg )Nr   symbolsza b cTpositiver;   r    rJ   rU      )sympy.core.symbolrz   r   r0   r"   r   r%   expandr   r   r   )rz   r2   r3   r4   rP   rA   s         rB   test_recursiver   p   sr   )g-GA!a!eaZKq1uqj[))A!aBZ.AAHHJQR	T!Wae_Q	!	#S!Q$q13Aa)?%@@	BBC	DE E E 	#Azk"3Q
{#33C!H<q!RjRVWAA;QR#d1gqsQqSy1}5a781<=c1a4%!Q$,Q319q=1
Q
C ?  	  !	"# # # IcAEAIMA#5"56Ar
DQRR
AAEAI&'( ( (IcAEAIMA#5"56Ar
DQRR
AAEAI&'( ( (rD   c                     SSK Jn   SSKJn  U" SSS9u  p#n[	        [        / / S// X#-  5      [        / / US-  /U* S-  /US-  S-  5      -  US[        45      R                  (       d   eU" S	SS
9n[	        [        U-  [        / / /S// /[        5      -  [        S[        45      [        US-   5      :X  d   e[	        [        U-  [        / / /S// /[        5      -  [        S[        4SS9[        US-   5      :X  d   e[        [	        [        U-  [        / / /S// /[        5      -  [        S[        4SS9[        5      (       d   e[        [        [        5      [        5      [        [        5      :X  d   eU" SSS
9u  pV[        [        [        U-  [        SU5      S   5      XeS-   -  US-   -  :X  d   e[        [        S-   S-  [        [        * 5      -  [        S[        5      S:X  d   eU" SSS
9u  pt[        [        [        U-
  SU-  -  S-  * 5      [        S[        5      u  p[        U5      [!        ["        5      U-  S[%        USU-  -  5      -
  -  :X  d   eU	S:X  d   e[        [        U* [        -  5      [        U[        -  5      -  [        S[        5      u  p[        U5      SXG-
  -  :X  d   e[        [        [        5      [        [        * S5      [        S5      S4:X  d   eU " [        [        [        5      [        S[&        5      S   5      [        [&        5      S-
  :X  d   eU " [        [        [        * 5      [        S[        5      S   5      S[        [        [&        [)        [        5      -  5      * [+        [        5      -  5      -
  :X  d   e[        [        [        S-  * 5      [        [        * [        5      [!        ["        5      S4:X  d   e[        [        [+        [        5      * 5      [        [        * [        5      S:X  d   e[        [        S[        -  S-
  S-  * 5      [        [        * [        5      [!        ["        5      S-  S4:X  d   e[        [        [+        S[        -  S-
  5      * 5      [        [        * [        5      S:X  d   e[        [        [        U-
  U-  S-  * S-  5      [!        S["        -  US-  -  5      -  [        [        * [        5      S:X  d   e[        [-        [        5      S-  [        [        * [        5      ["        S4:X  d   e[        [        [        * 5      [/        [        5      -  [        S[        5      [0        R2                  S4:X  d   eS n[5        S5       HM  n[	        [        [        * 5      [/        [        5      -  [        U-  -  [        S[        4SS9U" U5      :X  a  MM   e   [        [	        [        [        * 5      [/        [        U-   5      -  [        S[        4SS95      [!        S5      [/        U["        S-  -   5      -  S-  :X  d   eU" S5      u  pVn[        [        / / US-  /U* S-  /[        S-  5      [        / / US-  /U* S-  /[        S-  5      -  [        US-
  -  -  [        S[        5      SSSU-  S-
  -  -  [        SU-  S-   5      -  [        US-  US-  -   U-   5      -  [        U* S-  US-  -   U-
  S-   5      [        US-  US-  -
  U-
  S-   5      -  [        US-  US-  -   U-
  S-   5      -  -  [7        U5      S:  [7        U5      [1        S5      S-  :  -  [7        U5      S-  [7        U5      S-  -   [7        U5      -   S:  -  4:X  d   e[	        [/        [        U-  5      [/        [        U-  5      -  [        S[        4SS9[        [/        [        U-  5      [/        [        U-  5      -  [        S[        45      :X  d   e[	        [        [        S-  * 5      [9        [        5      -  [        S[        4SS9[!        ["        5      [;        S[0        R2                  5      -  S-  R                  5       :X  d   eSSKJn  U" SSS9n[        [	        [        [        * 5      [        U-  -  [        SS95      U" US-   [        5      :X  d   eU" SSS
9n[        S[        -
  U-  [/        U[        -  5      -  [        SS5      [!        ["        5      U-  [        US-   5      -  [        SUS-  [0        R2                  -   US-  S-   44SS[0        R2                  4[A        SS5      44US-  S-  5      -  S-  S4:X  d   eU" SSS
9u  pR[        [	        [        U-  [        U* [        S-  -  5      -  [        [        * [        45      5      XR* S-  [0        R2                  -
