
    g[                     D   d dl Z d dlZd dlZd dlmZ d dlmZmZ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 d dlmZmZmZmZmZmZmZmZmZmZ d dlmZm Z m!Z!m"Z"m#Z#m$Z$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/m0Z0m1Z1 d dl2m3Z3 d dl4m5Z5 d dl6m7Z8 d dl9m:Z: d dlm;Z; d dlm<Z< d dl=m>Z>  e>d          Z?ddhZ@ddhZAg ddfdZBd ZCd ZDd ZEd ZFd  ZGd! ZHd" ZId# ZJd$ ZKd% ZLd& ZMed'             ZNd( ZOd) ZPd* ZQd d+lRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ d, Zd d-lmZ d d.lmZ d d/lmZmZ d d0lmZmZmZmZ d d1lmZmZmZ d2 Zd d3lmZ d4 Zd d5lmZ d6 Zd d7lmZmZ d8 Zd d9lmZ d: Zd d;lmZ d d<lmZ d= Zed>             Zed?             Zd d@lmZ d dAlmZ d dBlmZ d dClmZ dD ZdE ZedF             ZdG ZdH ZdI ZdJ ZdK ZdL ZdM Zd dNlmZ d dOlmZmZ d dPlmZ d dQlmZmZ d dRlmZ d dSlmZ dT ZedU             ZedV             ZedW             Zd dXlmZ d dYlmZ dZ Zd d[lmZ d d\lmZ d] Zd^ Zd_ Zd` ZdS )a    N)meter)XFAILraisesignore_warnings)AtomBasic)SingletonRegistry)StrDummySymbolWild)
EIpioozoonanIntegerRationalFloatAlgebraicNumber)EqualityGreaterThanLessThan
RelationalStrictGreaterThanStrictLessThan
Unequality)Add)Mul)Pow)
DerivativeFunctionFunctionClassLambdaWildFunction)Interval)	vectorize)gmpy)SymPyDeprecationWarning)S)symbols)import_modulecloudpickle_assumptions_mhashis_EmptySetexpr_free_symbolsT c                    	 t           t                    rdD ]	t          t           	fd           dt          j        t          j        ddg}t          r|                    t          g           |D ] 		|v rt          	          r"t           t                    r- 	           }ndt          j        	          r)	                    	                                         }n't          j        t          j         	                    }t                     }t          |          }t!          |          t!          |          k    sJ |s	fd} | ||            || |           dS )z2 Check that pickling and copying round-trips.
    )r      c                  .    t          j                   S N)pickledumps)aprotocols   _/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/utilities/tests/test_pickling.py<lambda>zcheck.<locals>.<lambda>4   s    Q0I0I              c                 J   |D ]}|t           v r+t          | |          rt          ||          s
J |            7|t          v s|v rZt          t                    5  t          | |          t          ||          k    s
J |            	 d d d            n# 1 swxY w Y   t          | |          st          | |          }t          |d          sNt          ||          s
J |            t          ||          |k    s J t          ||          d|d            d S )N__call__z != z, protocol: )not_equal_attrshasattrdeprecated_attrsr   r*   getattr)r:   bdiattr
deprecatedr;   s        r<   czcheck.<locals>.cO   s    q q''q!}} 0&q!}}//a///***a:oo()@AA A A&q!}}1===q====A A A A A A A A A A A A A A A A q"1a==D"444 q&q!}}//a///&q!}}444RYZ[]^R_R_R_R_aeaeaegogo6p444q qs   -BB	B	N)
isinstancer   r   NotImplementedErrorcopydeepcopyr.   extendcallabletypeinspectismoduleloadsr9   r8   dirset)
r:   exclude
check_attrrL   	protocolsrH   d1d2rM   r;   s
   `  `     @r<   checkr_   .   s    !U K 	K 	KH&(I(I(I(I(IJJJJDIt}a3I (+''' & &wH 	8!T"" AAh'' 	8x~~a0011AAV\!X6677AVVVV2ww#b''!!!! 		q 	q 	q 	q 	q 	q  	
!Q	!QM& &r>   c                      t           t                      t          t                      t          t          fD ]} t	          |            d S r7   )r   r   r	   r+   r_   rM   s    r<   test_core_basicrb   g   s>    DFFE577,=qA  a r>   c                  >    t          t          d                     d S Nx)r_   r
