
    gS              $       )   d dl mZ d dlmZ d dlmZ d dlmZ d dlm	Z	 d dl
mZmZ d dlmZmZmZ d dlmZ d d	lmZ d d
lmZmZmZmZmZ d dlmZ d dlmZmZ d dl m!Z!m"Z" d dl#m$Z$m%Z% d dl&m'Z'm(Z( d dl)m*Z*m+Z+m,Z,m-Z- d dl.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4 d dl5m6Z6 d dl7m8Z8 d dlm9Z9m:Z:m;Z;m<Z<m=Z=m>Z> d dl?m@Z@mAZAmBZB d dlCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZM ddlNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZY  ed          ZZeZdu Z[d Z\d Z]efdZ^d ed          fd  ed           fd! ed"          fd# ed#          fd$ ed%          fd& ed%          fd' ed(          fd) ed(          fd* ed+          fd, ed-          fd. ed/          fd0 ed1          fgZ_d2d3d4d5 eRd6d7          fd8 eQdd          fd9 eQd d          fd: eRdd;          fd< eRd d          fd+eDfd=d;eDz  fd> eQ eRd?eD          d@          fdAeI fdBefdCeGeHz  fdD eRdd;          fdEeGeHz  fdFeGeHz  fdGeGeHz   fdH eQeGeHz   eG           fdI eR eQeDeE          eF          fdJ eQ eR edK          eH           eReG edL                              fgZ`dMdNdOdPdQd=d;eDz  fd>d?eDz  dz
  fdAeI fdCeGeHz  fdRdEeGeHz  fdFeGeHz  fdGeGeHz   fdHeHfdIeDeEz   eFz  fgZadSeGeHz  fdTeGeHz  fdUeGeHz  fdV eRd eSd;d@                    fdW eR eRd eSd;d@                    eE          fdX eR eRd eSd;d@                    dY          fdZ eRd; eSd?d@                    fd[ eReGeHz    eSeId@                    fd\ eRd] eSd?d@                    fg	ZbdSeGeHz  fdTeGeHz  fdUeGeHz  fdV edd;          fdWeEd;z  fd^dZ ed;d?          fd[eGeHz   eIz  fd\ ed]d?          fg	Zcd_ e9eDeE          fd` e:eDeE          fda e;eDeE          fdb e=eDeE          fdc e<eDeE          fdd e>eDeE          fde e<eDeE          fdf e>eDeE          fda eeDeE          fdc eeDeE          fdb eeDeE          fdd eeDeE          fd` eeDeE          fdg e9eGd;z  eHd;z  z   eId;z            fgZddheDd;z  fdi eSeD eRd eSd;d@                              fdjeD eQd?d          z  fdk edl           eVeDeEz            z  fdm eQ eSdnd            eRd@ eSdod                               fgZedheDd;z  fdi e+eD          fdjeDdoz  fdk edl           eVeDeEz            z  fdpgZfdq e6 eRdeD          eD          fdr e6 eRdeD          eD          fds e6 eRdeD          eO          fdt e6 eRdeDd;z  eEz
            eD          fdu e6 eRd eQeDeG                    eD          fdv e6 eRdd          eG          fdw e6 eRdd          eDd d]f          fdx e6 eRdeD          eDd df          fdy e6 eRdeD          eDeGeHf          fdz e6 eRdeD          eDeGeHf          fd{ e6 eRdeD          eDeGeHf          fd| e6 eRdeD          eDeGeHf          fd} e6 eRdeD          eDeGeHf          fd~ e6 eRdeD          eDeGeHf          fd e6 ePeF          eF ePeG           ePeH          f          fd e6 eRd eQ eQeGeH          eI                    eD          fd e6 eRd eRd eeFd@                              eF          fd e6 eRd eRd? eSeFd@                              eF          fd e6 eRd eRd eeDd@                              eD          fd e6 eRd eQ eRd eSeGd@                     eRd eeHd@                                        eD          fd e6 eRd eQ eRd eSeDd@                    d                    eD          fgZgdq e6eDeD          fdr e6eDeD          fds e6eDeO          fdt e6eDd;z  eEz
