
    g                     v   d dl mZmZ d dlmZmZmZmZ d dlm	Z	m
Z
mZmZ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 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&  ed          \  Z'Z( ed          Z) ed          Z*d Z+d Z,d Z-d Z.d Z/e&d             Z0d Z1d Z2d Z3d Z4d Z5d Z6dS )    )
DerivativeFunction)IRationaloopi)EqGeGtLeLtNe)Symbolsymbols)Abs	conjugate)explog)sqrt)sin)Integral)Matrix)limit)python)raisesXFAILzx,ythetaphic                     t          t          d           dz            dk    sJ t          t          d           dz            dk    sJ t          t                    dk    sJ t          t          dz            dk    sJ t          dt          z            d	k    sJ t          t          t          d
z  z            dk    sJ t          t          t          dd          z            dk    sJ t          t          dz  t          z   dz             dv sJ t          dt          z
            dv sJ t          ddt          z  z
            dv sJ t          dt          dd          t          z  t          z  z
            dv sJ t          t          t          z            dk    sJ t          t           t          z            dk    sJ t          t          dz   t          z            dv sJ t          dt          z   t          z            dv sJ t          dt          z  t          dz   z            dk    sJ t          dt          dd          t          dz   z  z
            dv sJ d S )N      ze = Rational(-1, 2)      ze = Rational(-13, 22)e = oozx = Symbol('x')
e = x**2zx = Symbol('x')
e = 1/xz*y = Symbol('y')
x = Symbol('x')
e = y/x**2z&x = Symbol('x')
e = x**Rational(-5, 2))z x = Symbol('x')
e = 1 + x + x**2z x = Symbol('x')
e = x + x**2 + 1z x = Symbol('x')
e = x**2 + x + 1)zx = Symbol('x')
e = 1 - xzx = Symbol('x')
e = -x + 1)zx = Symbol('x')
e = 1 - 2*xzx = Symbol('x')
e = -2*x + 1   )z/y = Symbol('y')
x = Symbol('x')
e = 1 - 3/2*y/xz0y = Symbol('y')
x = Symbol('x')
e = -3/2*y/x + 1z1y = Symbol('y')
x = Symbol('x')
e = 1 - 3*y/(2*x)z'x = Symbol('x')
y = Symbol('y')
e = x/yz(x = Symbol('x')
y = Symbol('y')
e = -x/y)z/y = Symbol('y')
x = Symbol('x')
e = 1/y*(2 + x)z/y = Symbol('y')
x = Symbol('x')
e = 1/y*(x + 2)z/x = Symbol('x')
y = Symbol('y')
e = 1/y*(2 + x)z-x = Symbol('x')
y = Symbol('y')
e = (2 + x)/yz-x = Symbol('x')
y = Symbol('y')
e = (x + 2)/y)z-y = Symbol('y')
x = Symbol('x')
e = y*(1 + x)z-y = Symbol('y')
x = Symbol('x')
e = y*(x + 1)
   z!x = Symbol('x')
e = -5*x/(x + 10))z7x = Symbol('x')
e = Rational(-3, 2)*x + Rational(-1, 2),x = Symbol('x')
e = -3*x/2 + Rational(-1, 2)r)   )r   r   r   xy     \/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/printing/tests/test_python.pytest_python_basicr/      s   8A;;,q.!!%:::::8B<<-"##'>>>>>"::!!!! !Q$<<88888!A#;;44444!ArE'??LLLLL	8B?? HI I I I !Q$(Q, $/ / / / / !a%== ' ' ' ' ' !ac'?? ) ) ) ) ) !hq!nnQ&q(()) .? ? ? ? ? !A#;;EEEEE1"Q$<<GGGGG1q5!) !; ; ; ; ; 1q5!) != = = = =
 "Q$B-  $HHHHH!hq!nna!e,,-- 2      r-   c                  <   t          dt          d          z            dk    sJ t          dt          d          z  dt          d          z  z             dk    sJ t          dt          d          z   t          d          d	          z             d
k    sJ d S )N   lambdaz(lambda_ = Symbol('lambda')
e = 5*lambda_   lambda_zRlambda__ = Symbol('lambda')
lambda_ = Symbol('lambda_')
e = 7*lambda_ + 5*lambda__forfor_   zCfor__ = Symbol('for')
for_ = Function('for_')
e = 5*for__ + for_(8))r   r   r   r,   r-   r.   (test_python_keyword_symbol_name_escapingr8   I   s    	&

 JK K K K1VH%%%&*;*;(;;<<bc c c c1VE]]?%5Xf%5%5a%8%8899ST T T T T Tr-   c                  b    t          d t          d          d          z            dk    sJ d S )Nr1   r5   r7   z$for_ = Function('for')
e = 5*for_(8))r   r   r,   r-   r.   *test_python_keyword_function_name_escapingr:   S   sN    	/(5//!