  -  SU-  S-   -  [        US-  [0        R2                  -   5      -  S-  :X  d   eg ) Nr   )r   ry   zs t muTrealr;   rU   r6   r{   rJ   r}   Fa brV   )   Tzsigma mu)r;   T)rJ   Tc                 |    SS[         S-  -   -  R                  [         U 5      R                  [         S5      SU -  -  $ NrJ   r;   rT   )r0   rd   rc   )rs   s    rB   rQ   test_meijerint.<locals>.res   s7    1q!t8""1a(--a3R!G;;rD      za b s
lowergammars   )integeralpharW   rT   r   za s)!sympy.core.functionr   r   rz   r"   r    r   is_Piecewiser0   r   r<   r!   r(   r   r%   r+   r   r   r   r   r   absr   r   r   rZ   ranger   r   r   'sympy.functions.special.gamma_functionsr   r   )r   rz   r6   r7   mur2   r3   sigmair4   _rQ   rs   r   r   s                  rB   test_meijerintr      sW	   *)xd+HA"WRaS"ac2b"r!tfs1ugq!tAv>?BZ!!-. . . 	d#AQT'2r(aS"Iq99Aq":Fa!e  QT'2r(aS"Iq99Aq":!#&+AEl3 3 3i1Wb"XRy!%D D!"Ar
E;         A*c!f444 54(DA&q!tQ15a89	E
AE   q1uqjaR0!Q;zIII 
T2IEcQVag$6#:":;Q2FDAA;$r(5.!d2qw<.@*@AAAA99c2#a%jU1W5q!R@DAA;!RZ.((( c!fa"a0SVTNBBB$SVQ15a89SVaZGGG$S!WaA6q9:	CQs1vXs1v%&&' ' ' c1a4%j!bS"5$r(D9IIIIc3q6'lAsB79DDDcAaC!Ga<-0!bS"=	b!T  c3qsQw<-0!bS"=JJJcQVUNQ#6"6q"89$qtE1H}:MM"b*-67 7 7d1gqj!bS"5"dCCC c1"gc!fnaB7AFFD>III<1XaRQ1,q!Rj$GF 	  
 Ic1"gc!a%j01a*dK aQAX.q01 1 1 gGA!gb"qseqbdVQqSA2rAaC5A2a4&!A#67781q5zBCDa
 
1qsQw<bdQh	'acAaCi!m(<	<!A!a!#$U1Q319q=1+<%==!A#!)a-!#$%
& UQY2a51Q46>*beAg1a.?"Q%.G!.KL	NO O O SAYs1a4y(1a*dCQT3q!t9$q!Rj12 2 2 S!Q$ZA&Ar
DA	b)Aqvv&	&q	(0023 3 3 CT"AIc1"gadlAt<=1q5!   Gd+Eq1uunSq\91aC	b%eai(	("uQw7Ga!7 2Aqvv"a(:;UAXb[*J 
JJK
LMQ	SS S S
 54(DAIad3r!Q$w</!bS">?	BqD166MR!GaK(qsQVV|)<<Q>? ? ?rD   c            	         SSK Jn Jn  [        [	        U" [
        [        5      U" [        [        5      -  [        -  [        S[        4SSS95      S[        [        [
        S-  [        S-  -
  -  5      -  [        [
        [        -
  -  [
        [        -   -  -  :X  d   e[        [	        U" [
        [        5      U" [
        [        5      -  [        -  [        S[        4SSS95      SS[
        -  -  :X  d   e[        [	        [        [        [        -  5      [        S-  S-
  [        [        R                  -   * -  -  [        S[        4SSS9S-  [        S-  [        -  [        [        5      -  [!        [        R                  [        -
  5      -  -  5      U" [        [        5      :X  d   e[	        [        U" S[        5      -  [        SS9[        U" S[        5      -  :X  d   e[	        [        U " S[        5      -  [        SS9[        U " S[        5      -  :X  d   e[	        U" S[        5      [        SS9U" S[        5      * :X  d   e[	        U" S[        5      S-  [        -  [        SS9U" S[        5      S-  U" S[        5      S-  -   * S-  :X  d   e[	        U" S[        5      S-  [        S-  -  [        SS9S	[        -  U" S[        5      S-  -  S[        -  U" S[        5      S-  -  -
  SU" S[        5      -  U" S[        5      -  -   U" S[        5      S-  [        -  -
  :X  d   e[	        U" S[        5      U" S[        5      -  [        SS9U" S[        5      S-  * S-  :X  d   e[	        [        S-  U" S[        5      -  U" S[        5      -  [        SS9[        S-  U" S[        5      S-  -  S-  :X  d   e[	        U" S[        5      U" S[        5      -  [        -  [        SS9[        U" S[        5      S-  -  [        U" S[        5      S-  -  -   U" S[        5      U" S[        5      -  -
  :X  d   e[	        U" S[        S-  5      [        -  [        SS9U" S[        S-  5      * S-  :X  d   eg )
Nr   besselibesseljTnoner    condsr;   rJ   r}   r   )sympy.functions.special.besselr   r   r%   r"   r2   r8   r3   r   r   r   r0   r1   r   rZ   r   r   r   s     rB   test_besselr      s   AIgamGAqM9!;aBZ!1 2	#b!A#!)n
r1q5z1q5123 3 3 IgamGAqM9!;aBZ!1 256!W= = =
 Ic!A#h1qa!&&jM'BB !Rj$fF1qb)%
*;;= > 	1   Qwq!}_a6!GAqM/IIIQwq!}_a6!GAqM/III WQ]At4AFFFWQ]A%a'D9
!Q-
WQ]A-
-.q01 1 1 WQ]A%ad*At<
1WQ]A!GAqM1$4 44
GAqM/'!Q-
'	(*1!Q-*:1*<	== = = WQ]71a=0!TB	A	!  QT'!Q-'15q$G	1WQ]Aa     WQ]71a=02AtD	
71a=!	a1q 00	0AqM'!Q-'
() ) ) WQ1%a'D9	AqD	!  rD   c                     SSK Jn   SSKJn  S nU" S[        S-  S-   -  5      [        [        5      U" [        5      -  :X  d   eU" [        [        S-  S-   -  5      [        [        5      U" [        5      -  :X  d   eU" [        [        * 5      [        -  5      U" [        S-