   r3   r>   r<   test_core_Strrf   k   s    	#c((OOOOOr>   c                      t           t          dd          t          t          dd          t          t          d          fD ]} t          |            d S )Nre   F)commutative_issue_3130)r   r   r   r_   ra   s    r<   test_core_symbolrj   n   s[     U3E222F=e444dDIIG  a r>   c                      t          d          t          dd          t          d          fD ]} t          |            t          t	          t          d                    fD ]} t          | d           d S )Nr?   r@   z1.2Fr[   )r   r   r   r_   r   sqrtra   s    r<   test_core_numbersrn   w   s{    ajj(1a..%,,7  atAww778 # #aE"""""# #r>   c                  H    t          d          dz   } t          |            d S )Nre   g      ?)r   r_   )ys    r<   test_core_float_copyrq   ~   s!    scA	!HHHHHr>   c                     t          d          } t          d          }t          t          | |          t          t          | |          t          t          | |          t          t	          | |          t
          t          | |          t          t          | |          t          t          | |          fD ]}t          |           d S )Nre   rp   )	r   r   r   r   r   r   r   r   r_   )re   rp   rM   s      r<   test_core_relationalrs      s    sAsAA[A5F5FA
Jq!4D4D!21a!8!8.Q""J
1a0@0@B   	a	 r>   c                  v    t          d          } t          t          | d          fD ]}t          |           d S Nre   rA   )r   r   r_   re   rM   s     r<   test_core_addrw      @    sA3q!99  a r>   c                  v    t          d          } t          t          | d          fD ]}t          |           d S ru   )r   r    r_   rv   s     r<   test_core_mulrz      rx   r>   c                  v    t          d          } t          t          | d          fD ]}t          |           d S ru   )r   r!   r_   rv   s     r<   test_core_powerr|      rx   r>   c                      t          d          } t          t          |           t          t          t          t
          fD ]}t          |           d S rd   )r   r"   r#   r$   r%   r&   r_   )re   fs     r<   test_core_functionr      sI    sA*Q--=&  a r>   c                      t          d          } t          t          d                    }|                    t                     t          | |           d S )Nr~      rZ   )r#   listrangeappendr.   r_   )r~   rZ   s     r<   test_core_undefinedfunctionsr      sK    A588nnG NN;	!Wr>   c                  B    t          d          } t          |            d S )Nr~   )r#   r_   )r~   s    r<   !test_core_undefinedfunctions_failr      s     	A	!HHHHHr>   c                  X    t           t          dd          fD ]} t          |            d S )Nr   r?   )r'   r_   ra   s    r<   test_core_intervalr      s5    A'  a r>   c                  V    t           t          d          fD ]} t          |            d S )Nr   )r(   r_   ra   s    r<   test_core_multidimensionalr      s3    1&  a r>   c                     g d} t           j         t           j        g}|d | D             z  }t          r|d gz  }t          d          t          d          t          d          t	          dd          t
          t          t          t          t           t          t          t          j        t          j        t          j        t          j        t          j        t          j        fD ]}|D ]} ||          |u sJ d S )N)r   r5   r?   r@   rA   c                     g | ]fd S )c                 R    t          j        t          j        |                     S r7   )r8   rW   r9   )re   protos    r<   r=   z,test_Singletons.<locals>.<listcomp>.<lambda>   s    &,v|Au'='=>> r>   r3   ).0r   s    @r<   
<listcomp>z#test_Singletons.<locals>.<listcomp>   s2     $ $ $ ?>>> $ $ $r>   c                 f    t                               t                               |                     S r7   )r.   rW   r9   )re   s    r<   r=   z!test_Singletons.<locals>.<lambda>   s"    k//0A0A!0D0DEE r>   r   r5   r?   )rP   rQ   r.   r   r   r   r   r   r   r   r   r+   GoldenRatioTribonacciConstant
EulerGammaCatalanEmptySetIdentityFunction)r\   copiersobjfuncs       r<   test_Singletonsr      s    Iy$-(G $ $"$ $ $ $G GEEFFWQZZXa^^RAS#q}a.BL!)QZ1CE $ $  	$ 	$D499#####	$$ $r>   );	Piecewise
lowergammaacosh
chebyshevu
chebyshevtlnchebyshevt_rootlegendre	Heaviside	bernoullicothtanhassoc_legendresignargasin
DiracDeltarerfAbs
uppergammabinomialsinhcoscotacosacotgammabellhermiteharmonicLambertWzetalog	factorialasinhacothcoshdirichlet_etaEijkloggammaerfceilingim	fibonacci