  eD          fdu e6eDeGz   eD          fdv e6deG          fdw e6deDd d]f          fdx e6eDeDd df          fdy e6eDeDeGeHf          fdz e6eDeDeGeHf          fd{ e6eDeDeGeHf          fd| e6eDeDeGeHf          fd} e6eDeDeGeHf          fd~ e6eDeDeGeHf          fd e6 ePeF          eF ePeG           ePeH          f          fd e6eGeHz   eIz   eD          fd e6 eeFd@          eF          fd e6d? eeFd@          z  eF          fd e6deDz  eD          fd e6deGz  deHz  z   eD          fd e6deDz  dz   eD          fgZhd eeDeD          fd eeDeK          fd e e4eD          eD          fd e ePeD          eD          fd e  ed          eD          eD          fgZid e3eO          fd e3eO          fd e/eG          fd eR e3eG           e0eH                    fd e3 e0eO                    fd e3 e0eO                    fd e1eD           e2eE          z  fd eR e3eD           eSd;d@                    fgZjd e8eGeDd?d          fd e8eGeDd?d          fd e8eGeDd?d          fd e8eGeDd?d          fd e8eGeDd?d          fd e8eGeDd?d          fd e8eGeDd?d          fd e8eGeDd?d          fd e8eGeDd?d          fd e8 eRd eSeDd@                    eDe          fg
Zkd e8deDz  eDe          fgZld e+eD          fd e+ eQeDeH                    fd eS e3eD           eSd?d@                    fd e* e3eD          eE          fd e* e3eD          eO          fd eT eRd eSdd@                              fgZmd e+eD          fd e+eDeHz             fd e* e3eD          d?          fd e* e3eD          eE          fd e* e3eD          eO          fd e+d;          fgZnd eWeD          fd eWd          fd eWeO          fd eW eQeDd                    fd eW eWeD                    fd eW eW eWeD                              fd eR eWdn           eWd]                    fgZod eeD          fd ed          fd eeO          fd eeDdz             fd e eeD                    fd e e eeD                              fd edn           ed]          z  fgZpd e	 eRdeI          eLdd?f          fd e	 eRdeI          eLdd?f          fd e	 eRdeI          eLdd?f          fd e	 eRdeI          eLdd?f          fd e	 eRdeLd;z            eLddf          fd e	 eRd eRd eS eWeM          d@                              eMd ef          fgZqd e	eIeLdd?f          fd e	eIeLdd?f          fd e	eIeLdd?f          fd e	eIeLdd?f          fd e	eLd;z  eLddf          fd e	d eeM          z  eMd ef          fgZrd eeDeGeHeIf          fd eeDeGeHeIf          fd eeDeGeHeIf          fd eeDeGeHeIf          fgZsd ePeD          fd ePeDeE          fd ePeDeEeF          fd  ed          eD          fd  edæ          eDeEz             fd  ed%           ed           ed                     fgZtd eVeD          fd eV e!eD                    fd eVeD           eVeE          z  fd eV eVeD           eVeE          z            fd e(eD          fd e'eD          fd eXeD          fd eXeD          fd e^eDd          fd e^eD          fd e^eDeEz            fd e^eD          fd e^eDeEz            fd e^eDd;          fd e^eDeG          fd e^eDdզ          fd e^eD eSeGd;                    fd e^eDd;          fd e^eDeG          fd eUeF          fd eU eUeF                    fd eU eQeDeE                    fd eUeD           eUeE          z   fd e\eGeH          fd e\eGeHeIeJz
  eDeEz            fd e]eGeH          fd e]eGeHeIeJz
  eDeEz            fd e@d+          fd eAd+          fd eB e@d+           eAd                    fgZud e!eD          fd e! e!eD                    fd e!eD           e!eE          z  fd e! e!eD           e!eE          z            fd e(eD          fd e'eD          fd e$eD          fd e$eD          fd e%eDd          fd e%eD          fd e%eDeEz            fd e%eD          fd e%eDeEz            fd e%eDd;          fd e%eDeG          fd e%eDdզ          fd e%eD eSeGd;                    fd e%eDd;          fd e%eDeG          fd e"eF          fd e" e"eF                    fd e"eDeEz             fd e"eD           e"eE          z   fd e,eGeH          fd e,eGeHeIeJz
  eDeEz            fd e-eGeH          fd e-eGeHeIeJz
  eDeEz            fd e@d+          fd eAd+          fd eB e@d+           eAd                    fgZvd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fd eReGeH          fgZwd eYeMeL          fd eYeMeL          fd eYeMeL          fd eYeMd           fd eSeD eYeMeL                    fgZxd eeMeL          fd eeMeL          fd eeMeL          fd eeMd           fdeD eeMeL          z  fgZyd eR eQeDeE          eF          fd eR eQeDeE          eF          fd eR eQeDeE          eF          fgZzd Z{d Z|d Z}d Z~d Zd Zd Zd  Zd Zd Zd Zd Zd Zed             Zd Zed             Zd	 Zd