  5      :X  d   eU" S[        S[        S-  -   5      -  5      U " S[        5      U" [        5      -  :X  d   e[        [        [        5      [        S[        S-  -   5      -  [        [        5      b   eU" [        [        S-  5      5      b   e[        [        [        S-  * 5      [        [        5      b   eg )Nr   r   )	Heavisidec                 >    [        [        U [        [        5      5      $ rF   )r   r,   r6   r7   fs    rB   invtest_inversion.<locals>.inv!  s    1!Q:;;rD   rJ   r;   )r   r   'sympy.functions.special.delta_functionsr   r6   r   r7   r   r   r   r,   )r   r   r   s      rB   test_inversionr     s    6A<q!Q$(|Ay| 3333q!Q$(|Ay| 3333sA2wqy>Yq1u----qa!Q$h GAqM)A,$>>>> tAwtA1H~5q!<DDDs1a4y>!!!sAqD5z1a0888rD   c                     SSK Jn   SSKJn  U " SSS9n[	        [
        U-  5      [        S[	        U5      -  [	        [        5      -  5      -  n[        U[        [        5      nUR                  (       a   eU " SSS	9nUR                  X%5      n[        U[        [        5      nUR                  (       d   eUR                  S   S   UR                  X%5      :X  d   eUR                  S
   S   (       d   eU" U[        [        S 5      nUR                  S
   S   U:X  d#  UR                  S
   S   UR                  :X  d   eg g )Nr   Symbol)InverseLaplaceTransformr2   Tr{   r   r3   r   rT   rJ   )r   r   sympy.integrals.transformsr   r   r   r   r6   r,   r7   r   rc   argsas_integral)r   r   r2   Fr   r3   f2ILTs           rB   !test_inversion_conditional_outputr   .  s   (BsT"ART
3r$q'z$q')**AAq!$A~~sA	qA	Q1	%B???771:a=AFF1L(((772;q>>
!!Q4
0C772;q>S BGGBKNcoo$EEE$E rD   c                  "   SSK Jn   SSKJn  U " SSS9nU " SSS	9nS
S[        -  -   nU " S5      n[        [        U[        -  5      [        [        5      R                  (       a   e[        [        U[        -  5      [        [        5      b   e[        [        U[        -  5      [        [        5      b   e[        [        U[        -  5      [        [        5      nUR                  (       d   e[        UR                  S   S   U5      (       d   eg )Nr   r   )
DiracDeltarP   Tr   r4   F)extended_realrJ   r;   r8   )r   r   r   r   r   r,   r   r6   r7   r   r<   r   )r   r   rP   r4   r2   r8   r   s          rB   %test_inversion_exp_real_nonreal_shiftr   C  s    (BsAs%(A	AaCAsA"3qs8Q2????s1Q3xA.666s1Q3xA.666C!Ha+A>>>affQilJ////rD   c            
      z   SSK Jn Jn  SSKJn  SSKJn  0 n[        U5        UR                  5        GHy  n[        U[        S9 GHb  u  pgp0 n
[        UR                  5      U/-    H=  n[        US5      (       a  UR                  (       a  U" SS5      X'   M2  U " S	S
5      X'   M?     [        U[        5      (       d  U" U
5      nU VVs/ s H  u  p[!        U5      PM     nnn[#        S U 5       5      (       d   eU" U VVs/ s H  u  nnUU-  PM     snn6 nUR%                  U
S9UR%                  U
S9nn['        [)        U5      [)        U5      5      nUS:  a%  [)        UU-
  5      R%                  5       S::  d   eGM=  [)        UU-
  5      U-  R%                  5       S::  a  GMc   e   GM|     g s  snnf s  snnf )Nr   )uniform	randrangerL   )r8   )key
propertiesrJ   ra   g      ?g       @c              3   |   #    U  H2  oR                   =(       d    UR                  " [        5      (       + v   M4     g 7frF   )r   hasr    ).0r0   s     rB   	<genexpr>$test_lookup_table.<locals>.<genexpr>g  s%     NX~~;QUU7^);;Xs   :<)rc   g|=)sympy.core.randomr   r   rN   rM   sympy.integrals.meijerintr8   r*   valuessortedr	   listfree_symbolshasattrr   r<   r#   allrs   minr   )r   r   rM   z_dummytablelformulatermscondhintrc   air   rf   expandedr   r0   r2   r3   rP   s                       rB   test_lookup_tabler   R  s   4"6E\\^*08H*I&GDD7//0G9<2|,,(B/DH&sC0DH = eT**d 6;;U6AAUH;NXNNNNN u5uVaQqSu56H99$9')>qACFCF#A1u1q5z||~...AE
1'')U222- +J  < 6s   	F1
F7c            
         SSK Jn   SSKJn  U" [	        [        [        S-  5      [        SS9R                  [        5      SS9S[        [        S-  5      -  [        [        SS5      5      -  S-  [        [        S	S5      5      -  :X  d   e[	        [        [        S-  5      [        SS9S[        -  [        [        S-  5      -  [        [        SS5      5      -  S[        [        S	S5      5      -  -  S[        [        SS5      5      -  U " [        SS5      [        S
-  5      -  S[        [        5      -  [        [        S	S5      5      -  -  -
  :X  d   eg )Nr   r   )	powdenestrV   Tr}   polarr;   r]   r   )r   r   sympy.simplify.powsimpr   r"   r   r0   rd   r   r   r   r   )r   r   s     rB   test_branch_bugr   s  s&   B0Ys1a4y!T:??BC1I+eHQN&;;A=eHQPQN>SST T TSAY40	!C1IeHQN++QuXa^/D-DE
E(1a.!
