
    \h!R                     Z   S 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JrJrJr  SSKJr  SSKJrJr  SSKJr  SS	KJrJr  SS
KJrJr  SSKJr  SSK J!r!J"r"J#r#  SSK$J%r%  SSK&J'r'J(r(  SSK)J*r*J+r+  SSK,J-r-J.r.J/r/  SSK0J1r1J2r3J4r4J5r6J7r7J8r8  SSK9J:r:  SSK;J<r<  SSK=J>r>  SSK?J@r@  SSKAJBrBJCrC  SSKDJErEJFrF  \R                  " 5       rHS rIS rJS rKS rLS rMS rNS rOS rPS  rQS! rRS" rSS# rTS$ rUS% rVS& rWS' rX\FS( 5       rYS) rZS* r[S+ r\S, r]S- r^\FS. 5       r_S/ r`S0 raS1 rbS2 rcS3 rdS4 reS5 rfg6)7zFTests for tools for solving inequalities and systems of inequalities.     )Sum)Function)IRationaloopi)EqGeGtLeLtNe)S)DummySymbol)Abs)explog)rootsqrt)	Piecewise)cossintan)Integral)AndOr)PolyPurePoly)	FiniteSetIntervalUnion)reduce_inequalitiessolve_poly_inequalityreduce_rational_inequalitiessolve_univariate_inequalityreduce_abs_inequality_solve_inequality)rootof)solve)solveset)Mod)xy)raisesXFAILc                  0   [        [        S[        5      S5      [        R                  /:X  d   e[        [        S[        5      S5      [        R
                  /:X  d   e[        [        [        S-   [        5      S5      [        S[        SS5      /:X  d   eg )Nr   z==   >TF)	psolver   r-   r   RealsEmptySetr   r!   r        ]/var/www/auris/envauris/lib/python3.13/site-packages/sympy/solvers/tests/test_inequalities.pytest_solve_poly_inequalityr;   $   sr    $q!*d#y000$q!*d#

|333(1q5!$c*xBe/L.MMMMr9   c                     [        [        [        S-  S5      //[        SS9[        S5      :X  d   e[        [	        [        S-  S5      //[        SS9[        S5      :X  d   e[        [        [        S-  S5      //[        SS9[        R                  :X  d   e[        R                  (       a6  [        [        [        S-  S5      //[        SS9[        R                  :X  d   e[        [        * [        5      (       d   e[        [        [        S-  S5      //[        SS9[        S5      R                  [        R                  5      :X  d   e[        [        [        S-  S5      //[        SS9[        S5      R                  [        R                  5      :X  d   e[        [        [        S-  S5      //[        SS9[        SS5      :X  d   e[        [	        [        S-  S5      //[        SS9[        SS5      :X  d   e[        [        [        S-  S5      //[        SS9[        SSSS5      :X  d   e[        [        [        S-  S5      //[        SS9[!        [        [        * S5      [        S[        5      5      :X  d   e[        [        [        S-  S5      //[        SS9[        SS5      R                  [        R                  5      :X  d   e[        [        [        S-  S5      //[        SS9[        SS5      R                  [        R                  5      :X  d   e[        [        [        S-  S5      //[        SS9[        S	S5      R#                  5       :X  d   e[        [	        [        S-  S5      //[        SS9[        S	S5      :X  d   e[        [        [        S-  S5      //[        SS9[        S	SSS5      :X  d   e[        [        [        S-  S5      //[        SS9[!        [        [$        * S	5      [        S[$        5      5      :X  d   e[        [        [        S-  S5      //[        SS9[!        [        [$        * S	SS
9[        S[$        SS95      :X  d   e[        [        [        S-  S5      //[        SS9[        S	S5      R                  [        R                  5      :X  d   e['        S5      n [        [        [        S-  S-
  S5      [        [        S-  S-
  S5      //[        SS9[        R                  :X  d   e[        [	        [        S-  S-
  S5      [        [        S-  S-
  S5      //[        SS9[        SS5      :X  d   e[        [	        [        S-  S-
  S5      [        [        S-  S-
  S5      //[        SS9[!        [        U * SSS5      [        SU SS5      5      :X  d   e[        [	        [        S-  S-
  S5      [        [        S-  S-
  S5      //[        SS9[!        [        U * SSS5      [        SU SS5      5      :X  d   e[        [        [        S-  S-
  S5      [        [        S-  S-
  S5      //[        SS9[!        [        U * SSS5      [        SU SS5      5      :X  d   e[        [        [        S-  S-
  S5      [        [        S-  S-
  S5      //[        SS9[!        [        U * SSS5      [        SU SS5      5      :X  d   e[        [        [        S-  S-
  S5      [        [        S-  S-
  S5      //[        SS9[!        [        U * SSS5      [        SSSS5      [        SU SS5      5      :X  d   e[        [        [        S-  S	5      //[        5      [        R(                  L d   eg )N   r   F
relationalr2   r4   T      ?g      )
right_open)	left_open)r%   r	   r-   r    r   r   r   r7   is_realr
   r6   r!   r   r   
complementr   r"   evalfinfr   false)ss    r:   +test_reduce_poly_inequalities_real_intervalrI   *   s   '