 ZdS (      )XFAIL)parse_latex_lark)import_module)Product)Sum)
DerivativeFunction)EooRational)Powevaluate)GreaterThanLessThanStrictGreaterThanStrictLessThan
Unequality)Symbol)binomial	factorial)Abs	conjugate)explog)ceilingfloor)rootsqrtMinMax)asincoscscsecsintan)Integral)Limit)EqNeLtLeGtGe)BraKetInnerProduct)
xyzabcdtkn   )thetaf_Add_Mul_Pow_Sqrt
_Conjugate_Abs
_factorial_exp	_binomiallarkNc                      t          | ddiS Nr   F)r    argss    _/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/parsing/tests/test_latex_lark.py_MinrO   "       %u%%%    c                      t          | ddiS rK   )r!   rL   s    rN   _MaxrS   &   rP   rQ   c                 ^    |t           k    rt          | d          S t          | |d          S )NFr   )r
   r   )r6   r7   s     rN   _logrU   *   s3    Avv1u%%%%1a%((((rQ   x_0zx_{0}zx_{1}x_azx_{a}zx_{b}zh_\thetaz	h_{theta}z
h_{\theta}zy''_1zy_{1}''zy_1''z
\mathit{x}r3   z\mathit{test}testz\mathit{TEST}TESTz\mathit{HELLO world}zHELLO world)0r   )1r=   )z-3.14gQ	(-7.13)(1.5)gQg      ?1+10+11*2   0*12xz3x - 1   z-cz\inftyz	a \cdot b1 \times 2 za / bza \div bza + bz	a + b - az	(x + y) zza'b+ab'za'zb')r\   gp=
c%)r]   r`   )r^   r=   )r_   r`   )ra   r   )re   r`   z\frac{a}{b}z\dfrac{a}{b}z\tfrac{a}{b}z\frac12z\frac12y	\frac1234"   z	\frac2{3}z\frac{a + b}{c}z\frac{7}{3}   )rf      zx = yzx \neq yzx < yzx > yzx \leq yzx \geq yzx \le yzx \ge yza^2 + b^2 = c^2zx^2zx^\frac{1}{2}z	x^{3 + 1}z
\pi^{|xy|}pi	5^0 - 4^0      )rk   r   z	\int x dxz\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 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{1}{x} + 1 dxz\frac{d}{dx} xz\frac{d}{dt} xz\frac{d}{dx} ( \tan x )z\frac{d f(x)}{dx}z\frac{d\theta(x)}{dx}r>   z\sin \thetaz\sin(\theta)z\sin^{-1} az\sin a \cos bz\sin \cos \thetaz\sin(\cos \theta)z(\csc x)(\sec y)z\frac{\sin{x}}2z\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\lim_{x \to \infty} \frac{1}{x}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x!z100!d   z\theta!z(x + 1)!z(x!)!zx!!!z5!7!z\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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h_{\theta}(x_0, x_1)z|x|z||x||z|x||y|z||x||y||z\lfloor x \rfloorz\lceil x \rceilz\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\log_2 xz\log_a xz\overline{z}z\overline{\overline{z}}z\overline{x + y}z\overline{x} + \overline{y}z
\min(a, b)z\min(a, b, c - d, xy)z
\max(a, b)z\max(a, b, c - d, xy)z\langle x |z| x \ranglez\langle x | y \rangler4   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\binom{n}{k}z\tbinom{n}{k}z\dbinom{n}{k}z\binom{n}{0}zx^\binom{n}{k}z\left(x + y\right) zz\left( x + y\right ) zz\left(  x + y\right ) zc                      ddh} t          t                    D ]R\  }\  }}|| v rt          d          5  t          |          |k    s
J |            	 d d d            n# 1 swxY w Y   Sd S )Nrr   rh   F)	enumerateSYMBOL_EXPRESSION_PAIRSr   r   expected_failuresi	latex_str
sympy_exprs       rN   test_symbol_expressionsr~     s    A&/0G&H&H H H""Iz!!!e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH H   A  A$	'A$	c                  X   dh} t          t                    D ]R\  }\  }}|| v rt          d          5  t          |          |k    s
J |            	 d d d            n# 1 swxY w Y   St          t                    D ]*\  }\  }}|| v rt          |          |k    s