!*Xa^QT"B
BAd2hJuU]^_abUcOdDd
e	ff f frD   c                      SSK Jn   [        [        [        S-
  5      [        SS9[        S[        -
  5      * :X  d   e[        U " S[        S-
  5      [        SS9U " SS[        -
  5      * :X  d   eg )Nr   r   rJ   Tr}   )r   r   r"   r   r0   r   r   s    rB   test_linear_subsr   ~  s^    6SQZD1c!a%j[@@@WQA&48WQA=N<NNNNrD   c            
      "  ^$^%^&^'^(^) SSK Jm$  SSKJn Jn  SSKJn  SSKJn  U" SSS9u  m&nU" S	SS
9u  m)nU " SSS
9m(S m'S m%[        T'" [        T&T)5      [        [        * [        4SS9S:X  d   e[        [        T'" [        T&T)5      -  [        [        * [        4SS9T&:X  d   e[        [        S-  T'" [        T&T)5      -  [        [        * [        4SS9T&S-  T)S-  -   :X  d   e[        [        S-  T'" [        T&T)5      -  [        [        * [        4SS9T&S-  ST&-  T)S-  -  -   :X  d   e[        T'" [        T&T)5      T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9S:X  d   e[        [        T'" [        T&T)5      -  T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9T&:X  d   e[        [        T'" [        T&T)5      -  T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9U:X  d   e[        [        [        -  T'" [        T&T)5      -  T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9T&U-  :X  d   e[        [        [        -   S-   T'" [        T&T)5      -  T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9ST&-   U-   :X  d   e[        [        [        -   S-
  T'" [        T&T)5      -  T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9ST&-   U-   :X  d   e[        [        S-  T'" [        T&T)5      -  T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9nUR                  [        5      (       a   e[        U5      T&S-  T)S-  -   :X  d   e[        [        S-  T'" [        T&T)5      -  T'" [        XE5      -  [        [        * [        4[        [        * [        4SS9US-  US-  -   :X  d   e[        T%" [        T(5      [        S[        4SS9S:X  d   e[        [        T%" [        T(5      -  [        S[        4SS9ST(-  :X  d   e[        [        S-  T%" [        T(5      -  [        S[        4SS9ST(S-  -  :X  d   eU$U%U&U'U(U)4S jnU" S5      S:X  d   eU" [        [        -  5      T&T(-  :X  d   eU" [        [        S-  -  5      T&S-  T(-  T)S-  T(-  -   :X  d   eT)S-  ST(S-  -  -   n[        U" [        [        -   S-   S-  5      U" [        [        -   S-   5      S-  -
  5      U:X  d   e[        U" [        [        -   S-
  S-  5      U" [        [        -   S-
  5      S-  -
  5      U:X  d   e[        U" [        [        -   S-  5      U" [        [        -   5      S-  -
  5      U:X  d   eU" SSS
9u  p[        U	S-
  -  S[        -   U	* U
-
  -  -  [!        X-   5      -  [!        U	5      -  [!        U
5      -  n[        U[        S[        4SS9S:X  d   e[        [        U-  [        S[        4SSS9nU" US   5      US   4XS-
  -  SU
:  4:X  d   e[        [        S-  U-  [        S[        4SSS9nUS   U
S:  :X  d   eU" US   US   S-  -
  5      X-   S-
  U	-  U
S-
  -  U
S-
  S-  -  :X  d   eU" SSS
9u  p[        US-
  -  [        * S-   US-
  -  -  [!        X-   5      -  [!        U5      [!        U5      -  -  n[        [        U[        SS4SS95      S:X  d   e[        [        [        U-  [        SS4SS95      XU-   -  :X  d   e[        [        [        S-  U-  [        SS4SS95      XS-   -  X-   -  X-   S-   -  :X  d   e[        [        [        [        -  U-  [        SS4SS95      [!        X-   5      [!        U[        -   5      -  [!        U5      -  [!        X-   [        -   5      -  :X  d   eU " SSSS9nSSUS-  -
  -  [        US-
  -  -  [#        [        S-  * S-  5      -  [!        US-  5      -  nU" [        U[        S[        4SS95      S:X  d   e[        [        [        U-  [        S[        4SS95      [%        S5      [!        US-   S-  5      -  [!        US-  5      -  :X  d   e[        [        [        S-  U-  [        S[        4SS95      U:X  d   eSU* S-  -  [!        US-  5      -  [        US-  S-
  -  -  [#        [        * S-  5      -  nU" [        U[        S[        4SS95      S:X  d   e[        [        [        U-  [        S[        4SS95      U:X  d   e[        [        [        S-  U-  [        S[        4SS95      XS-   -  :X  d   eU" [        [        U-
  [%        SU-  5      -  S-  U-  [        S[        4SS95      S[%        S5      -  [%        U5      -  :X  d   eU" SSS
9u  pnUU-  [        -  [        U-  UU-  -  -  S[        U-  X-  -  -   US-   -  -  n[        [        U[        S[        4SS95      S:X  d   e[        U-  n[        [        U[        S[        4SSS95      X-  [!        SSU-  -
