
    Xh0\                     L   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ZAdhZBg ddfdZCd ZDd ZEd ZFd  ZGd! ZHd" ZId# ZJd$ ZKd% ZLd& ZMd' ZNd( ZOd) ZPd* ZQd+ ZRd d,lSmTZT d- ZUd d.lVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ d/ Zd d0lmZ d d1lmZ d d2lmZmZ d d3lmZmZmZmZ d d4lmZmZmZ d5 Zd d6lmZ d7 Zd d8lmZ d9 Zd d:lmZmZ d; Zd d<lmZ d= Zd d>lmZ d d?lmZ d@ ZedA             ZedB             Zd dClmZ d dDlmZ d dElmZ d dFlmZ dG ZdH ZedI             ZdJ ZdK ZdL ZdM ZdN ZdO ZdP Zd dQlmZ d dRlmZmZ d dSlmZ d dTlmZmZ d dUlmZ d dVlmZ dW ZedX             ZedY             ZedZ             Zd d[lmZ d d\lmZ d] Zd d^lmZ d d_lmZ d` Zda Zdb Zdc ZdS )d    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_symbols_sage_T 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   u/var/www/tools.fuzzalab.pt/emblema-extractor/venv/lib/python3.11/site-packages/sympy/utilities/tests/test_pickling.py<lambda>zcheck.<locals>.<lambda>8   s    Q0I0I              c                 ^   |D ]'}|t           v r|t          v r+t          | |          rt          ||          s
J |            A|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: )dont_check_attrsnot_equal_attrshasattrdeprecated_attrsr   r*   getattr)r;   bdiattr
deprecatedr<   s        r=   czcheck.<locals>.cS   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loadsr:   r9   dirset)
r;   exclude
check_attrrN   	protocolsrJ   d1d2rO   r<   s
   `  `     @r=   checkra   2   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Q( (r?   c                      t           t                      t          t                      t          t          fD ]} t	          |            d S r8   )r   r   r	   r+   ra   rO   s    r=   test_core_basicrd   m   s>    DFFE577,=qA  a r?   c                  >    t          t          d                     d S Nx)ra   r
   r4   r?   r=   test_core_Strrh   q   s    	#c((OOOOOr?   c                      t           t          dd          t          t          dd          t          t          d          fD ]} t          |            d S )Nrg   F)commutative_issue_3130)r   r   r   ra   rc   s    r=   test_core_symbolrl   t   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@   rA   z1.2Fr]   )r   r   r   ra   r   sqrtrc   s    r=   test_core_numbersrp   }   s{    ajj(1a..%,,7  atAww778 # #aE"""""# #r?   c                  H    t          d          dz   } t          |            d S )Nrg   g      ?)r   ra   )ys    r=   test_core_float_copyrs      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 )Nrg   rr   )	r   r   r   r   r   r   r   r   ra   )rg   rr   rO   s      r=   test_core_relationalru      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 Nrg   rB   )r   r   ra   rg   rO   s     r=   test_core_addry      @    sA3q!99  a r?   c                  v    t          d          } t          t          | d          fD ]}t          |           d S rw   )r   r    ra   rx   s     r=   test_core_mulr|      rz   r?   c                  v    t          d          } t          t          | d          fD ]}t          |           d S rw   )r   r!   ra   rx   s     r=   test_core_powerr~      rz   r?   c                      t          d          } t          t          |           t          t          t          t
          fD ]}t          |           d S rf   )r   r"   r#   r$   r%   r&   ra   rg   fs     r=   test_core_functionr      sI    sA*Q--=&  a r?   c                  B    t          d          } t          |            d S )Nr   )r#   ra   )r   s    r=   test_core_undefinedfunctionsr      s    A	!HHHHHr?   c                  r    t          d          } t          d          }t           ||                      d S )N_long_unique_name_1_long_unique_name_2)r   r#   ra   r   s     r=   test_core_appliedundefr      s5    $%%A&''A	!!A$$KKKKKr?   c                  X    t           t          dd          fD ]} t          |            d S )Nr   r@   )r'   ra   rc   s    r=   test_core_intervalr      s5    A'  a r?   c                  V    t           t          d          fD ]} t          |            d S )Nr   )r(   ra   rc   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   r6   r@   rA   rB   c                     g | ]fd S )c                 R    t          j        t          j        |                     S r8   )r9   rY   r:   )rg   protos    r=   r>   z,test_Singletons.<locals>.<listcomp>.<lambda>   s    &,v|Au'='=>> r?   r4   ).0r   s    @r=   