tribonacci	conjugatetanchebyshevu_rootflooratanhrm   sinatanfflucasatan2	polygammaexpc                     g t           t          t          t          t          t
          t          t          t          t          t          t          t          t          t          t          t           t"          t$          t&          t(          t*          t,          t.          t          t0          t2          t4          t6          t8          t:          t<          t>          t@          tB          tD          tF          tH          tJ          tL          tN          tP          tR          R } tT          tV          tX          tZ          t\          t^          t`          tb          td          tf          th          f}tk          d          \  }}}tl          tn          tq          |||          ts          d|dk     f|dz  |dk    f|dz  df          tt          f}| D ]+}tw          |            ||          }tw          |           ,|D ],}tw          |            |||          }tw          |           -|D ]}tw          |           d S )Nx,y,zr   r   r?   r5   r@   T)<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   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_   )one_vartwo_varre   rp   zothersclsrM   s           r<   test_functionsr      s   Mu Mb M) MY M	 M4 M MMMM'M)+M-0M26M8;M=@MBFMHLMMM!M#+M-1M36M8AMCHM M M 'M )1M 36M 8?M ACM ENM 	M "	M $'	M ).	M 05	M 7:	M <@	M BG	M IL	M MG
 2z:z89gx=GgGAq!Q11r6{QT16NQT4LAAF   c


CFFa  c


C1IIa  c



 r>   )GeometryEntity)Point)CircleEllipse)LineLinearEntityRaySegment)PolygonRegularPolygonTrianglec                  j   t          dd          } t          dd          }t          dd          }t          dd          }t          t                      t           | t          t          | d          t          t          | dd          t          t	          | |          t
          t          | |          t          t          | |          t          t          | |          t          t          | |||          t          t          | dd          t          t          | ||          fD ]}t          |d           d S )	Nr5   r?   r@   r   rA   r   Frl   )r   r   r   r   r   r   r   r   r   r   r   r_   )p1p2p3p4rM   s        r<   test_geometryr      s    	q!B	q!B	q!B	q!B((%VVB]]Q""D$r2,,Rc3r2;;RRR((.2q!$$hR0D0DF # # 	aE"""""# #r>   )Integralc                  t    t          d          } t          t          |           fD ]}t          |           d S rd   )r   r   r_   rv   s     r<   test_integralsr     s>    sA$  a r>   )Logicc                  V    t           t          d          fD ]} t          |            d S Nr5   )r   r_   ra   s    r<   
test_logicr     s3    U1XX  a r>   )MatrixSparseMatrixc                      t           t          g d          t          t          ddgddgg          fD ]} t          | ddg           d S )	Nr5   r?   r@   r5   r?   r@   rA   _smat_matrL   )r   r   r_   ra   s    r<   test_matricesr     sa    fYYY''|aVaQRVDT7U7UV / /aWf-...../ /r>   )Sievec                  T    t           t                      fD ]} t          |            d S r7   )r  r_   ra   s    r<   test_ntheoryr  $  s1    UWW  a r>   )Pauli)Unitc                  n    t           t          t          t          d          fD ]} t          |            d S r   )r  r   r  r_   ra   s    r<   test_physicsr  -  s7    E5%((+  a r>   c                  D   ddl m} m} ddlm} ddlm}m} ddlm	}m
}m}m} ddlm}	 ddlm}
 ddlm} dd	lm} dd
lm} ddlm}m}m}m}m}m}m}m} ddl m!} ddl"m#} ddl$m%} |  | dd          ||||||||||	|
||||||||||||||fD ]}tM          |           d S )Nr   )ColorGradientColorScheme)ManagedWindow)Plot
ScreenShot)PlotAxesPlotAxesBasePlotAxesFramePlotAxesOrdinate)
PlotCamera)PlotController)	PlotCurve)PlotInterval)PlotMode)Cartesian2DCartesian3DCylindricalParametricCurve2DParametricCurve3DParametricSurfacePolar	Spherical)
PlotObject)PlotSurface)
PlotWindowg?g?)'&sympy.plotting.pygletplot.color_schemer	  r