QT1+u.1:1> > >'
QT1+u.1:1> > >'
QT1+u.12< < < 99 (
QT1+u.	 4 4"*B3"3"34 4 (
QT1+u.!() ) ) (
QT1+u.!() ) ) (
QT1+u.1:2q1AB B B'
QT1+u.19"aA A A'
QT1+u.19"at1LM M M'
QT1+u.hsB!R12 2 2 (
QT1+u.Q""177+, , , (
QT1+u."a##AGG,- - - ("	1c+ * )E+.7c.B.H.H.JK K K'
QT3-103;D#3FG G G'"	1c+ * )E+.6tS$.MN N N'
QT3-10htT"HS#$678 8 8 (
QT3-10htTd3cT*	,, , , ("	1c+ * )E+$''01 1 1 	QA'"	1q!+A1o*' )()*u>ABL L L'"QTAXq/2	1q!< * )e-09"a0@A A A'
QTAXq/2adQh?	+,aE
8QBE518Aq%3OPQ Q Q (
QTAXq/2adQh?	+,aE
8QBE40(1au2MNO O O (
QTAXq/2adQh?	+,aE
8QBD%0(1a2MNO O O (
QTAXq/2adQh?	+,aE
8QBD$/!Qd1KLM M M (
QTAXq/2adQh?	+,aE
8QBD$/"at1LAtT"$$ $ $
 ("QT3-(91=HHHr9   c                  >	   [        [        [        S-  S5      //[        SS9[        [        S5      :X  d   e[        [        [        S-  S5      //[        SS9[        [        S5      :X  d   e[        [	        [        S-  S5      //[        SS9S:X  d   e[        [        [        S-  S5      //[        SS9[        [	        [        * [        5      [	        [        [        5      5      :X  d   e[        [        [        S-  S5      //[        SS9[        [        [        [        * 5      [	        [        [        5      [        [        S5      5      :X  d   e[        [        [        S-  S5      //[        SS9[        [        [        [        * 5      [	        [        [        5      [        [        S5      5      :X  d   e[        R                  [        S5      4 GH  n U [        -  n[        [        [        S-  U 5      //[        SS9[        [        [        U * 5      [        [        U 5      5      :X  d   e[        [        [        S-  U 5      //[        SS9[        [        [        U * [        5      [        [        U 5      5      5      :X  d   e[        [	        [        S-  U 5      //[        SS9[        [        [	        U * [        5      [	        [        U 5      5      5      :X  d   e[        [        [        S-  U 5      //[        SS9[        [        [        [        U [        5      [	        [        U5      5      [        [        [        U * 5      [	        U* [        5      5      5      5      :X  d   e[        [        [        S-  U 5      //[        SS9[        [        [        [	        U* [        5      [	        [        U * 5      5      [        [	        U [        5      [	        [        U5      5      5      5      :X  d   e[        [        [        S-  U 5      //[        SS9[        [        [	        U* [        5      [	        [        U * 5      5      [        [	        U * [        5      [	        [        U 5      5      [        [	        U [        5      [	        [        U5      5      5      :X  a  GM   e   g )Nr=   r   Tr>   Fr@   )r%   r	   r-   r   r   r
   r   r   r   r   r   Oner   )onerF   s     r:   0test_reduce_poly_inequalities_complex_relationalrM   u   s   '
QT1+t-021a9 9 9'
QT1+t-021a9 9 9'
QT1+t-056 6 6'
QT1+t-03BsAJ1b	0JK K K'
QT1+t-Bq2#J1b	2a8,- - - (
QT1+t-Bq2#J1b	2a8,- - - qv"f+Asm_qT3r!cT{Bq#J'( 	( ( ,Asm_qT3BtQKAs,-. 	. . ,Asm_qT3BtQKAs,-. 	. . ,Asm_qT33r#qz2a:.Bq3$KSD!0MNOP 	P P ,Asm_qT33r3${Bq3$K0#baj"Q*2MNOP 	P P ,Asm_qT3s2sdA;1sd,2sdA;1c
+2c1:r!Sz*,, 	, ,# r9   c            
         [        / [        5      S:X  d   e[        [        S-  S[        -  -   S-   [        S-  S-
  -  S:  //[        SS9[        [        R                  " [
        * S5      [        SS	5      [        R                  " S
[
        5      5      :X  d   e[        S[        -  S-
  S[        -
  -  [        S-  S-   [        S-
  S-  -  -  S:  //[        SS9[        [        R                  " SS5      [        R                  " SS5      5      :X  d   e[        [        S-   [        S-
  -  S:*  //[        SS9[        R                  " S	S5      :X  d   e[        [        S-  S
[        -  -   S-   [        S-
  -  S:  //[        SS9[        [        R                  " SS	5      [        R                  " S[
        5      5      :X  d   e[        [        S-  S-
  [        S-
  S-  -  S:  //[        SS9[        [        R                  " SS5      [        R                  " SS
5      5      :X  d   e[        S[        -  S-   [        S
-   -  S:  //[        SS9[        [        R                  " [
        * S5      [        R                  " [        SS5      [
        5      5      :X  d   e[        [        S-
  [        -  S[        -
  :*  //[        SS9[        [        R                  " [
        * S5      [        R                  " SS
5      5      :X  d   e[        [        [
        :  [        S:  [
        * [        :  //[        SS9[        S[
        5      :X  d   eg )NFr=         r   r>   r4      
      r2      )	r%   r-   r"   r!   openr   Ropenr   Lopenr8   r9   r:   1test_reduce_rational_inequalities_real_relationalr\      s   'A.%777'a4!A#:>AqD2I
&!
