
    g-                        d dl mZmZ d dlmZ d dlmZ d dlmZ d dl	m
Z
 d dlmZmZ d dlmZ d dlmZmZ d d	lmZ d d
lmZmZmZmZmZ d dlmZ d dlmZmZ d dl m!Z!m"Z" d dl#m$Z$m%Z% d dl&m'Z'm(Z( d dl)m*Z*m+Z+ d dl,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2 d dl3m4Z4 d dl5m6Z6 d dlm7Z7m8Z8m9Z9m:Z:m;Z;m<Z< d dl=m>Z>m?Z? d dl@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZI  ed          ZJeJdu ZK ed          ZL ed          ZMd ZNd ZOd ZPd ZQd ZRd  ZSd! ZTd" ZUd# ZVd$ ZWd% ZXg d&d'd(d) eOd*d+          fd,eAfd-d.eAz  fd/eAd.z  fd0 ePeA ePd.d1                    fd2eA eNd3d4          z  fd5eF fd6eDeEz  fd7eDeEz  fd8eDeEz  fd9eDeEz   fd: eNeDeEz   eD           fd; e7eDd.z  eEd.z  z   eFd.z            fd< eO eNeAeB          eC          fd= eN eO ed>          eE           eOeD ed?                              fd@ edA          fdB edA          fdC eO eNeAeB          eC          fdD eO eNeAeB          eC          fdE eO eNeAeB          eC          fdF eO eNeAeB          eC          fdG eO eNeAeB          eC          fdH eNd4d4          fdI eNd d4          fdJ eOd4d.          fdK eOd d4          fdL eOd4d.          fdM e7eAeB          fdN e8eAeB          fdO e9eAeB          fdP e;eAeB          fdQ e:eAeB          fdR e<eAeB          fdS e:eAeB          fdT e<eAeB          fdU e(eA          fdV e'eA          fdW e>d,          fdX e?d,          fdY e1eL          fdZ e1eL          fd[ e-eD          fd\ eO e1eD           e.eE                    fd] e1 e.eL                    fd^ e1 e.eL                    fd_eDeEz  fd`eDeEz  fdaeDeEz  fdb ePd.d1          fdc eO ePd.d1          eB          fdd eO ePd.d1          de          fdf eOd. ePd3d1                    fdg eO e1eA           ePd.d1                    fdh eOeDeEz    ePeFd1                    fdi eOdj ePd3d1                    fdk e/eA           e0eB          z  fdl e6eDeAd3dmn          fdo e6eDeAd3dmn          fdp e6eDeAd3dmn          fdq e6eDeAd3dmn          fdr e6eDeAd3dmn          fds e6eDeAd3dtn          fdu e6eDeAd3dvn          fdw e6eDeAd3dtn          fdx e6eDeAd3dvn          fdyefdz e6 ePeAd1          eAe          fd{ eeAeA          fd| eeAeG          fd} eMeA          fd~ eMeAeB          fd eMeAeBeC          fd  ed          eA          fd  ed          eAeBz             fd e eMeA          eA          fd e  ed          eA          eA          fdN eeAeB          fd eSeA          fd eS e!eA                    fd eSeA           eSeB          z  fd eS eSeA           eSeB          z            fd ed           eSeAeBz            z  fd e4eAeA          fd e4eAeL          fd e4eAd.z  eBz
  eA          fd e4 eNeAeD          eA          fd e4d4eD          fd e4d4eAd djf          fd e4eAeAd d4f          fd e4eAeAeDeEf          fd e4eAeAeDeEf          fd e4eAeAeDeEf          fd e4eAeAeDeEf          fd e4eAeAeDeEf          fd e4eAeAeDeEf          fd e4 eMeC          eC eMeD           eMeE          f          fd e4 eNeAeD          eA          fd e4 eN eNeDeE          eF          eA          fd e4 eeCd1          eC          fd e4d3 eeCd1          z  eC          fd e4 eeAd1          eA          fd e4 eN ePeDd1           eeEd1                    eA          fd e4d3 ePeLd1          z  eL          fd e4 eN ePeAd1          d4          eA          fd ed          fd ed          fd ed          fd ed          fd ed          fd ed          fd  ed           ed           ed                    fd eTeA          fd eTd          fd eTeL          fd eT eNeAd4                    fd eT eTeA                    fd eT eT eTeA                              fd eO eTd           eTdj                    fd e+eA          fd e+ eNeAeE                    fd e* e1eA          d3          fd e* e1eA          eB          fd e* e1eA          eL          fd eQ eOd ePdd1                              fd eReC          fd eR eReC                    fd eR eNeAeB                    fd eReA           eReB          z   fdO eeAeB          fdQ eeAeB          fdP eeAeB          fdR eeAeB          fd ed,          fd edæ          fd edŦ          fd edǦ          fd eeFeHd4d3f          fd eeFeHd4d3f          fd eeFeHd4d3f          fd eeFeHd4d3f          fd eeHd.z  eHd4df          fd e eP eTeI          d1          eId ef          fd eeAeDeEeFf          fd eeAeDeEeFf          fd eeAeDeEeFf          fd eeAeDeEeFf          fd eUeA          fd eUeA          fd eVeAdͦ          fd eVeAe          fd eVeAeBz  e          fd eVeAe          fd eVeAeBz  e          fd eVeAd.          