
    Цi/                        S SK r S SKrS SKrS SKJr  S SKJrJrJrJ	r	J
r
JrJrJrJrJr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  S SKJ r J!r!  S SK"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.J/r/J0r0J1r1J2r2J3r3J4r4  S	 r5S
 r6S r7S r8S r9S r:S r;S r<S r=S r>S r?S r@S rAS rBS rCS rDS rES rFS rGS rHS rIS rJS rKS  rLS! rMS" rNS# rOS$ rPS% rQg)&    N)Q)SymbolFunctionFloatRationalIntegerIMulPowEqLtLeGtGeNe)exp	factorial
factorial2sinMinMax)And)Limit)raisesskip)
parse_exprstandard_transformationsrationalize
TokenErrorsplit_symbolsimplicit_multiplicationconvert_equals_signsconvert_xorfunction_exponentiationlambda_notationauto_symbolrepeated_decimals#implicit_multiplication_applicationauto_numberfactorial_notationimplicit_application_transformationTc                  6   [        S5      n 0 SSU -  _S[        S5      _S[        SS5      _S	SS[        -  -   _S
[	        U 5      _S[        U 5      _S[        U 5      _S[        U S-   5      S-
  _S[        SS5      _S[        SS5      _S[        SS5      _S[        SS5      _S[        SS5      _S[        SS5      _S[        SS5      _S[        SS5      _S [        S!S"5      _[        S#S$5      S%[        S5      * [        S&5      [        S'5      [        S5      /U R                  [        SS5      [        [        SSS(S)9[        SSS(S)9S(S)9[        [        U 5      U S*S+S,9[        R                  " U 5      S-.	EnUR                  5        H  u  p#[!        U5      U:X  a  M   e   [#        [$        S. 5        [#        [$        S/ 5        [#        [$        S0 5        [#        [$        S1 5        [#        [$        S2 5        [#        [$        S3 5        [#        [$        S4 5        g )5Nxz2*x   z3.00   z22/7      z2+3jzexp(x)zx!zx!!z(x + 1)! - 1   z3.[3]
   z.0[3]   z3.2[3]a   z1.3[12]i  iJ  z	1 + 3.[3]   z	1 + .0[3]   z
1 + 3.2[3]   z.[0011]i  z0.1[00102] + 1ii i i'  i'  i _7 Fevaluater   -)dir)	z1.[0191]z10!z-(2)z[-1, -2, 3]zSymbol("x").free_symbolszS('S(3).n(n=3)')zfactorint(12, visual=True)zLimit(sin(x), x, 0, dir="-")z	Q.even(x)c                  "    [        S[        5      $ Nr/   )r   r        d/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/parsing/tests/test_sympy_parser.py<lambda>#test_sympy_parser.<locals>.<lambda>?   s    301rD   c                      [        SS S9$ )Nr/   c                     gNr4   rC   r/   ys     rE   rF   5test_sympy_parser.<locals>.<lambda>.<locals>.<lambda>B   s    ArD   transformationsr   rC   rD   rE   rF   rG   A   s    36rD   c                      [        SS 4S9$ )Nr/   c                     grJ   rC   rK   s     rE   rF   rM   D   s    QrD   rN   rP   rC   rD   rE   rF   rG   C   s    3(89rD   c                      [        SSS9$ )Nr/   )rC   rN   rP   rC   rD   rE   rF   rG   E   s    jeDrD   c                      [        S0 / / 5      $ rB   rP   rC   rD   rE   rF   rG   F       jb"b9rD   c                      [        S/ / 0 5      $ rB   rP   rC   rD   rE   rF   rG   G   rU   rD   c                      [        S/ / 0 5      $ rB   rP   rC   rD   rE   rF   rG   H   rU   rD   )r   r   r   r	   r   r   r   r   free_symbolsr
   r   r   r   r   evenitemsr   r   	TypeError)r/   inputstextresults       rE   test_sympy_parserr_      sN   sA q1u a  	Q  	AaC	 
 	#a&  	il  	z!}  		!a%(1,  	"a  	!R  	(2r"  	8C%  	Xb!_  	Xb"%  	hsB'   	8As#! " 	(662# $ UD)WR['!*=$%NN!!QK&)1u%1u%' ).c!fa(DVVAY; FB $6))) ' 9 2 3
9 7 8
9 : ;
9DE
99:
99:
99:rD   c                      S[        SS5      0n [        [        4-   nU R                  5        H  u  p#[	        X!S9U:X  a  M   e   g )Nz0.123{   i  rN   )r   r   r   rZ   r   )r\   rO   r]   r^   s       rE   test_rationalizerb   K   sH    #t$F /+?O$@FJJJ 'rD   c                  X    / SQn U  H  n [        U5         e   g ! [         a     M!  f = f)N)zx!!!zx!!!!z(!))r   r   r\   r]   s     rE   test_factorial_failre   T   s9    %F 	t5   		s   