  5      -  [!        US-   SU-  -   5      -  UU-  S-   [!        U5      -  -  :X  d   e[        [        [        U-  [        S[        4SSS95      XS-  -  [!        SSU-  -
  5      -  [!        US-   SU-  -   5      -  UU-  S-   [!        U5      -  -  :X  d   eU" SSS
9u  nn[%        U[        -  U-  UU-  -  U[        -  U-   UU-   -  -  5      [        -  [!        US-  5      -  [!        US-  5      -  [!        UU-   S-  5      -  n[        [        U[        S[        4SS95      S:X  d   e[        [        [        U-  [        S[        4SSS95      UUS-
  -  :X  d   e[        [        [        S-  U-  [        S[        4SSS95      US-  US-   -  U-  US-
  -  US-
  -  :X  d   eU" SSS
9u  nn[%        US-  [&        -  5      [        [)        SS5      -  -  [#        U* [        U-
  S-  -  [        -  S-  US-  -  5      -  nS  nU" [        U[        S[        45      5      S:X  d   eU" [        [        U-  [        S[        45      5      U:X  d   eU" [        [        U-
  S-  U-  [        S[        45      5      US-  U-  :X  d   eU" [        [        U-
  S-  U-  [        S[        45      5      SUS!-  -  US-  -  :X  d   eU " S"SS
9n[        [%        US-  [&        -  5      [#        U* S-  [        U-
  -  5      -  [        U-
  [+        S#5      -  -  [        U[        45      S:X  d   eU" SSS
9u  pX-  [        U
S-
  -  -  XS-
  -  -  S[        U
-  X-  -  -   S-  -  n[        [        U[        S[        45      5      S:X  d   e[        [        [        U-  [        S[        4SS$95      [&        U	-  U
-  [-        [&        U
-  5      -  :X  d   e[        [        [        [        -  U-  [        S[        4SS$95      [&        U	[        -  -  [        -  U
-  [-        [&        [        -  U
-  5      -  :X  d   eU " SSS
9nU " S%SS
9nUU-  [        U-  US-
  -  -  [#        [        U-  U-  * 5      -  n[        [        U[        S[        45      5      S:X  d   e[        [        [        U-  U-  [        S[        45      5      UU-  [!        SUU-  -   5      -  :X  d   eSS&KJn  U" S'SS
9u  n n![        U!S-  -  [#        [        S-  U S-  -   * S-  U!S-  -  5      -  U" S[        U -  U!S-  -  5      -  n"[        U"[        S[        4SS9S:X  d   eU " S(SS)9nU " S*SS
9n[#        [3        [        U-
  5      * U-  5      S-  U-  n#[        U#[        [        * [        4SS9S:X  d   e[        [        U#-  [        [        * [        4SS9U:X  d   e[        [        S-  U#-  [        [        * [        4SS9SUS-  -  US-  -   :X  d   eU " SSS
9nU" T$" [        [5        [        5      [        US-
  -  -  [#        [        * 5      -  [!        U5      -  [        S[        45      5      5      [7        SU5      :X  d   eg )+Nr   )
expand_mul)r   rz   )	gammasimp)powsimpzmu1 mu2Tnonzerozsigma1 sigma2r{   lambdac                 n    S[        S[        -  US-  -  5      -  [        X-
  S-  * S-  US-  -  5      -  $ NrJ   r;   )r   r   r   )r0   r   r   s      rB   normal test_probability.<locals>.normal  s=    ad5!8m$$S16A+aq)@%AAArD   c                 &    U[        U* U -  5      -  $ rF   )r   )r0   rates     rB   exponential%test_probability.<locals>.exponential  s    CaL  rD   r}   rJ   r;   rV   rT   c                 @  > [        U T" [        T5      -  T" [        TT5      -  [        S[        4[        [        * [        4SS9n[        U T" [        T5      -  T" [        TT5      -  [        [        * [        4[        S[        4SS9nT" U5      T" U5      :X  d   eU$ )Nr   Tr}   )r"   r0   r1   r   )	r?   res1res2r   r   mu1r   r   sigma1s	      rB   Etest_probability.<locals>.E  s    k!T226!S&3IIQa"b\4Ak!T226!S&3IIRCq!Rj$@$:d#3333rD   z
alpha betaseparater   r   k)r   r|   za b pr   zd1 d2rU   zlamda muc                 >    [        U R                  [        5      5      $ rF   )r%   rewriter   rG   s    rB   <lambda>"test_probability.<locals>.<lambda>  s    (4<<#45rD   r]   r4   ri   )r   rs   )r   znu sigmar   r   r3   )r   r   r   r   rz   sympy.simplify.gammasimpr   r   r   r"   r0   r   r1   r   r
   r%   r   r   r   r   r   r   r   r   r   r   r   r   )*r   rz   r   r   mu2sigma2r   r   ansr   betabetadistjr2   r3   r   chi
chisquaredpdagumr   d1d2r   lamdar   distmysimpr4   distnrs   r   nur   ricelaplacer   r   r   r   r   r   s*                                       @@@@@@rB   test_probabilityr    s    /32.y$/HC_t<NFF(T*DB! VAsF+a"b\4HAMMMQvaf--B3|TJ  QT&C001rc2,M6FAI  QT&C001rc2,M6AcE&!)O#$ $ $VAsF+F1c,BB"b\AsB<?BCD D DQvaf--fQ.DD"b\AsB<?BEF F FQvaf--fQ.DD"b\AsB<?BEF F FQqS3//q#0FF"b\AsB<?BEc'J J Ja!eai3!77q#8NN"b\AsB<?BCc'C-P P Pa!eai3!77q#8NN"b\AsB<?