fd eVeAeD          fd eVeAdݦ          fd eVeA ePeDd.                    fdeAfd eNeDeE          fd e e2eA          eA          fd eWeIeH          fd eWeIeH          fd eWeIeH          fd eWeId           fd ePeA eWeIeH                    fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd eOeDeE          fd e4eAeA          fd eVeAd.          fd eVeAeD          fd eN ePdd            eOd1 ePdd                               fd eN eOd3eA          d1          fZYd ZZg dZ[d Z\g dZ]ed             Z^d Z_dS )    )raisesXFAIL)import_module)Product)SumAdd)
DerivativeFunctionMul)EooPow)GreaterThanLessThanStrictGreaterThanStrictLessThan
Unequality)Symbol)binomial	factorial)Abs	conjugate)explog)ceilingfloor)rootsqrt)asincoscscsecsintan)Integral)Limit)EqNeLtLeGtGe)BraKet)	xyzabctknantlr4Nthetafc                 &    t          | |d          S NF)evaluater   r5   r6   s     Z/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/parsing/tests/test_latex.py_AddrC   #       q!e$$$$    c                 &    t          | |d          S r?   r   rA   s     rB   _MulrG   '   rD   rE   c                 &    t          | |d          S r?   r   rA   s     rB   _PowrI   +   rD   rE   c                 $    t          | d          S r?   )r!   r5   s    rB   _SqrtrL   /   s    E""""rE   c                 $    t          | d          S r?   )r   rK   s    rB   
_ConjugaterN   3       Q''''rE   c                 $    t          | d          S r?   )r   rK   s    rB   _AbsrQ   7       q5!!!!rE   c                 $    t          | d          S r?   )r   rK   s    rB   
_factorialrT   ;   rO   rE   c                 $    t          | d          S r?   )r   rK   s    rB   _exprV   ?   rR   rE   c                 &    t          | |d          S r?   )r   rA   s     rB   _logrX   C   rD   rE   c                 &    t          | |d          S r?   )r   )r:   r9   s     rB   	_binomialrZ   G   s    Aq5))))rE   c                       ddl m} m}m} ~ ~~d S )Nr   build_parsercheck_antlr_versiondir_latex_antlr)&sympy.parsing.latex._build_latex_antlrr]   r^   r_   r\   s      rB   test_importra   K   sB              	)???rE   )0r   )1   )z-3.14gQ	z(-7.13)(1.5)gQg      ?r2   2x   zx^2zx^\frac{1}{2}z	x^{3 + 1}   rd   z-cz	a \cdot bza / bza \div bza + bz	a + b - aza^2 + b^2 = c^2z	(x + y) zza'b+ab'za'zb'zy''_1zy_{1}''zy_1''z\left(x + y\right) zz\left( x + y\right ) zz\left(  x + y\right ) zz\left[x + y\right] zz\left\{x + y\right\} zz1+1z0+1z1*2z0*1z1 \times 2 zx = yzx \neq yzx < yzx > yzx \leq yzx \geq yzx \le yzx \ge yz\lfloor x \rfloorz\lceil x \rceilz\langle x |z| x \ranglez\sin \thetaz\sin(\theta)z\sin^{-1} az\sin a \cos bz\sin \cos \thetaz\sin(\cos \theta)z\frac{a}{b}z\dfrac{a}{b}z\tfrac{a}{b}z\frac12z\frac12yz	\frac1234"   z	\frac2{3}z\frac{\sin{x}}2z\frac{a + b}{c}z\frac{7}{3}   z(\csc x)(\sec y)z\lim_{x \to 3} az+-)dirz\lim_{x \rightarrow 3} az\lim_{x \Rightarrow 3} az\lim_{x \longrightarrow 3} az\lim_{x \Longrightarrow 3} az\lim_{x \to 3^{+}} a+z\lim_{x \to 3^{-}} a-z\lim_{x \to 3^+} az\lim_{x \to 3^-} az\inftyz\lim_{x \to \infty} \frac{1}{x}z\frac{d}{dx} xz\frac{d}{dt} xzf(x)zf(x, y)z
f(x, y, z)zf'_1(x)zf_{1}'zf_{1}''(x+y)zf_{1}''z\frac{d f(x)}{dx}z\frac{d\theta(x)}{dx}z|x|z||x||z|x||y|z||x||y||z
\pi^{|xy|}piz	\int x dxz\int x d\thetaz\int (x^2 - y)dxz\int x + a dxz\int daz\int_0^7 dxz\int\limits_{0}^{1} x dxz\int_a^b x dxz\int^b_a x dxz\int_{a}^b x dxz\int^{b}_a x dxz\int_{a}^{b} x dxz\int^{b}_{a} x dxz\int_{f(a)}^{f(b)} f(z) dzz