  (sympy.plotting.pygletplot.managed_windowr  sympy.plotting.plotr  r  #sympy.plotting.pygletplot.plot_axesr  r  r  r  %sympy.plotting.pygletplot.plot_camerar  )sympy.plotting.pygletplot.plot_controllerr  $sympy.plotting.pygletplot.plot_curver  'sympy.plotting.pygletplot.plot_intervalr  #sympy.plotting.pygletplot.plot_moder  $sympy.plotting.pygletplot.plot_modesr  r  r  r  r  r  r  r  %sympy.plotting.pygletplot.plot_objectr  &sympy.plotting.pygletplot.plot_surfacer   %sympy.plotting.pygletplot.plot_windowr!  r_   )r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  rM   s                             r<   test_plottingr/  5  s   QQQQQQQQFFFFFF44444444kkkkkkkkkkkk@@@@@@HHHHHH>>>>>>DDDDDD<<<<<<R R R R R R R R R R R R R R R R R R R R@@@@@@BBBBBB@@@@@@}}S#..]tZ<'^<;&(95)Z   	a r>   c                      ddl m}  ddlm} ddlm} t           | d                     t           |dd                     t           |                       d S )	Nr   )r
  )r  )r  rainbowr5   F)visible)r"  r
  r$  r  r%  r  r_   )r
  r  r  s      r<   test_plotting2r3  P  s     CBBBBB((((((<<<<<< 
++i
 
 !!!	$$q%
 
 
 !!!	((**r>   )ZZ)QQ)lex)Polyc                      ddl m}  t          d          }t          t          ||          fD ]}t	          |           |  | |          fD ]}t	          |           d S )Nr   )PurePolyre   )sympy.polys.polytoolsr9  r   r7  r_   )r9  re   rM   s      r<   test_pickling_polys_polytoolsr;  m  s{    ......sADAJJ  a$  a r>   c            	      Z   ddl m} m}m} |  | t	          d          gt	          d          gt	          d          ggt                    fD ]}t          |dg           | |t	          d          t	          d          gt	          d          t	          d          gft                    fD ]}t          |           | |t          d          t          d          gt          d          t          d          t          d          gt                    fD ]}t          |           d S )Nr   )DMPDMFANPr5   r?   r@   repr   )sympy.polys.polyclassesr=  r>  r?  r4  r_   r5  )r=  r>  r?  rM   s       r<   test_pickling_polys_polyclassesrB  |  s+   555555555533A"Q%%2a55'2B778 % %aUG$$$$$33A1A17<<=  a331r!uu~1r!uubee'<bAAB  a r>   c                      ddl m}   | dt          t                    }| |fD ]}t	          |ddg           |j        |j        fD ]}t	          |ddgd           d S )Nr   )PolyRingr   r5   r   F)rZ   r[   )sympy.polys.ringsrD  r4  r6  r_   dtypeone)rD  ringrM   s      r<   test_pickling_polys_ringsrI    s    
 +*****8GR%%D ! !a!Q     j$(# 3 3a!QE222223 3r>   c                      d S r7   r3   r3   r>   r<   test_pickling_polys_fieldsrK    s    Dr>   c                  R    ddl m}  |  | dd          fD ]}t          |           d S )Nr   )PythonRationalr5      )"sympy.polys.domains.pythonrationalrM  r_   )rM  rM   s     r<   test_pickling_polys_elementsrP    sM    AAAAAA nnQ223  a r>   c                     ddl m}  ddlm} |  |             fD ]}t	          |d           | |            fD ]}t	          |d           t
          Lddlm} ddlm	} | |            fD ]}t	          |d           | |            fD ]}t	          |d           ddl
m} dd	lm} | |t          t          d
                    fD ]}t	          |d           | |            fD ]}t	          |d           d S )Nr   )PythonIntegerRing)PythonRationalFieldFrl   )GMPYIntegerRing)GMPYRationalField)AlgebraicField)ExpressionDomainr@   )%sympy.polys.domains.pythonintegerringrR  'sympy.polys.domains.pythonrationalfieldrS  r_   _gmpy#sympy.polys.domains.gmpyintegerringrT  %sympy.polys.domains.gmpyrationalfieldrU  "sympy.polys.domains.algebraicfieldrV  $sympy.polys.domains.expressiondomainrW  r5  rm   )rR  rS  rM   rT  rU  rV  rW  s          r<   test_pickling_polys_domainsr_    s   GGGGGGKKKKKK  !2!2!4!45 # #aE"""""!#6#6#8#89 # #aE"""""GGGGGGKKKKKK "??#4#45 	' 	'A!&&&&&#%6%6%8%89 	' 	'A!&&&&& BAAAAA FEEEEE nnRa99: # #aE"""""  0 0 2 23 # #aE"""""# #r>   c                      ddl m} m}m}m} |  |             fD ]}t          |           | |            fD ]}t          |           | |            fD ]}t          |           | | |                       fD ]}t          |           d S )Nr   )LexOrderGradedLexOrderReversedGradedLexOrderInverseOrder)sympy.polys.orderingsra  rb  rc  rd  r_   )ra  rb  rc  rd  rM   s        r<   test_pickling_polys_orderingsrf    s    . . . . . . . . . . . . 