+	,-qUDhmmRC$hr2&6a8LMN N N (qD2IA!Q$(QUQJ!6
7!
;	<=q 	hmmB"HMM!Q$789 9 9
 (1q51q5/Q*>)?(@!r1   (1a4!A#:>AE*BQ*F)G(H!hmmB#X]]1b%9:; ; ; (1a4"9q1uqj*@1*D)E(FhmmB"HMM!Q$789 9 9 (1Q37QU*;q*@)A(BAhmmRC$hnnXa^R&HIJ J J (1q5!)q1u*<)=(>hnnbS"%x~~a';<= = =
 (
b&!q&2#'	"#Q5:=Ea_M M Mr9   c                    ^ [        [        S-
  5      S:  n [        [        S[        5      [        [        S5      5      n[	        U 5      U:X  d   e[	        U [        5      U:X  d   e[	        [        [        S-
  5      5      [        [        S5      :X  d   e[	        [        S[        -  S-   5      S:  5      [        [        [        [        SS5      [        5      [        [        [        5      5      [        [        [        [        SS5      5      [        [        * [        5      5      5      :X  d   e[	        [        [        S-
  5      [        S[        -  S-
  5      -   S:  5      [        [        [        R                  [        5      [        [        S5      5      :X  d   e[	        [        [        S-
  5      [        S[        [        5      -  S-
  5      -   S:  5      [        [        [        S5      [        :  [        S	:  5      [        [        R                  [        :  [        S:  5      5      :X  d   e[        S
SS9m[        [        U4S j5        [	        [        S:  [        T/S9[        [        * [        :  [        S:  5      :X  d   eg )NrU   rO   r=   rX   irS      rR   r4   nrF)extended_realc                  8   > [        [        T S-
  5      S:  5      $ )NrU   rO   )r#   abs)r_   s   r:   <lambda>.test_reduce_abs_inequalities.<locals>.<lambda>   s    1#b1f+/Br9   symbols)rb   r-   r   r   r#   r	   r   r   r   r   r   Halfr   r/   	TypeError)eansr_   s     @r:   test_reduce_abs_inequalitiesrk      s   AE
QA
bAh1a
!Cq!S(((q!$+++s1q5z*bAh666AaC!G RA%:Bq"I!FBq(3"#RQZ022 2 2 s1q5zC	!a-    R]Bq!H56 6 6s1q5zC#a&1,==AB
3quqy!b&!3qvvz1q5#9:; ; ; 
E	*B
9BCq1uq"g6#rcAgq1u:MMMMr9   c                  4   [        [        [        S5      [        -  S5      5      [	        [        S5      S-  [        :*  [        [
        :  5      :X  d   e[        [        S-   S:  5      [	        [        R                  [        :  [        [
        :  5      :X  d   eg )Nr=   r2   r   )r#   r
   r   r-   r   r   r   NegativeOner8   r9   r:    test_reduce_inequalities_generalrn      sj    r$q'!)Q/0CQ	QB4OOOOq1uqy)S1BAF-KKKKr9   c                      [        [        [        S-  S5      S/5      [        [        S5      :X  d   e[        [        [        S-  S5      S/5      S:X  d   e[        [        S-  S:  5      [        R                  L d   eg )Nr=   r   TF)r#   r	   r-   r   truer8   r9   r:    test_reduce_inequalities_booleanrq      su    	AqD!d "1a) ) )1a4U34===q!tqy)QVV333r9   c                  6   [        [        [        S-  S5      [        [        S-  S5      /5      [	        [        [	        [        [        R                  [        5      [        [        [        5      5      [	        [        [        S5      [        [        * [        5      5      5      [        [	        [        [        R                  [        5      [        [        [        5      5      [	        [        [        S5      [        [        * [        5      5      5      5      :X  d   eg )Nr=   r2   r4   )r#   r
   r-   r.   r   r   r   r   rK   r   r   r8   r9   r:   %test_reduce_inequalities_multivariaters      s    1a4R1a[9:c
3r!%%|R2Y'R2YB3
)CD
3r!%%|R2Y'R2YB3
)CD?F F F Fr9   c                  H    [        [        S 5        [        [        S 5        g )Nc                  T    [        [        [        [        5      [        -   S5      5      $ Nr2   )r#   r
   r   r-   r8   r9   r:   rc   1test_reduce_inequalities_errors.<locals>.<lambda>   s    (;Bs1vz1<M(Nr9   c                  V    [        [        [        S-  [        -  [        -   S5      5      $ Nr=   r2   )r#   r