\int (x+a)z\int a + b + c dxz\int \frac{dz}{z}z\int \frac{3 dz}{z}z\int \frac{1}{x} dxz!\int \frac{1}{a} + \frac{1}{b} dxz#\int \frac{3 \cdot d\theta}{\theta}z\int \frac{1}{x} + 1 dxx_0zx_{0}zx_{1}x_azx_{a}zx_{b}zh_\thetaz	h_{theta}z
h_{\theta}zh_{\theta}(x_0, x_1)zx!z100!d   z\theta!z(x + 1)!z(x!)!zx!!!z5!7!   z\sqrt{x}z\sqrt{x + b}z\sqrt[3]{\sin x}z\sqrt[y]{\sin x}z\sqrt[\theta]{\sin x}z\sqrt{\frac{12}{6}}      z\overline{z}z\overline{\overline{z}}z\overline{x + y}z\overline{x} + \overline{y}z
\mathit{x}z\mathit{test}testz\mathit{TEST}TESTz\mathit{HELLO world}zHELLO worldz\sum_{k = 1}^{3} cz\sum_{k = 1}^3 cz\sum^{3}_{k = 1} cz\sum^3_{k = 1} cz\sum_{k = 1}^{10} k^2
   z"\sum_{n = 0}^{\infty} \frac{1}{n!}z\prod_{a = b}^{c} xz\prod_{a = b}^c xz\prod^{c}_{a = b} xz\prod^c_{a = b} xz\exp xz\exp(x)z\lg xz\ln xz\ln xyz\log xz\log xyz
\log_{2} xz
\log_{a} xz\log_{11} x   z\log_{a^2} xz[x]z[a + b]z\frac{d}{dx} [ \tan x ]z\binom{n}{k}z\tbinom{n}{k}z\dbinom{n}{k}z\binom{n}{0}zx^\binom{n}{k}za \, bza \thinspace bza \: bza \medspace bza \; bza \thickspace bz	a \quad bz
a \qquad bza \! bza \negthinspace bza \negmedspace bza \negthickspace bz\int x \, dxz\log_2 xz\log_a xz	5^0 - 4^0   z3x - 1c                  ^    ddl m}  t          D ]\  }} | |          |k    s
J |            d S )Nr   )parse_latex)sympy.parsing.latexr{   
GOOD_PAIRS)r{   	latex_str
sympy_exprs      rB   test_parseabler     sX    //////!+ ? ?	:{9%%333Y3333? ?rE   )&()z\frac{d}{dx}z(\frac{d}{dx})z\sqrt{}z\sqrtz\overline{}z	\overline{}z\mathit{x + y}z\mathit{21}z
\frac{2}{}z
\frac{}{2}z\int!z!0_^|z||x|z()z"((((((((((((((((()))))))))))))))))rm   z\frac{d}{dx} + \frac{d}{dt}zf(x,,y)zf(x,y,z\sin^xz\cos^2@#$%&*\~z\frac{(2 + x}{1 - x)}c                      ddl m} m} t          D ]4}t	          |          5   | |           d d d            n# 1 swxY w Y   5d S Nr   r{   LaTeXParsingError)r|   r{   r   BAD_STRINGSr   r{   r   r~   s      rB   test_not_parseabler   F  s    BBBBBBBB  # #	%&& 	# 	#K	"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	## #   9=	 =	)
z\cos 1 \coszf(,zf()za \div \div bza \cdot \cdot bza // bza +z1.1.1z1 +za / b /c                      ddl m} m} t          D ]4}t	          |          5   | |           d d d            n# 1 swxY w Y   5d S r   r|   r{   r   FAILING_BAD_STRINGSr   r   s      rB   test_failing_not_parseabler   Z  s    BBBBBBBB( # #	%&& 	# 	#K	"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	## #r   c                      ddl m} m} t          D ]6}t	          |          5   | |d           d d d            n# 1 swxY w Y   7d S )Nr   r   T)strictr   r   s      rB   test_strict_moder   b  s    BBBBBBBB( 0 0	%&& 	0 	0K	$////	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	00 0s   ;?	?	)`sympy.testing.pytestr   r   sympy.externalr   sympy.concrete.productsr   sympy.concrete.summationsr   sympy.core.addr	   sympy.core.functionr
   r   sympy.core.mulr   sympy.core.numbersr   r   sympy.core.powerr   sympy.core.relationalr   r   r   r   r   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr   r   $sympy.functions.elementary.complexesr   r   &sympy.functions.elementary.exponentialr   r   #sympy.functions.elementary.integersr   r   (sympy.functions.elementary.miscellaneousr    r!   (sympy.functions.elementary.trigonometricr"   r#   r$   r%   r&   r'   sympy.integrals.integralsr(   sympy.series.limitsr)   r*   r+   r,   r-   r.   r/   sympy.physics.quantum.stater0   r1   	sympy.abcr2   r3   r4   r5   r6   r7   r8   r9   r:   r;   disabledr<   r=   rC   rG   rI   rL   rN   rQ   rT   rV   rX   rZ   ra   r}   r   r   r   r   r   r    rE   rB   <module>r      sZ   . . . . . . . . ( ( ( ( ( ( + + + + + + ) ) ) ) ) )       6 6 6 6 6 6 6 6       & & & & & & & &             h h h h h h h h h h h h h h $ $ $ $ $ $ J J J J J J J J A A A A A A A A = = = = = = = = @ @ @ @ @ @ @ @ A A A A A A A A T T T T T T T T T T T T T T T T . . . . . . % % % % % % 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 / / / / / / / / / / / / / / / / / / / / / /	x	 	  T>wHSMM% % %% % %% % %# # #( ( (" " "( ( (" " "% % %* * *; ; ;~~~ ~ dd5#&&'	~
 