J |            +d S )N   F)rw   #UNEVALUATED_SIMPLE_EXPRESSION_PAIRSr   r   !EVALUATED_SIMPLE_EXPRESSION_PAIRSry   s       rN   test_simple_expressionsr     s9   &/0S&T&T H H""Iz!!!e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H '00Q&R&R D D""Iz!!!	**j888)8888D D   AA#	&A#	c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kt          D ]"\  } }t          |           |k    s
J |             #d S NF)%UNEVALUATED_FRACTION_EXPRESSION_PAIRSr   r   #EVALUATED_FRACTION_EXPRESSION_PAIRSr|   r}   s     rN   test_fraction_expressionsr         !F H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H "E D D	:	**j888)8888D D   AA	A	c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kd S r   )RELATION_EXPRESSION_PAIRSr   r   r   s     rN   test_relation_expressionsr     s    !: H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH Hr   c                  X   dh} t          t                    D ]R\  }\  }}|| v rt          d          5  t          |          |k    s
J |            	 d d d            n# 1 swxY w Y   St          t                    D ]*\  }\  }}|| v rt          |          |k    s
J |            +d S Nrc   F)rw   "UNEVALUATED_POWER_EXPRESSION_PAIRSr   r    EVALUATED_POWER_EXPRESSION_PAIRSry   s       rN   test_power_expressionsr     s9   &/0R&S&S H H""Iz!!!e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H '00P&Q&Q D D""Iz!!!	**j888)8888D Dr   c                  X   dh} t          t                    D ]R\  }\  }}|| v rt          d          5  t          |          |k    s
J |            	 d d d            n# 1 swxY w Y   St          t                    D ]*\  }\  }}|| v rt          |          |k    s
J |            +d S )N   F)rw   %UNEVALUATED_INTEGRAL_EXPRESSION_PAIRSr   r   #EVALUATED_INTEGRAL_EXPRESSION_PAIRSry   s       rN   test_integral_expressionsr     s9   &/0U&V&V @ @""Iz!!!e__ 	@ 	@#I..*<<<a<<<<	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ '00S&T&T D D""Iz!!!	**j888)8888D Dr   c                  Z   ddh} t          t                    D ]R\  }\  }}|| v rt          d          5  t          |          |k    s
J |            	 d d d            n# 1 swxY w Y   St          t                    D ]*\  }\  }}|| v rt          |          |k    s
J |            +d S )Nrc   rm   F)rw   DERIVATIVE_EXPRESSION_PAIRSr   r   ry   s       rN   test_derivative_expressionsr     s;   A&/0K&L&L H H""Iz!!!e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H '00K&L&L D D""Iz!!!	**j888)8888D Dr   c                      dh} t          t                    D ]R\  }\  }}|| v rt          d          5  t          |          |k    s
J |            	 d d d            n# 1 swxY w Y   Sd S r   )rw   TRIGONOMETRIC_EXPRESSION_PAIRSr   r   ry   s       rN   test_trigonometric_expressionsr     s    &/0N&O&O H H""Iz!!!e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH Hr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kd S r   )"UNEVALUATED_LIMIT_EXPRESSION_PAIRSr   r   r   s     rN   test_limit_expressionsr     s    !C H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH Hr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kt          D ]"\  } }t          |           |k    s
J |             #d S r   )!UNEVALUATED_SQRT_EXPRESSION_PAIRSr   r   EVALUATED_SQRT_EXPRESSION_PAIRSr   s     rN   test_square_root_expressionsr     s    !B H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H "A D D	:	**j888)8888D Dr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kt          D ]"\  } }t          |           |k    s
J |             #d S r   )&UNEVALUATED_FACTORIAL_EXPRESSION_PAIRSr   r   $EVALUATED_FACTORIAL_EXPRESSION_PAIRSr   s     rN   test_factorial_expressionsr     s    !G H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H "F D D	:	**j888)8888D Dr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kt          D ]"\  } }t          |           |k    s