#  ann../  a$&<&<&>&>?  a LL445  a r>   c                      ddl m} m} t          d          \  }}}|  | d          fD ]}t	          |           | |d|||f          fD ]}t	          |           d S )Nr   )MonomialOpsMonomialr   r@   r   )sympy.polys.monomialsrh  ri  r,   r_   )rh  ri  re   rp   r   rM   s         r<   test_pickling_polys_monomialsrk    s    ;;;;;;;;gGAq!;;q>>*  aQ1I667  a r>   c                     ddl m} m}m}m}m}m}m}m}m	}m
}	m}
m}m}m}m}m}m}m}m} |  |             fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           |	 |	            fD ]}t)          |           |
 |
            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           | |            fD ]}t)          |           d S )Nr   )HeuristicGCDFailedHomomorphismFailedIsomorphismFailedExtraneousFactorsEvaluationFailedRefinementFailedCoercionFailedNotInvertibleNotReversibleNotAlgebraicDomainErrorPolynomialErrorUnificationFailedGeneratorsErrorGeneratorsNeededUnivariatePolynomialErrorMultivariatePolynomialErrorOptionError	FlagError)sympy.polys.polyerrorsrm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r_   )rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  rM   s                       r<   test_pickling_polys_errorsr    s                                            ( !"4"4"6"67  a "4"4"6"67  a!2!2!4!45  a!2!2!4!45  a 0 0 2 23  a 0 0 2 23  ann../  a]]__-  a]]__-  aLLNN+  a;;==)  a001  a!2!2!4!45  a001  a 0 0 2 23  a ()B)B)D)DE  a)+F+F+H+HI  a ;;==)  a%  a r>   c                      ddl m} m} t          d          }|dz  |z   dz   }|  | |d          fD ]}t	          |           | ||t
                    fD ]}t	          |           d S )Nr   )CRootOfRootSumre   r@   )sympy.polys.rootoftoolsr  r  r   r_   r   )r  r  re   r~   rM   s        r<   test_pickling_polys_rootoftoolsr  }  s    88888888sA	1q1Awwq!}}%  awwq#'  a r>   )LatexPrinter)MathMLContentPrinterMathMLPresentationPrinter)PrettyPrinter)
prettyForm
stringPict)Printer)PythonPrinterc                      t           t                      t          t          t          t          t
          t          d          t          t                      t          t                      fD ]} t          |            d S )Nr:   )	r  r  r  r  r  r  r  r  r_   ra   s    r<   test_printingr    s[    LNN,@'
Joow		=oo   	a	 r>   c                  <    t          t                                 d S r7   )r_   r  r3   r>   r<   test_printing1r    s    	

 
 !!!!!r>   c                  <    t          t                                 d S r7   )r_   r  r3   r>   r<   test_printing2r    s    	
#
%
%&&&&&r>   c                  <    t          t                                 d S r7   )r_   r  r3   r>   r<   test_printing3r    s    	-//r>   )Limit)Orderc                      t          d          } t          d          }t          t          | |d          t          t          |           fD ]}t          |           d S )Nere   r5   )r   r  r  r_   )r  re   rM   s      r<   test_seriesr    sW    sAsAU1a^^UE!HH5  a r>   )Product)Sumc            	          t          d          } t          t          | | ddf          t          t          | | ddf          fD ]}t          |           d S )Nre   