<listcomp>z#test_Singletons.<locals>.<listcomp>   s2     $ $ $ ?>>> $ $ $r?   c                 f    t                               t                               |                     S r8   )r.   rY   r:   )rg   s    r=   r>   z!test_Singletons.<locals>.<lambda>   s"    k//0A0A!0D0DEE r?   r   r6   r@   )rR   rS   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?   )	FreeGroupc                  B    t          t          d          d           d S )Nzx, y, zFrn   )ra   r   r4   r?   r=   test_free_groupr      s#    	)I

5111111r?   );	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atanhro   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$          t&          t(          t*          t,          t.          t          t0          t2          t4          t6          t8          t:          t<          t>          t@          tB          tD          tF          tH          tJ          tL          tN          tP          tR          R } tT          tV          tX          tZ          t\          t^          t`          tb          td          tf          th          f}tk          d          \  }}}tl          tn          tq          |||          ts          d|dk     f|dz  |dk    f|dz  df          tt          f}| D ]+}tw          |            ||          }tw          |           ,|D ],}tw          |            |||          }tw          |           -|D ]}tw          |           d S )Nx,y,zr   r   r@   r6   rA   T)<r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r,   r   r   r   r   r   ra   )one_vartwo_varrg   rr   zothersclsrO   s           r=   test_functionsr      s   Mu Mb M) MY M	 M4 M MMMM'M)+M-0M26M8;M=@MBFMHLMMM!M#+M-1M36M8AMCHM M M 'M )1M 36M 8?M ACM ENM 	M "	M $'	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 )	Nr6   r@   rA   r   rB      Frn   )r   r   r   r   r   r   r   r   r   r   r   ra   )p1p2p3p4rO   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 rf   )r   r   ra   rx   s     r=   test_integralsr     s>    sA$  a r?   )Logicc                  V    t           t          d          fD ]} t          |            d S Nr6   )r   ra   rc   s    r=   
test_logicr     s3    U1XX  a r?   )MatrixSparseMatrixc                      t           t          g d          t          t          ddgddgg          fD ]} t          | ddg           d S )	Nr6   r@   rA   r6   r@   rA   rB   _smat_matrN   )r   r   ra   rc   s    r=   test_matricesr  "  sa    fYYY''|aVaQRVDT7U7UV / /aWf-...../ /r?   )Sievec                  T    t           t                      fD ]} t          |            d S r8   )r  ra   rc   s    r=   test_ntheoryr  *  s1    UWW  a r?   )Pauli)Unitc                  n    t           t          t          t          d          fD ]} t          |            d S r   )r	  r   r  ra   rc   s    r=   test_physicsr  3  s7    E5%((+  a r?   c                  D   ddl m} m} ddlm} ddlm}m} ddlm	}m
}m}m} ddlm}	 ddlm}
 ddlm} dd	lm} dd
lm} ddlm}m}m}m}m}m}m}m} ddl m!} ddl"m#} ddl$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$  %sympy.plotting.pygletplot.plot_windowr%  ra   )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  rO   s                             r=   test_plottingr3  ;  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  rainbowr6   F)visible)r&  r  r(  r  r)  r  ra   )r  r  r  s      r=   test_plotting2r7  V  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   )PurePolyrg   )sympy.polys.polytoolsr=  r   r;  ra   )r=  rg   rO   s      r=   test_pickling_polys_polytoolsr?  s  s{    ......sADAJJ  a$  a r?   c            	      Z   ddl m} m}m} |  | t	          d          gt	          d          gt	          d          ggt                    fD ]}t          |dg           | |t	          d          t	          d          gt	          d          t	          d          gft                    fD ]}t          |           | |t          d          t          d          gt          d          t          d          t          d          gt                    fD ]}t          |           d S )Nr   )DMPDMFANPr6   r@   rA   repr  )sympy.polys.polyclassesrA  rB  rC  r8  ra   r9  )rA  rB  rC  rO   s       r=   test_pickling_polys_polyclassesrF    s+   555555555533A"Q%%2a55'2B778 % %aUG$$$$$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   r6   )r\   F)r\   r]   )sympy.polys.ringsrH  r8  r:  ra   dtypeone)rH  ringrO   s      r=   test_pickling_polys_ringsrM    s    
 +*****8GR%%D ! !a!Q     j$(# 3 3a!QE222223 3r?   c                      d S r8   r4   r4   r?   r=   test_pickling_polys_fieldsrO    s    Dr?   c                  R    ddl m}  |  | dd          fD ]}t          |           d S )Nr   )PythonRationalr6      )"sympy.polys.domains.pythonrationalrQ  ra   )rQ  rO   s     r=   test_pickling_polys_elementsrT    sM    AAAAAA nnQ223  a r?   c                     ddl m}  ddlm} |  |             fD ]}t	          |d           | |            fD ]}t	          |d           t