J |             #d S r   ) UNEVALUATED_SUM_EXPRESSION_PAIRSr   r   EVALUATED_SUM_EXPRESSION_PAIRSr   s     rN   test_sum_expressionsr     s    !A H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H "@ D D	:	**j888)8888D Dr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kd S r   )$UNEVALUATED_PRODUCT_EXPRESSION_PAIRSr   r   r   s     rN   test_product_expressionsr   '  s    !E H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH Hr   c                      h d} t          t                    D ]R\  }\  }}|| v rt          d          5  t          |          |k    s
J |            	 d d d            n# 1 swxY w Y   Sd S )N>   r   rc   rm   F)rw   !APPLIED_FUNCTION_EXPRESSION_PAIRSr   r   ry   s       rN   !test_applied_function_expressionsr   ,  s    !		&/0Q&R&R H H""Iz!!!e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH Hr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kt          D ]"\  } }t          |           |k    s
J |             #d S r   ),UNEVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRSr   r   *EVALUATED_COMMON_FUNCTION_EXPRESSION_PAIRSr   s     rN    test_common_function_expressionsr   7  s    !M H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H "L D D	:	**j888)8888D Dr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kd S r   ) SPACING_RELATED_EXPRESSION_PAIRSr   r   r   s     rN   test_spacingr   @  s    !A H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH Hr   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kt          D ]"\  } }t          |           |k    s
J |             #d S r   )%UNEVALUATED_BINOMIAL_EXPRESSION_PAIRSr   r   #EVALUATED_BINOMIAL_EXPRESSION_PAIRSr   s     rN   test_binomial_expressionsr   G  r   r   c                      t           D ]J\  } }t          d          5  t          |           |k    s
J |             	 d d d            n# 1 swxY w Y   Kd S r   )MISCELLANEOUS_EXPRESSION_PAIRSr   r   r   s     rN   test_miscellaneous_expressionsr   P  s    !? H H	:e__ 	H 	H#I..*<<<i<<<<	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	HH Hr   )sympy.testing.pytestr   sympy.parsing.latex.larkr   sympy.externalr   sympy.concrete.productsr   sympy.concrete.summationsr   sympy.core.functionr   r	   sympy.core.numbersr
   r   r   sympy.core.powerr   sympy.core.parametersr   sympy.core.relationalr   r   r   r   r   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr   r   $sympy.functions.elementary.complexesr   r   &sympy.functions.elementary.exponentialr   r   #sympy.functions.elementary.integersr   r   (sympy.functions.elementary.miscellaneousr   r   r    r!   (sympy.functions.elementary.trigonometricr"   r#   r$   r%   r&   r'   sympy.integrals.integralsr(   sympy.series.limitsr)   r*   r+   r,   r-   r.   r/   sympy.physics.quantumr0   r1   r2   	sympy.abcr3   r4   r5   r6   r7   r8   r9   r:   r;   r<   
test_latexr>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   disabledrO   rS   rU   rx   r   r   r   r   r   r   r   r   r   r   r   r    EVALUATED_LIMIT_EXPRESSION_PAIRSr   r   r   r   r   r   r   r   r   r   r   r   r   r   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    rQ   rN   <module>r      s'    & & & & & & 5 5 5 5 5 5 ( ( ( ( ( ( + + + + + + ) ) ) ) ) ) 4 4 4 4 4 4 4 4 . . . . . . . . . .             * * * * * * f f f f f f f f f f f f f f $ $ $ $ $ $ H H H H H H H H ? ? ? ? ? ? ? ? ; ; ; ; ; ; ; ; > > > > > > > > I I I I I I I I I I I I R R R R R R R R R R R R R R R R . . . . . . % % % % % % 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 h h h h h h h h h h h h h h h h h h h h h h h h h h}V 4<& & && & &  ) ) ) ) VVG__vvgVVG__vvg&&%%&FF;''(vvi  !vvi  !FF3KK vvf~~&vvf~~&ff]334   dd5#&&'TT!QZZTT!QZZTT!QZZTT!QZZ	1I
AENTT!QZZ$$%
QBKO1q5TT!QZZ q1u!a%q1u44Ar??#44Q