))c                     ^ / SQn U  H  m[        [        U4S j5        M     / SQn U  H  m[        [        [        4U4S j5        M     g )N)z1[1]z.1e1[1]z0x1[1]z1.1j[1]z
1.1[1 + 1]z0.1[[1]]z0x1.1[1]c                     > [        T 5      $ NrP   r]   s   rE   rF   $test_repeated_fail.<locals>.<lambda>g   s
    *T"2rD   )z0.1[z0.1[1z0.1[]c                     > [        T 5      $ rh   rP   ri   s   rE   rF   rj   l   s
    *T2BrD   )r   r[   r   SyntaxErrorrd   s    @rE   test_repeated_failrm   `   sB     F
 y23  (F
K(*BC rD   c                  p    [        S5      [        SS5      :X  d   e[        S5      [        SS5      :X  d   eg )Nz.[1]r4   	   z1 + .[1]r5   )r   r   rC   rD   rE   test_repeated_dot_onlyrp   o   s4    f!Q///j!Xb!_444rD   c                  x    SS 0n S[        S5      0nUR                  5        H  u  p#[        X S9U:X  a  M   e   g )Nmy_functionc                     U S-   $ )Nr0   rC   r/   s    rE   rF   !test_local_dict.<locals>.<lambda>v   s    QrD   zmy_function(2)   
local_dict)r   rZ   r   )rx   r\   r]   r^   s       rE   test_local_dictry   t   sG    J 	'!*F $6&@@@ 'rD   c                  ~    [         [        [        4-   n [        SSS9n[        S5      n[	        SSU0U S9X!-  :X  d   eg )NwT)realrL   yxr/   rx   rO   r   r    r!   r   r   )tr{   rL   s      rE   test_local_dict_split_implmultr      sD     M3J#LLAsAsAdAwBacIIIrD   c                     ^ [        S5      n S[        S5      0m[        STS9TS   " U 5      :X  d   eS[        S5      0m[        [        U4S j5        g )Nr/   foobarfoo(x)rw   bazc                     > [        ST S9$ )Nr   rw   rP   )ds   rE   rF   /test_local_dict_symbol_to_fcn.<locals>.<lambda>   s    ja@rD   )r   r   r   r   r[   )r/   r   s    @rE   test_local_dict_symbol_to_fcnr      sP    sA	 Ah1-5!<<<	uA
9@ArD   c                      S[         0n S[        [        S5      [        S5      5      0nUR                  5        H  u  p#[        X S9U:X  a  M   e   g )Nr   zQ & Sr   Sglobal_dict)r   r   rZ   r   )r   r\   r]   r^   s       rE   test_global_dictr      sR    &K 	VC[&+.F $8FBBB 'rD   c                  V   0 n [        SU 5        [        [        5      nUR                  5        H*  u  p#[	        U[
        R                  5      (       d  M&  X0U'   M,     [        U S'   [        U S'   U R                  S5        S[        0nU  H  n[        X$S9nU[        U5      :X  a  M   e   g )Nzfrom sympy import *maxminr   r   )execvarsbuiltinsrZ   
isinstancetypesBuiltinFunctionTyper   r   popr   r   )default_globalsbuiltins_dictnameobjr   s        rE   test_no_globalsr      s     O	0NM"((*	c54455$'D! + !OE OE !F#K7fTl"""  rD   c                  H    [        [        S 5        [        [        S 5        g )Nc                      [        S5      $ )Nz(()rP   rC   rD   rE   rF   !test_issue_2515.<locals>.<lambda>   	    z%0rD   c                      [        S5      $ )Nz"""rP   rC   rD   rE   rF   r      r   rD   )r   r   rC   rD   rE   test_issue_2515r      s    
:01
:01rD   c                      [        S5      n Sn[        USS9[        USS9:X  d   e[        USS9R                  SU S-   -  5      (       d   eg )Nr/   z2*(x+1)r   r=   Fr0   r4   )r   r   equals)r/   es     rE   test_issue_7663r      sR    sAAa!$