   r-   r.   r8   r9   r:   rc   rw      s    (;Bq!tAvz1<M(Nr9   )r/   NotImplementedErrorr8   r9   r:   test_reduce_inequalities_errorsr{      s    
 NO
 NOr9   c                     [        [        [        -   S:  [        /S9[        S[        -
  :  :X  d   e[        [        [        -   S:  [        /S9[        [        :  [        [        * S-   :  -  :X  d   e[        [	        S[        [        -
  5      [        /S9[	        [        [        5      :X  d   e[        [        S[        [        -
  5      [        /S9[        [        [        5      :X  d   eg )Nr2   re   r   )r#   r-   r.   r   r	   r   r8   r9   r:   test__solve_inequalitiesr}      s    q1uqy1#61q1u9EEEq1uzA37AFqQBQRF{;SSSSr!QU|aS9R1XEEEr!QU|aS9R1XEEEr9   c            	      "   S[         S-  -  S-  [         [        SS5      -  -
  [        SS5      -   S:  n [        U 5      [        [         [        SS5      [	        S5      S-  -   :  [	        S5      * S-  [        S	S5      -
  [         :  5      :X  d   eg )
NrW   r=   -   rS   !   r   ii     )r-   r   r#   r   r   )eqs    r:   test_issue_6343r      s    	AqDQxA&	&"a	81	<Br"Aa 49Q;..c
1xA0NQR0RST T Tr9   c                  n   [        [        S-  S-
  S:  5      [        [        R                  [        :  [        S:  5      :X  d   e[        [        S-  S-
  S:*  5      [        [        R                  [        :*  [        S:*  5      :X  d   e[        [        S-  S-
  S:  5      [        [        [        * [        :  [        S:  5      [        [        [        :  [        R                  [        :  5      5      :X  d   e[        [        S-  S-
  S:  5      [        [        [        * [        :  [        S:*  5      [        [        R                  [        :*  [        [        :  5      5      :X  d   e[        S-  [        -   S-
  n [        U S:  5      n[        [        [        U S5      [        :*  [        [        :  5      [        [        * [        :  [        [        U S5      :*  5      5      nX:X  d   e[        [        [        * S-   S-  5      S:  5      [        [        R                  [        :  [        S:  5      :X  d   eg )Nr=   r2   r   r4   rX   	   )r#   r-   r   r   rm   r   r   rK   r*   r)   r   Zero)r   soltrus      r:   test_issue_8235r      s   q!tax!|,AMMAq1u%& & &q!tax1}-AMMQQ'( ( (q!tax!|,
3sQwBQVQUUQY!789 9 9q!tax1}-
3sQwR #aeeqj!b&"9:; ; ; 
AAB
a.C
SA!#QV,c2#'1r1;M.N
OC:: rAvk"Q&'3qvvz1q5+AAAAr9   c            
         [        S[        [        [        S-  [        SS45      -   S-
  :*  [        /5      [        [        [        S-  [        SS45      * S-   :  :X  d   e[	        S5      n [        U " [        5      [        SS45      n[        S[        U-   [        S-  -   :*  [        /5      [        [        S-  * [        U " [        5      [        SS45      -
  :  :X  d   eg )Nr   r=   r2   rO   f)r#   r-   r   r.   r   r   )r   ri   s     r:   test_issue_5526r     s    q	HQTAq!9%%) *,-30	
x1q!Qi((1,	,. . . 	AAaD1a)AqAEAqDL01#6	
q!tec!A$Aq	**	*, , ,r9   c                  b  ^^^ [        [        S-  S:  [        SS9[        [        [        * S5      [        S[        5      5      :X  d   e[        [        S-  S:  [        5      [        [        [        S[        5      [        [        [        5      5      [        [        [        S5      [        [        * [        5      5      5      :X  d   e[        [        S-
  [        S-
  -  [        S-
  -  S:  [        SS9[        [        SS5      [        S[        5      5      :X  d   e[        [        S-
  [        S-
  -  [        S-
  -  S:  [        5      [        [        [        S[        5      [        [        S5      5      [        [        S[        5      [        [        [        5      5      5      :X  d   e[        [        S-
  [        S-
  -  [        S-
  -  S:  [        [        SS5      S	9[        [        [        S5      [        [        S5      5      :X  d   e[        [        S-  S[        -  -
  S-