          Lddlm} ddlm	} | |            fD ]}t	          |d           | |            fD ]}t	          |d           ddl
m} dd	lm} | |t          t          d
                    fD ]}t	          |d           | |            fD ]}t	          |d           d S )Nr   )PythonIntegerRing)PythonRationalFieldFrn   )GMPYIntegerRing)GMPYRationalField)AlgebraicField)ExpressionDomainrA   )%sympy.polys.domains.pythonintegerringrV  'sympy.polys.domains.pythonrationalfieldrW  ra   _gmpy#sympy.polys.domains.gmpyintegerringrX  %sympy.polys.domains.gmpyrationalfieldrY  "sympy.polys.domains.algebraicfieldrZ  $sympy.polys.domains.expressiondomainr[  r9  ro   )rV  rW  rO   rX  rY  rZ  r[  s          r=   test_pickling_polys_domainsrc    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.orderingsre  rf  rg  rh  ra   )re  rf  rg  rh  rO   s        r=   test_pickling_polys_orderingsrj     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   rA   r   )sympy.polys.monomialsrl  rm  r,   ra   )rl  rm  rg   rr   r   rO   s         r=   test_pickling_polys_monomialsro    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.polyerrorsrq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  ra   )rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  rO   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RootSumrg   rA   )sympy.polys.rootoftoolsr  r  r   ra   r   )r  r  rg   r   rO   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  ra   rc   s    r=   test_printingr    s[    LNN,@'
Joow		=oo   	a	 r?   c                  <    t          t                                 d S r8   )ra   r  r4   r?   r=   test_printing1r    s    	

 
 !!!!!r?   c                  <    t          t                                 d S r8   )ra   r  r4   r?   r=   test_printing2r    s    	
#
%
%&&&&&r?   c                  <    t          t                                 d S r8   )ra   r  r4   r?   r=   test_printing3r    s    	-//r?   )Limit)Orderc                      t          d          } t          d          }t          t          | |d          t          t          |           fD ]}t          |           d S )Nerg   r6   )r   r  r  ra   )r  rg   rO   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 )Nrg   r@   rB   )r   r  r  ra   rx   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*   ra   )ws    r=   test_deprecation_warningr    s&    	Ef{|||A	!HHHHHr?   c                      t          j        t          j        t          j                            t          j        k    sJ d S r8   )r9   rY   r:   r+   Halfr4   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@   )r9   rY   ro   )datas    r=   !test_unpickle_from_older_versionsr    s5    	8 	 <a((((((r?   )rW   rR   r9   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$   r%   r&   sympy.sets.setsr'   sympy.core.multidimensionalr(   sympy.external.gmpyr)   r^  sympy.utilities.exceptionsr*   r+   r,   sympy.externalr-   r.   rF   rH   rE   ra   rd   rh   rl   rp   rs   ru   ry   r|   r~   r   r   r   r   r   r   sympy.combinatorics.free_groupsr   r   sympy.functionsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   ro   r   r   r   r   r   r   r   r   sympy.geometry.entityr   sympy.geometry.pointr   sympy.geometry.ellipser   r   sympy.geometry.liner   r   r   r   sympy.geometry.polygonr   r   r   r   sympy.integrals.integralsr   r   sympy.core.logicr   r   sympy.matricesr   r   r  sympy.ntheory.generater  r  sympy.physics.paulialgebrar  r	  r  r3  r7  sympy.polys.domains.integerringr8  !sympy.polys.domains.rationalfieldr9  ri  r:  r>  r;  r?  rF  rM  rO  rT  rc  rj  ro  r  r  sympy.printing.latexr  sympy.printing.mathmlr  r  sympy.printing.pretty.prettyr   sympy.printing.pretty.stringpictr  r  sympy.printing.printerr  sympy.printing.pythonr  r  r  r  r  sympy.series.limitsr  sympy.series.orderr  r  sympy.concrete.productsr  sympy.concrete.summationsr  r  r  r  r  r4   r?   r=   <module>r     s0
      % % % % % % ? ? ? ? ? ? ? ? ? ? ( ( ( ( ( ( ( ( 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 6 6 6* * * * * * * * * * * * * * * * * * * * * * * *7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7                                      $ $ $ $ $ $ 1 1 1 1 1 1 - - - - - - > > > > > > " " " " " " % % % % % % ( ( ( ( ( (mM**     
 DR 4 4 4 4v      # # #              
    
  
$ $ $ 6 5 5 5 5 52 2 2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?   