1u(EEEEa!$++AqsG4444rD   c                  t    SSSSS.n U R                  5        H  u  p[        USS9[        USS9:X  a  M   e   g )N4*-3z(-4)*3z(-2)*x*yzx*(-4)*x)r   z-4*3z-2*x*yzx*-4*xFr=   rZ   r   r\   r]   r^   s      rE   #test_recursive_evaluate_false_10560r      sE    	F $/:fu3UUUU 'rD   c                      / SQn U  H?  n[        USS9nU[        U5      s=:X  a   [        UR                  5       5      :w  a  M<   e   e   [        [        SSS95      S:X  d   e[        [        SSS95      S:X  d   eg )N)!zAbs(0)zim(0)zre(0)zsign(0)zarg(0)zconjugate(0)zacos(0)zacot(0)zacsc(0)zasec(0)zasin(0)zatan(0)zacosh(0)zacoth(0)zacsch(0)zasech(0)zasinh(0)zatanh(0)zcos(0)zcot(0)zcsc(0)zsec(0)zsin(0)ztan(0)zcosh(0)zcoth(0)zcsch(0)zsech(0)zsinh(0)ztanh(0)zexp(0)log(0)zsqrt(0)Fr=   zln(0)r   zcbrt(0)z0**(1/3))r   strdoit)r\   caseexprs      rE   test_function_evaluate_falser      s    F $/s4y4C		$444444  z'E23x???z)e45CCCrD   c                  p    SSS.n U R                  5        H  u  p[        USS9[        USS9:X  a  M   e   g )Nz(-10)/5z
(-10)/(-5))z-10/5z-10/-5Fr=   r   r   s      rE   test_issue_10773r      s?    F $/:fu3UUUU 'rD   c                      [         [        [        4-   n [        S5      n[        S5      n[        S5      n[	        S5      U:X  d   e[	        SU S9X-  :X  d   eg )Nr/   rL   xyrN   r   )rO   r/   rL   r   s       rE   test_split_symbolsr      s]    .$&=?@OsAsA	B dr!!!dO<CCCrD   c                      [         [        [        4-   n [        S5      n[        S5      n[        S5      n[	        S5      n[        SU S9X2-  US-   -  :X  d   e[        SU SU0S	9X4" US-   5      -  :X  d   eg )
Nr/   rL   afzay(x+1)rN   r4   zaf(x+1))rO   rx   )r   r    r!   r   r   r   )rO   r/   rL   r   r   s        rE   test_split_symbols_functionr      s    .$&=?@OsAsAsAA iAQS!A#YNNNi"%a*-.q1vX6 6 6rD   c                     [         [        [        4-   n [        S5      n[        S5      n[        S5      n[	        S5      n[        SU S9[        U5      S-  :X  d   e[        SU S9[        U5      U-  :X  d   e[        SU S9[        U5      U-  :X  d   e[        S	U S9[        U" U5      5      :X  d   e[        S
U S9X4" U5      -  :X  d   eg )Nr/   rL   r   zsin^2(x)rN   r0   zsin^y(x)zexp^y(x)zE^y(x)za^y(x))r   r#   r$   r   r   r   r   r   )r   r/   rL   r   yfcns        rE   test_functional_exponentr      s     K1H#IIAsAsAsAC=Dj!4Q!CCCj!4Q!CCCj!4Q!CCCh2c$q'lBBBh2a$q'lBBBrD   c                  J   ^  [         [        4-   m [        [        U 4S j5        g )Nc                     > [        ST S9$ )Nz(1,2),(3,4]rN   rP   rN   s   rE   rF   @test_match_parentheses_implicit_multiplication.<locals>.<lambda>  s    z-XrD   )r   r!   r   r   rN   s   @rE   .test_match_parentheses_implicit_multiplicationr     s    ..01O
:XYrD   c                      [         [        4-   n [        S5      n[        S5      n[        SU S9[	        SU5      :X  d   e[        SU S9[	        X!5      :X  d   e[        SU S9[	        [	        SU-  U5      S5      :X  d   eg )	Nr/   rL   z1*2=xrN   r0   zy = xz(2*y = x) = FalseF)r   r"   r   r   r   )rO   r/   rL   s      rE   test_convert_equals_signsr   
  s    .-01OsAsAg?2a8KKKg?2a8KKK)'),.r!A#qz5,AB B BrD   c                  ^    [        S5      n [        S5      n[        S5      U" U 5      :X  d   eg )Nr/   r   zf(x))r   r   r   )r/   r   s     rE   test_parse_function_issue_3539r     s+    sAAf1%%%rD   c                      [        SSSS9[        SSSS9[        SSSS9[        SSSS9[	        SSSS9[        SSSS9S.n U R                  5        H  u  p[        USS9U:X  a  M   e   g )Nr4   r0   Fr=   )z1 < 2z1 <= 2z1 > 2z1 >= 2z1 != 2z1 == 2)r   r   r   r   r   r   rZ   r   r   s      rE   test_issue_24288r     sz    Aq5)QE*Aq5)QE*QE*QE*F $/6999 'rD   c                      [         [        4-   n [        S5      n[        S5      n[        SU S9nX#s=:X  a  SU-  SU-  -  :X  d   e   e[        SU S9nX!S-  U-  S	-  :X  d   eg )
