
    g]	                         d 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 dd	lmZ dd
lmZ ddlmZmZmZ  edd          \  ZZd ZdS )z:Tests for tools for manipulation of rational expressions.     )together)Mul)Rational)Eq)S)symbols)exp)sin)Integral)xyzzA,BF)commutativec                     t          d          dk    sJ t          d          dk    sJ t          t          t          z  t          z            t          t          z  t          z  k    sJ t          t          t          z             t          t          z   k    sJ t          dt          z            dt          z  k    sJ t          dt          z  dz             t          dz   t          z  k    sJ t          dt          z  dz             dt          z  dz   t          z  k    sJ t          dt          z  t          z             t          dz  dz   t          z  k    sJ t          dt          z  t          j        z             t          dz   dt          z  z  k    sJ t          t          j        t          dz  z             t          t          j        t          dz   d          k    sJ t          dt          z  dt          z  z             dt          z  t          z   t          t          z  z  k    sJ t          dddt          z  z   z            t          dt          z   z  k    sJ t          t          ddt          z  z   z            t          dz  dt          z   z  k    sJ t          dt          z  dt          z  z   dt          z  z             t          t          z  t          t          z  z   t          t          z  z   t          t          z  t          z  z  k    sJ t          ddt          z   dt          z  z   dt          z  z   z            t          t          z  t          t          z   t          t          z  z   t          t          z  t          z  z   z  k    sJ t          dt          t          z  z  dt          t          z  dz  z  z             t          dz  t          dz  z  dt          t          z  z   z  k    sJ t          dt          t          z  z  dt          t          z  dz  z  z             t          d	z  t          d	z  z  dt          dz  t          dz  z  z   z  k    sJ t          dt          d
z  t          z  z  dt          t          z  dz  z  z             t          d	z  t          dz  z  t          dz  t          dz  z   z  k    sJ t          ddddd
ddddt          z  z   z  z   z  z   z  z   z            t          dd          ddt          z  z   ddt          z  z   z  z  k    sJ t          ddt          dz   dz  z  z             dt          dz   dz  z   t          dz   dz  z  k    sJ t          ddt          dt          z   z  z  z             dt          dt          z   z  z   t          dt          z   z  z  k    sJ t          dt          t          dz   z  z  dt          t          dz   z  z  z             ddt          z  z   t          dt          z   z  dt          z   z  z  k    sJ t          dddt          z  dz   dz  z  z             dt          dz   dz  z  dz   dt          dz   dz  z  z  k    sJ t          t          dt          z  dt          z  z                       t          dt          z  dt          z  z             k    sJ t          t          dt          z  dt          z  z             d          t          t          t          z   t          t          z  z            k    sJ t          dt          t                    z  dt          t          t                    z  z  z             dt          z   t          t          t                    z  z  k    sJ t          dt          dt          z            z  dt          t          dt          z            z  z  z             dt          t                    t          z  z   t          t          dt          z            z  z  k    sJ t          t          dt          z  dt          z  z   t                              t          t          t          z   t          t          z  z  t                    k    sJ t          t          dt          z  dt          z  z   ddt          z  z                       t          t          t          z   t          t          z  z  t          dz   t          z            k    sJ t          t          t          z  dz  t          t          z  dz  z             t          t          z  dz  t          t          z  dz  z   k    sJ d S )Nr            F)evaluate      i         	      w   i     T)deep)r   r   r   r   r   Halfr   r   r
   r	   r   r   AB     `/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/polys/tests/test_rationaltools.pytest_togetherr(      s]   A;;!A;;!AaCE??ac!e####AE??a!e####AaC==AaCAaC!GQ	))))AaC!G1q!++++AaC!GA1,,,,AaC!&L!!a!eac]2222AFQqSL!!SQ%G%G%GGGGGAaC!A#I1Q37QqS/1111Aq1Q3wK  Aq1uI----Aq1Q3wK  AqD!a%L0000AaC!A#I!O$$1qsQqS1Q3q5(AAAAAAq1uqs{QqS()**ac1q51Q3;1Q3F.GGGGGAqsGa1qj())QWQW_a!A#g-FFFFFAqsGa1qj())QWQW_a!Q$q!t)m-LLLLLAq!tAvJAaC!8+,,BBA10MMMMMAq1a!QA!G_"5566788As1usSU{345 5 5 5 A1q51*$%%!q1uqj.1q51*)DDDDDA1a!e9%&&1q!a%y=1a!e9*EEEEE	1a!e91a!e9%' '+,qs7QAYA5F*GH H H HA1Q37Q,&''Aq1uqjL1,<q!a%!|+LLLLLC!ac	NN##s1Q319~~5555C!ac	NN...#q1uqsm2D2DDDDDAc!ffHq!CFF(|+,,Q3q660BBBBBAc!A#hhJAc!A#hhJ/00QQ\Ac!A#hhJ4OOOOOHQqS1Q3Y**++xQ1q/I/IIIIIBqsQqSy!ac'**++r1q51Q3-!a%/K/KKKKKQqS2I1r	)**qsRi1Q3).CCCCCCCr&   N)__doc__sympy.polys.rationaltoolsr   sympy.core.mulr   sympy.core.numbersr   sympy.core.relationalr   sympy.core.singletonr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr	   (sympy.functions.elementary.trigonometricr
   sympy.integrals.integralsr   	sympy.abcr   r   r   r#   r$   r(   r%   r&   r'   <module>r4      s   @ @ . . . . . .       ' ' ' ' ' ' $ $ $ $ $ $ " " " " " " % % % % % % 6 6 6 6 6 6 8 8 8 8 8 8 . . . . . .          wu%(((1-D -D -D -D -Dr&   