  S:  [        SS9[        [        S
[        S5      * S-  [        R                  -   SS5      [        [        R                  [        S5      S-  -   [        SS5      5      :X  d   e[        [        S-  [        S-  -
  [        -   S-
  S:  [        SS9[        S[        S5      :X  d   e[        [        [        -   [        S[        -  -   -  S:  [        5      [        [        S5      :X  d   e[        [        S-
  [        S-
  -  [        -   [        S-
  [        S-
  -  S[        -  -   -  S:  [        5      [        [        [        S5      [        [        S5      5      :X  d   e[        [        S-
  [        S-
  -  [        -   [        S-
  [        S-
  -  S[        -  -   -  [        S-
  -  S:  [        5      [        [        S5      :X  d   e[        [         S 5        [        [        S-  [        -
  S-
  S:  [        5      [        [#        [        S-  [        -
  S-
  S5      [        :  [        [        :  5      :X  d   e[        S[        S-
  -  S:  [        5      [        [        S5      [        :  [        [        :  5      :X  d   e[        S-
  [        S-
  -  R%                  5       n [        [        S-
  U -  S:*  [        5      [        [        * :  [        S:  -  ['        [        S5      -  :X  d   e[)        S5      m[        [*        U4S j5        [)        SSS9m[        [*        UU4S j5        [)        SSS9m[        TT-  S:  T5      T* S-  T:  :X  d   e[        TT-  S:  T5      S:X  d   e[        TT-  S:  T5      S:X  d   e[-        S5      S-  [/        S5      S-  -   S-
  m[        [*        U4S j5        [        [*        U4S j5        [        [*        S 5        [        [*        S 5        [        [0        S 5        [        S-  [        -   [        [        S-   -  -
  m[        TS:  [        SS9[        R2                  L d   e[        TS:*  [        SS9[        R4                  L d   e[        [*        S 5        g )Nr=   rS   Fr>   rR   r2   rO   r   domainr4   rU   Tc                  l    [        [        S-  S[        -  [        -  -
  S-   [        -  S:  [        5      $ )Nr=   rO   r   isolver-   r   r8   r9   r:   rc   2test_solve_univariate_inequality.<locals>.<lambda>+  s*    1qs1uq(8!';a'? Cr9   r^   nc                  B   > [        [        [        5      T :*  [        SS9$ )NFr>   )r   r   r-   r   s   r:   rc   r   :  s    s1v{A%(Pr9   c1positivec                  (   > [        TT -  S:  T 5      $ Nr   )r   )r   r   s   r:   rc   r   <  s    qtax(<r9   )negativec                  8   > [        [        S-  T :  [        5      $ Nr=   )r   r-   zeros   r:   rc   r   C  s    q!td{A(>r9   c                  F   > [        [        S-  T [        -  :  [        5      $ r   r   r   s   r:   rc   r   D  s    	1tAvq)r9   c                  D    [        S[        [        -
  -  S:  [        5      $ )Nr2   r=   r   r-   r.   r8   r9   r:   rc   r   F      q!a%y1}a(@r9   c                  D    [        S[        [        -
  -  S:  [        5      $ )Nr2   r   r   r8   r9   r:   rc   r   G  r   r9   c                  >    [        [        [        -
  S:  [        5      $ r   r   r8   r9   r:   rc   r   H  s    fQUQY2r9   c                  |    [        [        [        [        5      S-  [	        [        5      S-  -   S5      [        5      $ ry   )r   r	   r   r-   r   r8   r9   r:   rc   r   O  s*    
3q619s1vqy !$a))r9   )r   r-   r"   r!   r   r   r   r   r   r    r	   r   r   rg   r   r/   
ValueErrorr)   expandr   r   rz   r   r   rh   r7   r6   )denr   r   r   s    @@@r:    test_solve_univariate_inequalityr     s   !Q$!)Q51U8RC;LB6   !Q$!)Q2c"Q(Bq"I&>Bq"I
B3
A $   1q51q5/1q5)Q.eDhq!nhq"o./ / /1q51q5/1q5)Q.2
3r!QxAq"C1a"Q)$<=> > >1q51q5/1q5)A-q9Q?K
2a8R1X   !Q$1*q.1$aE:hrDG8A:.d;qvvQ	)2tT:	<< < < !Q$A+/A%)1?B   1q51qs7#a'+r!Qx777AEAE?Q&!a%!a%1Q3)>?!CQG2bQRTUhXZ[\^_X`KaaaaQUQUOa'1q51q5/AaC*?@1q5IAMqQUWXY[\U]]]]
JCD !Q$(Q,"A&F1a4!8a<#a'R01 1 1 !QU)a-#s1Q4!8QV'<<<<EAE?