Nnz2**n * 3**nz2**n3**nrN   r0   r1   n12n34   "   )r   r(   r   r   )rO   r   expr1expr2s       rE   test_split_symbols_numericr   &  s}     	,.	/  	sA}%Ez?CE&QT!Q$Y&&&&&xAEbDF2IrD   c                  8    [        S5      [        S5      :X  d   eg )Nu   α)r   r   rC   rD   rE   test_unicode_namesr   4  s    dvd|+++rD   c                  0   [         R                  S:  a  [        S5        [        S5      S:X  d   e[        S5      [        S5      s=:X  a  [	        SS5      :X  d   e   e[        S	5      [        S
5      s=:X  a  [	        SS5      :X  d   e   e[        S5      [        S5      s=:X  a  [	        SS5      :X  d   e   e[        S5      [        S5      s=:X  a  [	        SS5      :X  d   e   e[        S5      [        S5      s=:X  a  [	        SS5      :X  d   e   eg )N)r1      z2test_python3_features requires Python 3.8 or newer123_456i@ z1.2[3_4]z1.2[34]ic  i  z1.2[012_012]z1.2[012012]i  iM  z.[3_4]z.[34]r   c   z.1[3_4]z.1[34]   i  z123_123.123_123[3_4]z123123.123123[34]l   [.X,i)sysversion_infor   r   r   rC   rD   rE   test_python3_featuresr   8  s   
& AB i F***j!Z	%:PhsC>PPPPPPn%M)BXhsTWFXXXXXXh:g#6J(2r:JJJJJJi Jx$8NHS#<NNNNNN,-<O1PvT\]kmuTvvvvvvrD   c                  r    [        S5      n [        SSU 0[        [        4-   S9nUR                  U 1:X  d   eg )Nr/   z	E**x(1+x)r~   )r   r   r   r(   rX   )r/   eqs     rE   test_issue_19501r   F  sA    sA	KS!H 	,.	/
1B ??qc!!!rD   c                  B   SSK Jn   [        [        5      S:X  d   e[        S   [        :X  d   e[        S   [
        :X  d   e[        S   [        :X  d   e[        S   [        :X  d   e[        S   [        :X  d   e[        S   [        :X  d   e[        S	   [        :X  d   e[        S
   [        :X  d   e[        S   [        :X  d   e[        S   [        :X  d   e[        S   [        :X  d   e[        S   [        :X  d   e[         S S [         S   s=:X  a  ["        :X  d   e   e[        n[         S   U[        U5      S-
     US   4:X  d   e[         S S2S4   ["        US   4-   :X  d   e[%        SSS9SU S-  -  S-  :X  d   e[%        SSS9['        SU -  5      :X  d   eg )Nr   rt   r   r4   r0   r1   rv         r3   r   ro   r5      )r   r4   r0   r1   rv   )r;   r   z0.3x^2allrN   zsin 3ximplicit)	sympy.abcr/   lenr,   r%   r&   r'   r)   r*   r(   r#   r+   r!   r"   r$   r   r-   r   r   r   )r/   r   s     rE   test_parsing_definitionsr   N  s   2%%%10001,,,1!22221,,,1!33331!DDDD1,,,1!55551!88881!55552"99992+---Ra5AiL<$<<<<<<AU8#a&1*qt,,,,RaRU8/1Q4'9999h6!AqD&)CCCh
;s1Q3xGGGrD   c                      / SQn U  H  u  p[        U5      [        U5      :X  a  M   e   [        [        S5      5      S:X  d   eg )N))zabs(x)zAbs(x))z	max(x, y)z	Max(x, y))z	min(x, y)z	Min(x, y))z	pow(x, y)z	Pow(x, y)zpow(38, -1, 97)23)r   r   )casesbuilt_in_func_callsympy_func_calls      rE   test_builtinsr   e  sK    E 05+,-O1LLLL 05z+,-555rD   c                  P    [        [        S 5        SS 0n [        SU 5      SL d   eg )Nc                      [        SSS05      $ )Nr/    r4   rP   rC   rD   rE   rF   "test_issue_22822.<locals>.<lambda>r  s    z#Aw7rD   some_parameterzsome_parameter is NoneT)r   
ValueErrorr   )datas    rE   test_issue_22822r   q  s-    
:78d#D.5===rD   )Rr   r   r   sympy.assumptionsr   
sympy.corer   r   r   r   r   r	   r
   r   r   r   r   r   r   r   sympy.functionsr   r   r   r   r   r   sympy.logicr   sympy.seriesr   sympy.testing.pytestr   r   sympy.parsing.sympy_parserr   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r_   rb   re   rm   rp   ry   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rC   rD   rE   <module>r      s        f f f f E E   -    /;dK	D5
AJBC#*2
5VD V	D6
CZB&

:,w"H.	6>rD   