S3   	!Q$vaf--fQ.DDrc2,RCd	<AuuSzz>A;#q&619,,,,QT&C0031GG"b\AsB<?	CF   [D)Aq":tDIIIQ{1d++aBZF	$  QT+a..Ar
DI	$'	    Q4199QqS6SXQq!tV9Qtfain4444
!)aai
CAq1uqy1n%!a%!)a78C???Aq1uqy1n%!a%!)a78C???Aq1uqjMAa!eHaK/0C777 ,6KE519~q1u66uU\7JJ	uDk"HX1bz48A===!H*q!Rj$jIAadOQqT"uQh'7T&BBBB!Q$x-!QTLAQ4D1HQqTAaD!G^$)95(@
()AXM)" " " " 54(DA1q5zA26QU++E!%L8%(58:KLHIhAq	4@AQFFFIaj1a)TBC	q5	  Iad8maAYEF	q5	151519%& & &Iad8maAYEFaeU1q5\!%(*5+;;< < < 	sD40A
a!A#g,q1q5z
!#q!teAg,
.uQqSz
9C9S1a*d;<AAAIaeaBZ>?Qq1uai  qs+, , ,Iad3hAr
DABaGGG aRT51:%a!A#'l23r!t9<J9Z!QTBCqHHHIa
lQ2JEF!KKKIad:o1bz4HI	q5	  YQQqS	 1A5j@1a* " #&'QiQ&78 8 8 g-GA!aCE1Q3!A#,AqDIQ77EIeaBZ>?1DDD
E'CIcAq":t6J U1qs7^+E!a%!A#+,>>qS1WeAh&(( ( ( IaeaBZVL a4a!A#g.uQUQqS[/AAqS1WeAh&(( ( (
 Wt,FBr!tbj2r6!BqD2Ib#99:1<	r!t	2a4[	!!&R{!3	4AIa!QT:;q@@@IacAq":t6J R!V% % %Iad1fq!Rj$fM QQ*BF3R!V<= = = 
T2IE2a
AQ00eVQVaK5G5I!5KBPQE5Q1RRD5F)D1a*-.!333)AdFQ2J/0B666)QVaK,q!Rj9:b!eEkIII)QVaK,q!Rj9:aAgeQh>NNNN 	sT"AT!A#b&\#qbdAFm"44a"fqx5GGBK!$%& & &
 ,6KEZTAX&uax'88	
QWU[ 	 1$%E
 IeaBZ01Q666Iag1bz@A
5c"T'l"# # # Iad5j1a*FCD
5!8Ad3r!tDy>)* * * 	sT"AsT"AeGQuWA&&sQuWqL='99EIeaBZ01Q666Iad5j1a*56qq1Q3w      7
T2IBUAX:cAqD2q5L/!+E1H455ga2eQh6OODTAq":t4999 
4	 BsT"A3q2v;,q.!!#A%GWq2#rlD9Q>>>QwYRCd;rAAAQT'\AsB<>	!Q$Q   	sT"AZ	#a&QU*;CG*CE!H*L !Rj!* + ,/8A? ? ?rD   c                  x   SSK Jn   SSKJn  SSKJnJnJnJnJ	nJ
n  [        [        [        [        [        * [         -  5      [         ["        -  -  [         S[$        4SSS9R'                  U5      R)                  SS	95      5      U" ["        [        5      :X  d   e[        [        [        * [         -  5      [         -  [         S[$        4SSS9R'                  U5      R)                  5       U" S[        5      :X  d   e[        [        [        * [         -  5      [         S
-  -  [         S[$        4SSS9R'                  U5      R)                  5       U" S
[        5      R'                  U5      R'                  U5      :X  d   e[        [        [        * [         -  5      [         S-  -  [         S[$        4SSS9R'                  U5      R)                  5       U" S[        5      R'                  U5      R'                  U5      R)                  5       :X  d   eU " SSS9n[        [+        [         5      * [         -  [         U[$        4SS9R)                  5       U" U5      :X  d   e[        [-        [         5      * [         -  [         U[$        4SS9R)                  5       U" U5      [.        S
-  -
  :X  d   e[        [-        [         5      [         -  [         S[        4SS9U" [        5      :X  d   e[        U" [         5      [         -  [         S[        4SS9U" [        5      :X  d   e[        [        [         * 5      [         -  [         SS9R)                  5       R'                  U5      [0        [.        -  U" S[         5      -
  :X  d   e[        [        [         * 5      [         S
-  -  [         SS9R'                  U5      R)                  5       U" S[         5      [        [         * 5      [         -  -
  [0        [.        -  -
  :X  d   eU " SSS9n	[        [+        U	5      U	-  U	SS9R)                  5       R3                  U	5      S   U" U	5      :X  d   e[        [5        U	5      U	-  U	SS9R)                  5       R3                  U	5      S   U" U	5      :X  d   e[        U" S[         5      [         SS9R'                  U5      R)                  5       [         U" S[         5      -  [        [         * 5      -
  :X  d   e[        U" S
[         5      [         SS9R'                  U5      R)                  5       [         S
-  * U" S[         5      -  S
-  [         [        [         * 5      -  S
-  -   [        [         * 5      S
-  -
  :X  d   e[        [        [        U" ["        [         5      [         SS9R'                  U5      R)                  SS	95      5      U" ["        S-   [         5      * :X  d   e[        U" [         5      [         SS9[         U" [         5      -  [+        [         5      -   :X  d   e[        U" U	5      U	SS9R)                  5       X" U	5      -  [-        U	5      -
  :X  d   e[        U" [         5      [         SS9[         U" [         5      -  [5        [         5      -
  :X  d   e[        U" U	5      U	SS9R)                  5       X" U	5      -  U" U	5      -
  :X  d   e[        U" [         5      [        [         * 5      -  [         S[$        4SS9[.        S-  :X  d   e[        U" S[         5      [-        [         5      -  [         S[$        4SS9[7        S
5      S