"
"
$C1q5#+"A&	
bSQUbAh&' ' ' 	c
A
 PQ	td	#B
 <=cD!A!B$)R aRTBY///!B$(B4'''!B$(B5(((q619s1vqy 1$D
 >?
 ! 
 @A
 @A
923a4!8aQiD$(A%0AJJ>>>$!)Q51QWW<<<  !) *r9   c                  (   [        [        [        5      [        R                  :  [        SS9[        [        S[        S-  SS5      [        R                  " [        [        SS5      -  S[        -  5      5      :X  d   e[        [        [        5      [        R                  :  [        SS9[        [        S-  [        [        SS5      -  SS5      :X  d   e[        [        [        5      [        R                  :  [        SS9[        [        S-  [        [        SS5      -  SS5      :X  d   e[        [        [        5      [        R                  :  [        SS9[        [        S[        S-  5      [        R                  " [        [        SS5      -  S[        -  5      5      :X  d   e[        [        [        5      [        R                  :  [        SS9[        [        R                  " S[        S	-  5      [        R                  " [        S-  [        5      5      :X  d   e[        [        [        5      [        R                  :*  [        SS9[        [        [        R                  5      [        R                  " [        S[        -  5      5      :X  d   e[        [        [        5      [        R                  :*  [        SS9[        R                   :X  d   e[        [        [        5      [        S
5      :  [        SS9[        R"                  :X  d   e[        [        [        5      [        R$                  :  [        SS9[        R                   :X  d   e[        [        [        5      [        R                  :  [        SS9[        R"                  :X  d   eg )NFr>   r      TrU   r=   rO   rS   rR   )r   r   r-   r   rg   r"   r!   r   rY   r   r   r   rZ   r   rK   r    r6   r7   rm   r8   r9   r:   test_trig_inequalitiesr   S  s   #a&166/17hq"Q$t,hmmBx1~<MqQSt.TUV V V#a&166/17Ar(1a.($56 6 6#a&166/17Ar(1a.($56 6 6#a&AFF"A%8hq"Q$8Aq>0A1R4!HIJ J J #a&155.!6hnnQ1%x}}RT2'>?@ @ @ #a&AFF"A%8iAbD!9:; ; ; #a&AEE/17177BBB#a&1R5.!6!**DDD#a&AMM)1?177JJJ#a&155.!6!**DDDr9   c                     [        [        S-  S:  [        SS9[        R                  :X  d   e[        [        S-  S:  [        SS9[        R                  R	                  [        5      :X  d   e[        [        S-  S:  [        SS9[        R
                  :X  d   e[        [        S-  S:  [        SS9[        R
                  R	                  [        5      :X  d   eg )Nr=   r   Fr>   T)r   r-   r   r6   as_relationalr7   r8   r9   r:   test_issue_9954r   j  s    !Q$!)Q51QWW<<<!Q$!)Q40AGG4I4I!4LLLL!Q$(A%0AJJ>>>!Q$(A$/1::3K3KA3NNNNr9   c            	      6   [        [        S-  [        S-  -
  S-   S5      n [        [        [        5      S[	        [        S5      -  -   S:  5      [        [        S[        :  [        U S-  :  5      [        U S-  [        :  [        [        :  5      5      :X  d   eg )NrU   r=   r2   r   rO   r   )r)   r-   r*   r   r   r   r   r   )rs    r:   test_slow_general_univariater   q  s}    q!tad{Q"Aa1T!QZ<'!+,
3q1ua!Q$hQTAXq2v!678 8 8r9   c                  (   S[         -
  [        S[         -
  5      -
  n [        [        S[         5      [        [         [        5      5      n[        U S[         5      U:X  d   eS[         -
  [        S[         -
  S-  5      -
  n [        U S:  5      U:X  d   eg )Nr2   <r=   r   )r-   rb   r   r   r   r'   r   r#   )r   rj   s     r:   test_issue_8545r   x  sy    	
QQU	B
bAh1b	
"C S!,333	
Qq1uqj!	!BrAv&#---r9   c                     [        [        * [        :  [        5      [        [        * [        :  [        [        :  5      :X  d   e[        [        [        :  [        5      [        [        * [        :  [        [        :  5      :X  d   eg )N)r   r   r-   r   r8   r9   r:   test_issue_8974r     sX    2#'1bS1Wa"f!5555"q&!RC!GQV 4444r9   c                     [        SS[        S[        -  S-
  5      -  -   S:  5      [        [        * :  [        [	        S5      S-  :  -  [        [        S5      -  :X  d   e[        [        S[        [        5      -  5      S-
  [        5      [        [        S5      :X  d   e[        SS[        SS[        -  -
  5      -  -   S[        5      [        [        [        * [        :  [        S:  5      [        [        R                  [        :  [        [        SS5      :  5      [        [        SS5      [        :  [        [        :  5      5      :X  d   e[        [        S	 5        g )
Nr4   r2   r   r=   rW   r   rO   rS   c                  h    [        SS[        SS[        [        5      -  -
  5      -  -   S[        5      $ )NrW   r2   r   )r'   rb   r   r-   r8   r9   r:   rc   "test_issue_10198.<locals>.<lambda>  s3    3B3	Ad1gI< : 5Q r9   )r#   rb   r-   r   r   r   r   r	   r'   r   r   r   r   r/   r   r8   r9   r:   test_issue_10198r     s!   