1I~ AaCL~ QTN~ ttAttAr{{++,~ 1dd1ajj=!~ QBK~ 1q5~ q1u~ !a%~ q1u~ 44!aR==!~  AqD1a4KA../!~" 44Q

A&&'#~$ dd66$<<++TT!VVD\\-B-BCCD%~& vvi  !'~( vvi  !)~* dd441::q112+~, TT!QZZ 3 34-~.  dd1ajj!!4!45/~0 dd441::q1121~2 TT!QZZ 3 343~4 TT!QZZ5~6 TT!QZZ7~8 TT!QZZ9~: TT!QZZ;~< TT!QZZ =~> rr!Qxx?~@ ""Q((A~B rr!QxxC~D rr!QxxE~F ""Q((G~H ""Q((I~J AqK~L AqM~N 5588$O~P $Q~R SSXXS~T SSXXU~V SSZZ W~X cc%jj!Y~Z TT!WW[~\ ttCCFFCCFF++,]~^ ##cc%jj//*_~` 33ss5zz??+a~b QUc~d a!ee~f a!eg~h ai~j $$ttAr{{A&&'k~l 44QR(()m~n 44442;;''(o~p cc!ffdd1bkk223q~r a!eTT!R[[112s~t TT!TT!R[[))*u~v ##a&&Q-(w~x %%1aT2223y~z !%%1aT":":":;{~| !%%1aT":":":;}~~ %eeAq!&>&>&>?~@ %eeAq!&>&>&>?A~B eeAq!5556C~D eeAq!5556E~F EE!Qs3334G~H EE!Qs3334I~J OK~L (ttAr{{Ar)B)BCM~N 