r?   rA   )r   r  r  r_   rv   s     r<   test_concreter    s\    sAwq1a),,c3q1a)3D3DE  a r>   c                  H    t          ddd          } t          |            d S )Nmessagez1.0zactive-deprecations)deprecated_since_versionactive_deprecations_target)r*   r_   )ws    r<   test_deprecation_warningr    s&    	Ef{|||A	!HHHHHr>   c                      t          j        t          j        t          j                            t          j        k    sJ d S r7   )r8   rW   r9   r+   Halfr3   r>   r<   test_issue_18438r    s1    <QV,,--777777r>   c                  X    d} t          j        |           t          d          k    sJ d S )Nsi   ^       sympy.core.powerPowsympy.core.numbersIntegerKR}bhHalf)R}bR}b.r?   )r8   rW   rm   )datas    r<   !test_unpickle_from_older_versionsr    s5    	8 	 <a((((((r>   )rU   rP   r8   sympy.physics.unitsr   sympy.testing.pytestr   r   r   sympy.core.basicr   r   sympy.core.singletonr	   sympy.core.symbolr
   r   r   r   sympy.core.numbersr   r   r   r   r   r   r   r   r   r   sympy.core.relationalr   r   r   r   r   r   r   sympy.core.addr   sympy.core.mulr    sympy.core.powerr!   sympy.core.functionr"   r#   r$   r%   r&   sympy.sets.setsr'   sympy.core.multidimensionalr(   sympy.external.gmpyr)   rZ  sympy.utilities.exceptionsr*   r+   r,   sympy.externalr-   r.   rD   rF   r_   rb   rf   rj   rn   rq   rs   rw   rz   r|   r   r   r   r   r   r   sympy.functionsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rm   r   r   r   r   r   r   r   r   sympy.geometry.entityr   sympy.geometry.pointr   sympy.geometry.ellipser   r   sympy.geometry.liner   r   r   r   sympy.geometry.polygonr   r   r   r   sympy.integrals.integralsr   r   sympy.core.logicr   r   sympy.matricesr   r   r   sympy.ntheory.generater  r  sympy.physics.paulialgebrar  r  r  r/  r3  sympy.polys.domains.integerringr4  !sympy.polys.domains.rationalfieldr5  re  r6  r:  r7  r;  rB  rI  rK  rP  r_  rf  rk  r  r  sympy.printing.latexr  sympy.printing.mathmlr  r  sympy.printing.pretty.prettyr   sympy.printing.pretty.stringpictr  r  sympy.printing.printerr  sympy.printing.pythonr  r  r  r  r  sympy.series.limitsr  sympy.series.orderr  r  sympy.concrete.productsr  sympy.concrete.summationsr  r  r  r  r  r3   r>   r<   <module>r     s
      % % % % % % ? ? ? ? ? ? ? ? ? ? ( ( ( ( ( ( ( ( 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 6 6 6* * * * * * * * * * * * * * * * * * * * * * * *7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7                                      $ $ $ $ $ $ 1 1 1 1 1 1 - - - - - - > > > > > > " " " " " " % % % % % % ( ( ( ( ( (mM**    DR 2 2 2 2r      # # #                   
  
$ $ $ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 1 0 0 0 0 0 & & & & & & 2 2 2 2 2 2 2 2 @ @ @ @ @ @ @ @ @ @ @ @ D D D D D D D D D D# # # / . . . . .   # " " " " "  
 0 / / / / / / // / /
 ) ( ( ( ( (  
 - , , , , , $ $ $ $ $ $     4   . / . . . . . 0 0 0 0 0 0 % % % % % % & & & & & &	 	 	   3 3 3	 	 	"  09# 9# 9#x  0  T T TB
 
 
 . - - - - - Q Q Q Q Q Q Q Q 6 6 6 6 6 6 C C C C C C C C * * * * * * / / / / / /   " " " ' ' '    & % % % % % $ $ $ $ $ $   , + + + + + ) ) ) ) ) )  
  8 8 8
) ) ) ) )r>   