Qs1Q37|^a!%&"WQqT!V$<r!Qx$GH H H s1T!W9~115AqAAA aA!Gn!4c1=
3sQwAAFFQJHQN*+S!Q!1CQV-L	NN N N :   !r9   c                      [        [        [        5      S:  5      S:X  d   e[        [        [        5      S:  [        R
                  S9[        R
                  :X  d   eg )Nr=   Tr   )r*   r   r-   r+   r   r6   r8   r9   r:   test_issue_10047r     sD     Q!$$$CFQJqww/177:::r9   c                      [        [        [        5      S:  5      [        [        R
                  [        :  [        [        S5      :  5      :X  d   eg )Ni  )r*   r   r-   r   r   r   r   r8   r9   r:   test_issue_10268r     s4    Q$3qvvz1s4y=#AAAAr9   c                      [        S5      n [        [        [        5      U :*  [        SS9[	        [
        R                  U S:  4[        U * U 5      S45      :X  d   eg )Nr   Fr>   r   T)r   r   r   r-   r   r   r7   r!   r   s    r:   test_isolve_Setsr     sU    c
A#a&A+qU31::q1u%!Q'>?@ @ @r9   c            	      Z   [        SS5      n [        SSS9n[        US-
  US-
  -  US-
  -  S:  XS	9[        US5      :X  d   e[        S5      n[        US-   S:  U[        R
                  S	9US
:*  U[        * :  -  [        [        US5      S5      -  :X  d   e[        SU-  S-   S:  U[        R
                  S	9US:  U[        :  -  [        [        US5      S5      -  :X  d   e[        US-  SU-  -   S-
  S:  U[        R
                  S	9US
:  US:*  -  [        [        US5      S5      -  :X  d   e[        US-  SU-  -   S-
  S:  U[        R
                  S	9US:  U[        :  -  [        [        US5      S5      -  US:*  U[        * :  -  [        [        US5      S5      -  -  :X  d   eg )Nr   rO   r-   Fr   r2   r=   rS   r   rW   r4   rQ   )r    r   r   r	   r   Integersr   r,   )domr-   s     r:   %test_integer_domain_relational_isolver     s   
Aq/CsA1q51q5/1q5)A-q=AqIIIsA!a%!)Qqzz2GRC 2c!Qi#334 4 4!a%!)a-1::6GB2c!Qi#334 4 416AE>A%*AajjAGQ2c!Qi#334 4 416AE>A%*AajjA!VB2c!Qi#33RAG$3q!9a(88:: : :r9   c                     [        [        [        5      [        [        S[        5      5      [        S[        5      :X  d   e[        SS5      n [        S[        -  R                  [        5      S:  [        U 5      U :X  d   e[        [        [        S-
  5      [        -  S:*  [        [        R                  5      [        R                  " SS5      :X  d   eg )Nr   r2   rT   r   r^   )r+   r   r.   r!   r   r    r-   diffr   r   r6   r[   )is    r:   test_issue_10671_12466r     s    CFAx2/9Q3CCCCBAQqSJJqMA%q!,111SQZ\a'AGG4q!  r9   c                  &   [         [        [        [        [        [
        4 Ho  n [        U " [        S5      [        5      R                  [        :X  d   e[        U " [        R                  [        5      [        5      R                  [        :X  a  Mo   e   [        [	        S[        -  S-
  [        5      [        5      [	        [        S5      :X  d   e[	        [        R                  [        5      n[        U[        5      U:X  d   e[        S-  [        [        5      [        [        5      [        [        5      -   [        S[        -   -  4 H:  nS H1  nSU-  U-
  S:  n[        U[        SS9X#[        S5      -  :  :X  a  M1   e   M<     [        S[        S-  -  S[        -  -   S-
  S:  [        SS9[        [        S-   -  [        R                  :  :X  d   e[        [	        [        [        -  S5      [        5      [	        [        [        -  S5      :X  d   e[!        SSS9n[        [	        [        U-  S5      [        5      [	        [        SU-  5      :X  d   e[        [        U-  S:  [        5      [        U-  S:  :X  d   e[!        S	SS
9n[        U[        -  S:  [        5      [        R"                  [        :  [        U:  -  :X  d   e[        U[        -  S:  [        SS9S[        -  SU-  :  :X  d   e[	        S[        -