-  :X  d   eg)z$Test various exponential integrals. r   r   )r   )ChiCiEiShiSiexpintrJ   Tr   r   )funcr;   rV   r7   r{   r}   rR   r   rU   N)r   r   %sympy.functions.elementary.hyperbolicr   'sympy.functions.special.error_functionsr  r  r  r  r  r  r%   r   r"   r   r8   r0   r1   r   r   r   r   r   r   r   as_independentr   r   )
r   r   r  r  r  r  r  r  r7   rR   s
             rB   test_expintr  K  s    ):VVJyaRT1a4!QF '&/&&d&"35 69?1F F F S!AYq[1a*d!##*76?668q!   S!AYq!t^aBZ!##*76?668q!R ((01 1 1 S!AYq!t^aBZ!##*76?668q!R ((0779: : : 	sT"Ac!fWQYAr
D9@@BbeKKKc!fWQYAr
D9@@B
11  SVAX1ay$72a5@@@T!WQYAq	48CFBBBS!WQY40779AA&I	"va|  S!WQT\1d3;;FCJJL!Q<#qb'!)#ad*+ + + 	s$ASVAXq$/668GGJ1Ma5  T!WQY40779HHKANq6   VAq\1d gfoffh!F1aL.3r7*BC C CVAq\1d gfoffh	
AfQl1qaRy{*S!WQY67 7 7 Jy1q &wvvv4v/@B C	Aq	   RUAt,"Q%#a&0@@@@RUAt,3352a53q69IIIISVQ-3q6DG1CCCCSVQ-446!CF(T!W:LLLLRU3r7]Q2J=AEEEVAq\#a&(1a*dCs1vaxOOOrD   c            
      T   SSK Jn Jn  SSKJnJn  SSKJn  SSKJ	nJ
nJnJn  SSKJn	Jn
  U
" U" [         5      [         ["        SS9U" ["        5      * [$        S	-  -   ["        -  SS4:X  d   eU
" U" [         5      [         ["        SS9U" ["        5      ["        -  [&        * ["        S	-  S
:  4:X  d   eU
" U" [         5      [         ["        SS9[)        ["        S-  5      [)        S
S
["        S	-  -  -
  5      -
  S	["        -  -  [&        * ["        S	-  S
:  4:X  d   eU
" U" [*        [         5      [         ["        5      S
S  S[-        [*        5      S:  [-        [*        5      S:  -  4:X  d   eU	" U" S
[         5      [         -  [         ["        SS9nUS   R/                  SS9R1                  5       US
   4[3        S["        S
S	[$        -  -  :  ["        SS	[$        -  -  :  -  4S	[5        S[$        S	-  -  ["        S	-  -  S
-   5      -  S45      ["        S:  4:X  d   e[7        U" [         5      U" S[         5      -  [         S[&        4SS9[)        S
[5        S	5      -   5      :X  d   e[7        U" [         5      U" S
[         5      -  [         S[&        4SS9[)        [8        R:                  [5        S	5      S	-  -   5      :X  d   e[7        S
[         -  [5        S
[         S	-  -
  5      -  [         SS9[3        U " S
[         -  5      * [=        [         S-  5      S
:  4[>        U" S
[         -  5      -  S45      :X  d   eg )Nr   )r   acoth)r   atanr   )r  E1r  r  )fourier_transformlaplace_transformTr$   r;   rJ   r   rT   F)noconds)deeprY   r}   ) r  r   r   (sympy.functions.elementary.trigonometricr   r!  r   r   r  r  r"  r  r  r   r#  r$  r0   r6   r   r   r   r2   r   factorr   r   r   r"   r   rZ   r   r   )r   r   r   r!  r   r  r"  r  r  r#  r$  r  s               rB   
test_messyr)    s   DE6JJQbeQD9AwhAoq !T*+ , + SVQD9a
RCA># # # # SVQD9	QWA!Q$J	'!A#.QTAX>? ? ? ?
 WQ]Aq1!"5	
RURZBqEBJ'() ) ) GAqM!OQ5
ACFMMtM$++-s1v6	AAqtHR2Y78d2b!e8AqD=1,--t4
6781u	>> > > RU71a=(1a*dCAQK  RU71a=(1a*dCAFFT!WQY      QqSa!Q$h'D9E!A#J;AGq 01Ad1Q3iK3FGH H HrD   c                      [        [        [        * [        S-  -  5      [        [        * [        4SS9[        * [        [        5      -  [        [        [        -  S-  5      -  :X  d   eg )Nr;   Tr}   rU   )r"   r   r   r0   r   r   r   rW   rD   rB   test_issue_6122r+    sQ    S!AqD\AsB<>	
48C"QK     rD   c                      S[         -  [        [        [         -  -   [        SS5      -  -  n [	        U [         SS9nUR                  [        5      (       a   eg )NrJ   rV   Tr}   )r0   r2   r3   r   r"   r   r   )r?   antis     rB   test_issue_6252r.    sF    Q3AaC(1a.((DT1d+DxxrD   c                      [        [        [        [        -  5      S[        S-  -   -  [        [        * [        45      R                  5       R                  [        5      [        [        S5      -  :X  d   eg r   )r"   r   r   r0   r   r%   r   r   rW   rD   rB   test_issue_6348r0    sW    S1Xq1a4x(1rc2,7@@BJJ3Oc"g:  rD   c            	          SSK Jn Jn  [        [	        [        [        [        S-  -  S-  5      [        5      5      U" [        5      :X  d   e[        [	        [        [        [        S-  -  S-  5      [        5      5      U " [        5      :X  d   eg )Nr   fresnelcfresnelsr;   )	r  r3  r4  r   r"   r   r   r0   r   r2  s     rB   test_fresnelr5    sa    LyR1WQY34CCCyR1WQY34CCCrD   c                  N    [        [        [        [        -  -  [        5      b   eg rF   )r(   r0   rW   rD   rB   test_issue_6860r7    s    1a4+333rD   c                  d   [        [        [        S[        -  S-   5      -  [        5      R                  5       n U [        S[        -  S-   5      S[        S-  -  [        -   S-
  -  S-  :X  d   eU R	                  [        [
        R                  [