A&&'dd66$<<++TT!VVD\\-B-BCCD+' #2 
AENA	
QBK1q5q1u!a%q1u1AEQ;% !& QUa!ea!eaa%%&$$ttAttAr{{++Q//044QQ,,b11244442;;''(a!eTT!R[[112TT!TT!R[[))*
) % QUa!ea!e!Q !a%88Aq>>"!a%1%XXa^^$
' # rr!Qxx""Q((rr!Qxxrr!Qxx""Q((""Q((AqAq~~a##$((1a..!  A&&'++a##$**Q""#AqD1a4KA../ $ Q!VttAttAttAr{{334451Q

?#FF4LLDDQKK/044Q

DDTT!QZZ$8$899:& " Q!VttAww16FF4LLDDQKK/0$   88DDAJJ**+hhttAqzz1--.aU334((4416A:#6#6::;xxQQ

 3 3Q778$$q!**a(()XXdd1ajj1a)445 ((441::1ay"A"ABxxQ

Q1I667xxQ

Q1I667$$q!**q!Qi889$$q!**q!Qi88988DDAJJAq	::;88DDAJJAq	::;"HHQQqTTAqqttQQqTT?$C$CD88DDDDaQ,?,?$@$@!DDE88DDDDCC2JJ,?,?$@$@!DDEXXdd1dd1dd1bkk.B.B&C&CQGGHXXdd1dd1cc!Rjj.A.A&B&BAFFG)Xdd1dd44442;;//aQ1D1DEEFFJJL$$q$$ttAttAr{{7K7KQ2O2O*P*PRS!T!TU-) %4 88Aq>>"hhq!nn%E**+((16A:q112xxAq))*!Q XXa!Q++, ((1q!Qi"8"89xxAq!9--.xxAq!9--.!aAY//0!aAY//088A1ay11288A1ay112"HHQQqTTAqqttQQqTT?$C$CD88AEAIq11288CC2JJ223XXa##a**na889XXa!eQ//0)88AEAEM1+E+EF!a%!)Q!7!78+' #2 

1a(()

1a(()CCFFA!6!67::aaddA../zz*;((7*;*;A*>*>BBC  SSZZ cc%jj!TT!WWttCCFFCCFF++,##cc%jj//*33ss5zz??+##a&&33q66/*cc!ffdd1bkk223	"  %%1aT2223 %%1aT":":":; %%1aT":":":;$eeAq!&>&>&>?$eeAq!&>&>&>?eeAq!5556eeAq!5556EE!Qs3334EE!Qs3334'ttAttAr{{/C/CQ)K)KL& " (q1ua)<)<=$  
 $$q''dd441::&&'$$ss1vvttAr{{334 $$ss1vvq//*ttCCFFE223UU44DDBKK#8#899:	% ! $$q''dd1q5kk"$$ss1vvq//*$$ss1vvq//*ttCCFFE223TT!WW%#  JJqMMjjooE""#**TT!QZZ(()zz**Q--(()jjJJqMM22334dd::a==**Q--001* & IIaLLiinn5!!"))AE""#yy1&&'ii		))A,,//001iillYYq\\)*( $ CCQ

Q1I667##dd1ajj1a)445CCQ

Q1I667##dd1ajj1a)445ss4416??Q2J??@*SaajjmmR0011	2	2Q2J??A$   CCAq!9--.##a!Q++,CCAq!9--.##a!Q++,ss16Aq":667*CCIIaLL0@1a*,M,MN"  WWQAq	223771q!Qi001WWQAq	223771q!Qi001	( $ aaddO1aAAaAJJ#(##A&&')hhy))!a%001XXk66'??FF7OO<<>% ! TT!WWttCCFF||Q$$q''!"$$ttAwwa())*5588$$QattAr{{ttAwwQUQa!eDDAJJDDAJJTT!R[[!dd1dd1ajj))*$$q!**$$q!**jjmm$JJqMM!:!:;**TT!QZZ001#ZZ]]ZZ]]%BCDDAJJttAq!a%Q778DDAJJttAq!a%Q778SSXXSSXX||CCHHcc#hh??@? 0 ,F SSVVss33q66{{AQ ##cc!ffss1vvo&&'5588$$AQss1bzzss1vvAE

AQUCC1IICC1IISSBZZ cc!TT!QZZ(()##a))##a))iill#99Q<<!8!89))AE**+#YYq\\IIaLL%@ACC1IIss1aQA667CC1IIss1aQA667SSXXSSXX||CCHHcc#hh??@=. *D Q

Q

#Q

ttAqzz"Q

a$441::DDAJJQ

441::&$$q!**%DDAJJ'$    ii1oo&yyA'yyA'ii1oo&Q		!Q001) % hhq!nn%xx1~~&xx1~~&hhq!nn%XXa^^+,' # dd441::q112TT!QZZ 3 34dd1ajj!!4!45" H H HD D DD D DH H H
D D DD D DD D DH H HH H HD D DD D DD D DH H H
 H H HD D D H H HD D DH H H H HrQ   