
    \h                     p   S SK Jr  S SKJr  S SKJr  S SKJrJrJ	r	  S SK
Jr  S SKJrJr  S SKJrJrJr  S SKJr  S S	KJr  S S
KJr  S SKJr  S SKJr  S SKJr  S SKJ r   S SK!J"r"  S SK#J$r$J%r%  S SKJ&r&  S SK'J(r(J)r)J*r*J+r+J,r,J-r-  S SK.J/r/  S SK0J1r1  S SK2J3r3J4r4  S SK5J6r6  S SK7J8r8J9r9  S SK:J;r;  S r<S r=S r>S r?g)    )Sum)Add)Mul)Integeroopi)Pow)EqNe)DummySymbolsymbols)	factorial)exp)sqrt)	Piecewise)
DiracDelta)gamma)Integral)simplify)IndexedIndexedBase)ExprCondPair)PoissonBetaExponentialPMultinomialMultivariateBeta)Normal)PoissonDistribution)CompoundPSpaceCompoundDistribution)MarginalDistribution)pspacedensity)ignore_warningsc            	         [        S5      n [        SSS9n[        USS5      n[        X5      n[        [	        U5      [
        5      (       d   e[        U[        X"R                  5      5      [        U5      :X  d   e[        SSS	5      n[        S
US5      n[        U5      " S5      R                  5       [        S5      S[        [        5      -  -  :X  d   e[        [        U[        US	5      5      " U 5      5      [        S5      [        U S	-
  S-  * S-  5      -  S[        [        5      -  -  :X  d   e[        [        U5      " U 5      5      [        S5      [        U S-  * S-  5      -  S[        [        5      -  -  :X  d   eg )NxlTpositive      N1r      N2
         )r   r   r   
isinstancer%   r"   r&   r
   symbolr!   r    doitr   r   r   r   )r)   r*   rateXr/   r1   s         R/var/www/auris/envauris/lib/python3.13/site-packages/sympy/stats/tests/test_mix.pytest_densityr;      sI   sAsT"A1a=DAfQi00001b{{+,0CA0FFFF	a	B	b!	B2;q> DHbbk$::::GB2q	*1-.Qa!eaZKM""Ad2hJ/0 0 0GBKN#tBxQTE"H'=r$r({'KKKK    c                     [        SSS9u  pn[        SSX5      n[        SXS   5      n[        XCS   45      n[	        [        S5      [        [        [	        [        S5      [        [        SSS9[        [        [        S5      5      [        S5      5      5      [        [        S	SS9[        [        [        S5      5      [        S
5      5      5      [        [        [        [        [        S5      5      [        S5      5      5      [        S5      5      [        [        [        [        [        S5      5      [        S
5      5      5      [        S5      5      5      [        [        [        [        [        S5      5      [        S5      5      [        [        [        S5      5      [        S
5      5      5      [        S5      5      5      [        [        S5      S5      5      [        [        [        SSS95      [        S5      5      [        [        [        SSS9[        [        [        S5      5      [        S5      5      5      5      [        [        [        [        [        S5      5      [        S5      5      5      [        S5      5      [        [        [        [        S5      5      [        S5      5      [        [        SSS9[        S5      5      5      [        [        [        [        S5      5      [        S
5      5      [        [        [        [        S5      5      [        S5      5      [        S5      5      5      5      nU" U5      U:X  d   eg )Nza1 p1 p2Tr+   Cr-   Br   p1p2r0   a1)r   r   r   r$   r   r   r   r   r   r	   r   r   r   r
   r   r   )rC   r@   rA   r>   r?   MGRmgrcs          r:   test_MarginalDistributionrF   )   s_   d3JBBCB#AbA$'A
qQ4'
*Cvc{Il3wqztd#W[-EAJ& fTD1Ks$gaj13	'+fSk2GAJ?@'"+N	'+fSk2GAJ?@'"+N4P s7;vc{+WQZ8Ks$gaj134;AJ@'A T"$ &)vdT/J)KBK&F4$7Ks$gaj13 4gk&+.
;<gbkJF3K('!*5td#WR[13F3K('!*5F3K('!*5wr{CEFD  q6T>>r<   c                  v   [        SS5      n [        SU 5      n[        [        U5      [        5      (       d   e[        [        U5      R                  [
        5      (       d   eUR                  R                  R                  S5      R                  5       [        S5      [        [        S5      5      -  :X  d   eg )NYr0   ZrB   )	r   r5   r%   r"   distributionr#   pdfr7   r   )rH   rI   s     r:   test_compound_distributionrM   @   s    QAQAfQi0000fQi,,.BCCCC88  $$Q',,.#b'#c"g,2FFFFr<   c                     [        SS5      [        SS5      p[        S5      n[        [	        [        S5      [        [        U* 5      [        US-
  5      -  US[        45      -  [        U5      -  US[        45      U[        * S45      n[        [	        [        S5      [        [        U* 5      [        US-
  5      -  US[        45      -  [        U5      -  US[        45      US[        45      n[        [        X-   S5      5      S:X  d   e[        [        X-   S5      5      S:X  d   e[        [        5         [        X-   S:  SS	9R                  [        5      R                  U5      (       d   e[        X-   S:  SS	9R                  [        5      R                  U5      (       d   e S S S 5        g ! , (       d  f       g = f)
NrH   r0   EkrB   r-   r   F)evaluate)r   r   r   r   r   r   r   r   r   r   r
   r   r'   UserWarningrewritedummy_eq)rH   rO   rP   expr1expr2s        r:   test_mix_expressionrW   G   s   3?KQ/qc
ASR#qb'*QU2C*CaBZ " l2J "#bS!.ESR#qb'*QU2C*CaBZ " l2J "#Q-ERq\?aRq\?a		%U+33H=FFuMMMMU+33H=FFuMMMM 
&	%	%s   9A1F44
GN)@sympy.concrete.summationsr   sympy.core.addr   sympy.core.mulr   sympy.core.numbersr   r   r   sympy.core.powerr	   sympy.core.relationalr
   r   sympy.core.symbolr   r   r   (sympy.functions.combinatorial.factorialsr   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   'sympy.functions.special.delta_functionsr   'sympy.functions.special.gamma_functionsr   sympy.integrals.integralsr   sympy.simplify.simplifyr   sympy.tensor.indexedr   r   r   sympy.statsr   r   r   r   r   r   sympy.stats.crv_typesr    sympy.stats.drv_typesr!   sympy.stats.compound_rvr"   r#   sympy.stats.joint_rvr$   sympy.stats.rvr%   r&   sympy.testing.pytestr'   r;   rF   rM   rW    r<   r:   <module>rp      sq    )   0 0   * 6 6 > 6 9 : > 9 . , 7 =7 7 ( 5 H 5 * 0L.GNr<   