  [        S[        -  S-
  -  5      n[        U[        5      [        [        S5      :X  d   e[        [        [        S[        -  S-
  -  :  [        5      [        [        R                  :  [        [        S5      -  :X  d   eg )Nr2   r=   )r   r2   r   T)linearnz)nonzeroar   )r   r   r   r
   r	   r   r(   r-   lhsr   rK   r.   r   r   r   rg   r   r   )opiefxcri   r   r   s          r:   test__solve_inequalityr     s   2r2r2& Aq1-11Q666 AEE1q155::: ' R!a^Q/2a8;;;	AEE1BR#r)))!tSVSVc!f_aQi8A"q1A$Q$7qtV    9
 Qq!tVac\A-11TB	1q5	AFF  R!QZ+r!A#qz999	d	#BR"a[!,1ad;;;QrTAXq)adQh777sT"AQqS1Wa(QVVaZAE,BBBBQqS1Wa5!A#!)DDD
1q5!QqS1W+AQ"bAh...QAaC!G_a0QZ2a84KKKKr9   c                    ^  SSK Jm   T " [        * [        5      S:X  d   eT " [        R                  [        S5      5      S:X  d   eT " [        R                  [        5      T " [        [        R                  5      s=:X  a  S:X  d   e   eT " [        R                  [        * 5      T " [        * [        R                  5      s=:X  a  [        R
                  :X  d   e   eT " [        R                  [        5      T " [        [        R                  5      s=:X  a  [        SS5      :X  d   e   eT " [        R                  [        * 5      T " [        * [        R                  5      s=:X  a  S:X  d   e   eT " [        [        5      T " [        [        5      s=:X  a  [        S-   :X  d   e   eT " [        [        * 5      T " [        * [        5      s=:X  a  [        S-
  :X  d   e   e[        [        U 4S j5        g )	Nr   _ptrO   r=   r4   rR   r2   c                  B   > T " [        SSS9[        R                  5      $ )Nr   T)infinite)r   r   rK   r   s   r:   rc   test__pt.<locals>.<lambda>  s    s5t#<aeeDr9   )sympy.solvers.inequalitiesr   r   r   rK   rg   rm   r   r-   r/   r   r   s   @r:   test__ptr     sd   .sB<1quuadq   quub>SQUU^0q00000quurc?c2#quuo777777q}}b!SQ]]%;NxANNNNNq}}rc"c2#q}}&=CCCCCCq":R,q1u,,,,,q2#;#rc1+.Q.....
:DEr9   c                      [        [        [        S5      S:*  [        5      [        S:*  [        R                  [        :  -  :X  d   eg )NrO   r=   r   )r(   r   r-   r   r   r8   r9   r:   test_issue_25697r     s2    SAY!^Q/AFqvvz3JJJJr9   c                      [        S[        [        5      :  5      [        [        [        [        5      :  5      R	                  [        S5      :X  d   eg )NrO   )r#   rb   r-   r   subsr8   r9   r:   test_issue_25738r     s@    q3q6z 
 c!f-222q9: : :r9   c                      [        [        [        [        5      -  S:*  5      [        [        :*  [        [        :  -  [        * [        :  [        [        * :*  -  -  :X  d   eg rv   )r#   r   r   r-   r   r8   r9   r:   test_issue_25983r     sI    r#a&yA~.B!GB3GbSSTWYZ_a^aYaLb2ccdcr9   N)g__doc__sympy.concrete.summationsr   sympy.core.functionr   sympy.core.numbersr   r   r   r   sympy.core.relationalr	   r
   r   r   r   r   sympy.core.singletonr   sympy.core.symbolr   r   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   r   $sympy.functions.elementary.piecewiser   (sympy.functions.elementary.trigonometricr   r   r   sympy.integrals.integralsr   sympy.logic.boolalgr   r   sympy.polys.polytoolsr   r   sympy.sets.setsr    r!   r"   r   r#   r$   r5   r%   r&   r   r'   r(   sympy.polys.rootoftoolsr)   sympy.solvers.solversr*   sympy.solvers.solvesetr+   sympy.core.modr,   	sympy.abcr-   r.   sympy.testing.pytestr/   r0   rE   rF   r;   rI   rM   r\   rk   rn   rq   rs   r{   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r8   r9   r:   <module>r      s8   L ) ( 2 2 8 8 " - 4 ; ? : B B . ' 0 6 6; ; + ' +   . 	hhjNHIV%,P!MHN&L
4FP
FTB&,;*|E.O 8 8.5
	!;B @ @:$L8
FK:
er9   