 !HI I I I I Ir-   c                  :   t          t          t          t                              dk    sJ t          t	          t          t                              dk    sJ t          t          t          t                              dk    sJ t          t          t          t                              dk    sJ t          t          t          t                              dk    sJ t          t          t          t          dz   z  t          dz                      dv sJ d S )	Nz,x = Symbol('x')
y = Symbol('y')
e = Eq(x, y)z*x = Symbol('x')
y = Symbol('y')
e = x >= yz*x = Symbol('x')
y = Symbol('y')
e = x <= yz)x = Symbol('x')
y = Symbol('y')
e = x > yz)x = Symbol('x')
y = Symbol('y')
e = x < yr    r!   )z7x = Symbol('x')
y = Symbol('y')
e = Ne(x/(1 + y), y**2)z7x = Symbol('x')
y = Symbol('y')
e = Ne(x/(y + 1), y**2))	r   r	   r*   r+   r
   r   r   r   r   r,   r-   r.   test_python_relationalr<   X   s    "Q((OOOOO"Q((MMMMM"Q((MMMMM"Q((LLLLL"Q((LLLLL"QAY1%%&& +E E E E E E Er-   c                     t          dt          z  t          t                    z             dv sJ t          t          d                    dk    sJ t          dt	          dd          z            dk    sJ t          t          dt
          z                       dk    sJ t          dt
          z   t	          dd          z            dk    sJ t          dt	          dd	          z            d
k    sJ t          t          t                              dk    sJ t          t          t          t          dz  dz   z                      dv sJ t          d          } t           | t                              dk    sJ t           | t          t                              dk    sJ t           | t          t          dz   z  t                              dv sJ t          t          t          t          dz             dz                       dv sJ t          t          dz   t	          dd          z  dz   t	          dd          z            dv sJ t          t          t                    dz            dk    sJ d S )Nr!   z x = Symbol('x')
e = 2*x + exp(x)ze = sqrt(2)r    r'   ze = 2**Rational(1, 3)ze = sqrt(2 + pi)ze = (2 + pi)**Rational(1, 3)   ze = 2**Rational(1, 4)zx = Symbol('x')
e = Abs(x))z%x = Symbol('x')
e = Abs(x/(1 + x**2))z%x = Symbol('x')
e = Abs(x/(x**2 + 1))fz*x = Symbol('x')
f = Function('f')
e = f(x)z=x = Symbol('x')
y = Symbol('y')
f = Function('f')
e = f(x, y))zEx = Symbol('x')
y = Symbol('y')
f = Function('f')
e = f(x/(1 + y), y)zEx = Symbol('x')
y = Symbol('y')
f = Function('f')
e = f(x/(y + 1), y))z)x = Symbol('x')
e = sqrt(1 + sqrt(1 + x))z)x = Symbol('x')
e = sqrt(sqrt(x + 1) + 1))zAx = Symbol('x')
e = (1 + (1 + x)**Rational(1, 3))**Rational(1, 3)zAx = Symbol('x')
e = ((x + 1)**Rational(1, 3) + 1)**Rational(1, 3)zx = Symbol('x')
e = sin(x)**2)
r   r*   r   r   r   r   r   r   r+   r   )r?   s    r.   test_python_functionsr@   c   s   !A#A,#FFFFF$q''??m++++!Xa^^#$$(?????$q2v,,#555551r6HQNN*++/MMMMM!Xa^^#$$(?????#a&&>>:::::Aq!taxL 66 6 6 6
 	A!!A$$<<IIIII!!Aq''??`````!!Aq1uIq//"" 'T T T T T
 $QUq())** /6 6 6 6 6
 QUXa^^+q08Aq>>ABB GN N N N N
 #a&&!) @@@@@@@r-   c            	         t          t          d          \  } }t          t          | |t          z  z                       dk    sJ t          t          t          | |t          z  z                                 dk    sJ d S )Nabz_     _
a - I*bz _     _
 a - I*b
e       )mapr   r   r   r   r   )abs     r.    test_python_functions_conjugatesrF      su    vtDAq9Q1W%%''+=====9SQqS\\**,,0NNNNNNNr-   c                  B   t          t          t                    t          d          } t          |           dk    sJ t          t          t                    t          d          t          z   }t          |          dk    sJ t          t          t                    t          dz  z   t          t          d          }t          |          dk    sJ t          dt          z  t          z  t          t          d          t          dz  z   }t          |          dv sJ d S )NF)evaluatez)x = Symbol('x')
e = Derivative(log(x), x)z-x = Symbol('x')
e = x + Derivative(log(x), x)r!   zCx = Symbol('x')
y = Symbol('y')
e = Derivative(x**2 + log(x), x, y))zBx = Symbol('x')
y = Symbol('y')
e = x**2 + Derivative(2*x*y, y, x)zBx = Symbol('x')
y = Symbol('y')
e = Derivative(2*x*y, y, x) + x**2)r   r   r*   r   r+   )f_1f_2f_3f_4s       r.   test_python_derivativesrM      s   
SVVQ
/
/
/C#;;FFFFF
SVVQ
/
/
/!
3C#;;JJJJJ SVVad]Aq5
9
9
9C#;;OP P P P QqSUAq5
1
1
1AqD
8C#;; P P P P P P Pr-   c                     t          t          t                    t                    } t          |           dk    sJ t          t          dz  t                    }t          |          dk    sJ t          t          dt          z  z  t                    }t          |          dk    sJ t          t          dz  t          ddf          }t          |          dk    sJ t          t          dz  t          t	          dd          df          }t          |          dk    sJ t          t          dz  t
          dz  z  t          t
                    }t          |          d	k    sJ d S )
Nz'x = Symbol('x')
e = Integral(log(x), x)r!   z%x = Symbol('x')
e = Integral(x**2, x)z*x = Symbol('x')
e = Integral(x**(2**x), x)r    z-x = Symbol('x')
e = Integral(x**2, (x, 1, 2))r(   z;x = Symbol('x')
e = Integral(x**2, (x, Rational(1, 2), 10))z=x = Symbol('x')
y = Symbol('y')
e = Integral(x**2*y**2, x, y))r   r   r*   r   r   r+   )rI   rJ   rK   rL   f_5f_6s         r.   test_python_integralsrQ      sH   
3q661

