
    sg-                     *   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dë      fd edū      fd edǫ      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 eVeAdͫ      fd eVeAe      fd eVeAeBz  e      fd eVeAe      fd eVeAeBz  e      fd eVeAd.      fd eVeAeD      fd eVeAdݫ      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_y)    )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     Q/var/www/html/venv/lib/python3.12/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} ~ ~~y )Nr   build_parsercheck_antlr_versiondir_latex_antlr)&sympy.parsing.latex._build_latex_antlrr]   r^   r_   r\   s      rB   test_importra   K   s      	)?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                  P    ddl m}  t        D ]  \  }} | |      |k(  rJ |        y )Nr   )parse_latex)sympy.parsing.latexr{   
GOOD_PAIRS)r{   	latex_str
sympy_exprs      rB   test_parseabler     s1    /!+ ?	:9%3>Y>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                  z    ddl m} m} t        D ]  }t	        |      5   | |       d d d          y # 1 sw Y   +xY wNr   r{   LaTeXParsingError)r|   r{   r   BAD_STRINGSr   r{   r   r~   s      rB   test_not_parseabler   F  s?    B  #	%& 	#	"	# 	##	# 	#   	1:	)
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                  z    ddl m} m} t        D ]  }t	        |      5   | |       d d d          y # 1 sw Y   +xY wr   r|   r{   r   FAILING_BAD_STRINGSr   r   s      rB   test_failing_not_parseabler   Z  s?    B( #	%& 	#	"	# 	##	# 	#r   c                  ~    ddl m} m} t        D ]   }t	        |      5   | |d       d d d        " y # 1 sw Y   -xY w)Nr   r   T)strictr   r   s      rB   test_strict_moder   b  sA    B( 0	%& 	0	$/	0 	00	0 	0s   3<	)`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      sT   . ( + )  6  &   h h $ J A = @ A T T . % 8 8 0 / / /	x	  T>wSM%%%#("("%*;~~~ ~ d5#&'	~
 
1I~ AaCL~ QTN~ tAtAr{+,~ 1d1aj=!~ QBK~ 1q5~ q1u~ !a%~ q1u~ 4!aR=!~  AqD1a4KA./!~" 4Q
A&'#~$ d6$<+T!VD\-BCD%~& vi !'~( vi !)~* d41:q12+~, T!QZ 34-~.  d1aj!!45/~0 d41:q121~2 T!QZ 343~4 T!QZ5~6 T!QZ7~8 T!QZ9~: T!QZ;~< T!QZ =~> r!Qx?~@ "Q(A~B r!QxC~D r!QxE~F "Q(G~H "Q(I~J AqK~L AqM~N 58$O~P $Q~R SXS~T SXU~V SZ W~X c%j!Y~Z T!W[~\ tCFCF+,]~^ #c%j/*_~` 3s5z?+a~b QUc~d a!ee~f a!eg~h ai~j $tAr{A&'k~l 4QR()m~n 442;'(o~p c!fd1bk23q~r a!eT!R[12s~t T!T!R[)*u~v #a&Q-(w~x %1aT23y~z !%1aT":;{~| !%1aT":;}~~ %eAq!&>?~@ %eAq!&>?A~B eAq!56C~D eAq!56E~F E!Qs34G~H E!Qs34I~J OK~L (tAr{Ar)BCM~N 
1a()O~P 
1a()Q~R adOS~T 1aU~V AaAJW~X #(#A&'Y~Z )hy)!A#./[~\ :adA./]~^ z*;(7*;A*>BC_~` *Q"#a~b T!Wc~d tCF|e~f QQ g~h $tAwtAw'(i~j F4L$qs)+,k~l 8Aq>"m~n E*+o~p (1a4!8Q/0q~r xQ
A./s~t !Q u~v Xa!Q+,w~x !(1q!Qi"89y~z xAq!9-.{~| xAq!9-.}~~ !aAY/0~@ !aAY/0A~B 8A1ay12C~D 8A1ay12E~F #HQqTAqtQqT?$CDG~H HT!QZ+,I~J 8DaQ$7;<K~L 8C2J23M~N XaAr
lA67O~P Xc!Rj!45Q~R *d42;Ar
+Q/1S~V ,aUB')W~Z  $tAr{A*>!BC[~\ VG_]~^ vg_~` VG_a~b vgc~d &%&e~f F;'(g~h Xk6'?F7O<>i~l JqMm~n joo~p E"#q~r *T!QZ()s~t z*Q-()u~v jJqM234w~x d:a=*Q-01y~z $q'{~| d41:&'}~~ $s1vq/*~@ $s1vq/*A~B tCFE23C~D U4DBK#89:E~F jm$G~H  JqM!:;I~J *T!QZ01K~L $Z]Z]%BCM~N ~a#$O~P (1a.!Q~R  A&'S~T +a#$U~V F3K W~X vf~&Y~Z vf~&[~\ f]34]~^ CAq!9-._~` #a!Q+,a~b CAq!9-.c~d #a!Q+,e~f s1a4!Q45g~h +jmR	 1a*-/i~l WQAq	23m~n 71q!Qi01o~p WQAq	23q~r 71q!Qi01s~t Qu~v aw~x tAr{y~z tAqz{~| QqS!}~~ Q
~@ ac1A~B DAJC~D DAJE~F T!R[!G~H d1d1aj)*I~J QKK~L aM~N  CFA!67O~P i1o&Q~R yA'S~T yA'U~V i1o&W~X Q	!Q01Y~Z Q
[~\ Q
#]~^ Q
_~` tAqz"a~b Q
c~d a$e~f 41:g~h DAJi~j Q
k~l 41:&m~n $q!*%o~p DAJ'q~r hq!n%s~t $q!*u~v $q!*w~x 4Q
DT!QZ$89:y~z T!QZ$%{~
B?'R#  # #0rE   