        R                  5      [        SS5      :X  d   eg )Nr;   rV   r]   )	r(   r0   r   together_eval_intervalr   NegativeOneOner   r   s    rB   test_issue_7337r=    s    QtAaC!G}_a099;AQqS1WqAvzA~.q0000Aq}}aee4AFFFrD   c                  2   [        [        [        5      [        [        * [        -  5      -  [        5      [        * S-
  [        [        5      -  [        * S-   [        [        * 5      -  -   [        [        * [        -  5      -  S-  [        S-  S-
  -  :X  d   eg r   )r(   r   r0   r   r7   rW   rD   rB   test_issue_8368r?    s    QQBqD	 115
aQA263r7**C1I:667:89:A:C C C CrD   c                      SSK Jn Jn  [        S[	        [
        [        -
  S-  U S-  -   5      S-  -  [        SU4[
        SU45      S[	        SUS-  U S-  -  -   5      -  U -  SU -  -
  :X  d   eg )Nr   hwrJ   r;   rV   )	sympy.abcrB  rC  r"   r   r1   r0   rA  s     rB   test_issue_10211rE    sv    aacAX1_-q00Aa7QqGD	$q1a419}
a!A#%& & &rD   c                      SSK Jn   U " SSS9u  p[        S[        [        S-  US-  -   5      S-  -  [        U* U45      SU-  US-  [        US-  US-  -   5      -  -  :X  d   eg )	Nr   ry   zy LTr{   rJ   r;   rV   )r   rz   r"   r   r0   )rz   r1   Ls      rB   test_issue_11806rH    su    )54(DAQtAqD1a4K(!++a!QZ8	!QT$q!tad{##$% % %rD   c            
      Z   SSK Jn   SSKJnJn  [        US-  US-  US-  -
  S-  -  USS9nSUS	-  -  US
-  -  [        S[        S
S5      4[        SS5      4US-  [        S[        -  [        -  5      -  US-  -  5      -  nU R                  X4-  R                  5       S	S5      (       d   eg )Nr   )RR)RrP   r;   g      ?Tr}   gUUUUUU?g      ?rV   g      r]   g-q=)sympy.polys.domains.realfieldrJ  rD  rK  rP   r"   r   r   r   r   r   almosteqrs   )rJ  rK  rP   r   rf   s        rB   test_issue_10681rN    s    0!Q$1QT	C''D9A	3q!tE4!Q"88Aq>:K"#Q$y1R'8"8A"=? 	?A;;wwy#u----rD   c                  r    SSK Jn   U " SSS9n[        S[        S-  -  [        [        U45      SU-  :X  d   eg )	Nr   r   r2   Tr{   rJ   r;   rT   )r   r   r"   r0   r   )r   r2   s     rB   test_issue_13536rP    s8    (sT"AQq!tVaQZ(BqD000rD   c                      SSK Jn   U " S5      nU " S5      n[        [        X-  5      X-  -  USS9R	                  US5      R                  [        [        US-  5      US-  -  USS95      (       d   eg )Nr   r   r0   rs   Tr}   r;   )r   r   r"   r   rc   equals)r   r0   rs   s      rB   test_issue_6462rS    st    (sAsA SYqt^Q5::1a@GGc!Q$i1na68 8 8 8rD   c                      [        [        [        -   [        * -  [        SS9[        * S[        [        -  -   S[        -
  -  -  [        [        [        -  -  [        [        -  -
  -  :X  d   eg )NTr}   rJ   )r"   r3   r7   r2   rW   rD   rB   test_indefinite_1_bugrU    sV    a!er]At4A!Gq1u;M8MqQRTUQUvXY[\X\}8]]]]rD   c            	         [        S[        [        [        -
  S-  S-
  5      -  SS9[	        [        [        [        -
  5      [        [        [        -
  S-  5      S:  4[        * [        [        [        -
  5      -  S45      :X  d   eg )NrJ   r;   Tr}   )r"   r   r0   r   r   r   r
   r   rW   rD   rB   test_pr_23583rW    so    QtQUQJqL))48eAElCQ
Oa$78A2d1q5k>4:PQR R RrD   c                      [        [        [        S-  * 5      [        SS4SS9[        [        5      S-  [        S5      -  :X  d   eg )Nr;   r   Tr}   r]   )r"   r   r0   r   r   r   rW   rD   rB   0test_integrate_function_of_square_over_negativesrZ    s:    S!Q$Z!Bq48DHQJQ<OOOOrD   c                      SSK Jn   U " SSS9n[        [        U[        S-   -  5      [        SS4SS	9[        S
U-  5      U-  :X  d   eg )Nr   ry   r1   Tr   rJ   rT   g      пr}   g      ?)r   rz   r"   r   r0   r   )rz   r1   s     rB   test_issue_25949r\    sH    )T"AT!QU)_q"endCtDQRF|TU~UUUrD   N)kr   r   sympy.core.numbersr   r   r   r   sympy.core.singletonr   sympy.core.sortingr	   $sympy.functions.elementary.complexesr
   r   r   r   &sympy.functions.elementary.exponentialr   r   r   r  r   r   r   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   r   r'  r   r   r   r   r  r   r   r   r   r   sympy.functions.special.hyperr   r    sympy.integrals.integralsr!   r"   sympy.simplify.hyperexpandr#   sympy.simplify.simplifyr%   r   r&   r'   r(   r)   r*   r+   r,   sympy.testing.pytestr-   r   r.   r/   rb   rD  r0   r1   r2   r3   r4   r5   r6   r7   r8   r[   r^   rj   rn   rw   r   r   r   r   r   r   r   r   r   r  r  r)  r+  r.  r0  r5  r7  r=  r?  rE  rH  rN  rP  rS  rU  rW  rZ  r\  rW   rD   rB   <module>ri     sa   + 4 4 " / I I H H C C 9 J K K ? F : ; 2 ,- - - &+ / / /&TRM
$"#3 ($ g? g?T-`9"F*0 3 3@fO C? C?L 3P 3Pl#HL 

D4GC
&%.18^RPVrD   