C#;;DDDDD
1a4

C#;;BBBBB 1q!t9a
 
 C#;;GGGGG 1a4!Q
#
#C#;;JJJJJ
1a4!Xa^^R0
1
1C NO O O O 1a419a
#
#C#;;[[[[[[[r-   c                      t          t          t          dz  dz   dgt          t          t          z   gg                    } d}| |k    sJ d S )Nr!   r    zSx = Symbol('x')
y = Symbol('y')
e = MutableDenseMatrix([[x**2 + 1, 1], [y, x + y]]))r   r   r*   r+   )pss     r.   test_python_matrixrU      sF    v1Q{Q!H-..//A_A666666r-   c                      t          t          t          t          t                              dk    sJ t          t          t          dz  t          d                    dk    sJ d S )Nr$   r!   r   ze = 0)r   r   r*   r   r,   r-   r.   test_python_limitsrW      sT    %1b//""h....%1a##$$//////r-   c                  v    t          d          } t          d          }| |z  }t          |          dk    sJ d S )Nza_{b}rE   z/a_b = Symbol('a_{b}')
b = Symbol('b')
e = a_b*b)r   r   )a_brE   exprs      r.   test_issue_20762r[      s?    
//CsAq5D$<<NNNNNNNr-   c                  2    t          t          d            d S )Nc                  .    t          t          d          S )Ngarbage)method)r   r*   r,   r-   r.   <lambda>ztest_settings.<locals>.<lambda>   s    fQy999 r-   )r   	TypeErrorr,   r-   r.   test_settingsrb      s    
999:::::r-   N)7sympy.core.functionr   r   sympy.core.numbersr   r   r   r   sympy.core.relationalr	   r
   r   r   r   r   sympy.core.symbolr   r   $sympy.functions.elementary.complexesr   r   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   sympy.integrals.integralsr   sympy.matrices.denser   sympy.series.limitsr   sympy.printing.pythonr   sympy.testing.pytestr   r   r*   r+   thphr/   r8   r:   r<   r@   rF   rM   rQ   rU   rW   r[   rb   r,   r-   r.   <module>rr      sL   6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4 4 4 4 : : : : : : : : : : : : : : : : / / / / / / / / A A A A A A A A = = = = = = = = 9 9 9 9 9 9 8 8 8 8 8 8 . . . . . . ' ' ' ' ' ' % % % % % % ( ( ( ( ( ( . . . . . . . .wu~~1VG__VE]]0 0 0fU U UI I I
E E E A  A  AF O O OP P P&\ \ \2  
0 0 0O O O; ; ; ; ;r-   