1a(()O~P 

1a(()Q~R aaddOS~T 1aU~V AAaAJJW~X #(##A&&'Y~Z )hhy))!A#../[~\ ::aaddA../]~^ zz*;((7*;*;A*>*>BBC_~` **Q""#a~b TT!WWc~d ttCCFF||e~f QQ g~h $$ttAwwttAww''(i~j FF4LL$$qs))+,k~l 88Aq>>"m~n E**+o~p ((1a4!8Q//0q~r xxQ

A../s~t !Q u~v XXa!Q++,w~x !((1q!Qi"8"89y~z xxAq!9--.{~| xxAq!9--.}~~ !aAY//0~@ !aAY//0A~B 88A1ay112C~D 88A1ay112E~F #HHQQqTTAqqttQQqTT?$C$CDG~H HHTT!QZZ++,I~J 88DDaQ$7$7;;<K~L 88CC2JJ223M~N XXaAr

lA667O~P XXcc!Rjj!445Q~R *Xdd442;;Ar

++Q//1S~V ,XaUB'')W~Z  $$ttAr{{A*>*>!B!BC[~\ VVG__]~^ vvg_~` VVG__a~b vvgc~d &&%%&e~f FF;''(g~h XXk66'??FF7OO<<>i~l JJqMMm~n jjooo~p E""#q~r **TT!QZZ(()s~t zz**Q--(()u~v jjJJqMM22334w~x dd::a==**Q--001y~z $$q''{~| dd441::&&'}~~ $$ss1vvq//*~@ $$ss1vvq//*A~B ttCCFFE223C~D UU44DDBKK#8#899:E~F jjmm$G~H  JJqMM!:!:;I~J **TT!QZZ001K~L $ZZ]]ZZ]]%BCM~N ~~a##$O~P ((1a..!Q~R   A&&'S~T ++a##$U~V FF3KK W~X vvf~~&Y~Z vvf~~&[~\ ff]334]~^ CCAq!9--._~` ##a!Q++,a~b CCAq!9--.c~d ##a!Q++,e~f ss1a4!Q445g~h +SjjmmR	 	 1a*--/i~l WWQAq	223m~n 771q!Qi001o~p WWQAq	223q~r 771q!Qi001s~t Qu~v aw~x ttAr{{y~z ttAqzz{~| QqS!}~~ Q

~@ ac1A~B DDAJJC~D DDAJJE~F TT!R[[!G~H dd1dd1ajj))*I~J QKK~L aM~N  CCFFA!6!67O~P ii1oo&Q~R yyA'S~T yyA'U~V ii1oo&W~X Q		!Q001Y~Z Q

[~\ Q

#]~^ Q

_~` ttAqzz"a~b Q

c~d a$e~f 441::g~h DDAJJi~j Q

k~l 441::&m~n $$q!**%o~p DDAJJ'q~r hhq!nn%s~t $$q!**u~v $$q!**w~x 44Q

DDTT!QZZ$8$899:y~z TT!QZZ$$%{~
B? ? ?' ' 'R# # #    # # #0 0 0 0 0rE   