
    h                     T    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
Jr  S rS rg)	    )Function)symbols)exp)variance_prop)RandomSymbolVariance
Covariancec                     [        S5      u  pn[        S5      =u  p4n[        U 5      n[        U5      n[        [        U5      5      n[        [        U5      5      n	[        S5      " U 5      n
X-   Xx-   Xa-   Xx-   X-   U-   Xx-   U	-   SU -  SU-  X-  XqS-  -  XS-  -  -   SU -  XpS-  -  X-  XqS-  -  XS-  -  -   US-  -  [	        U 5      U[	        SU -  5      -  [	        SU -  5      SU-  [	        SU -  5      -  [	        U * U-  5      US-  U-  [	        SU-  U -  5      -  U
[        U
5      0nUR                  5        H  u  p[        XS9nX:X  a  M   e   g )	Nx y zphi tf         )consts)r   r   r   r   r   itemsr   )xyzphitr   avar_xvar_yvar_zr   casesinpoutobss                  [/var/www/fran/franai/venv/lib/python3.13/site-packages/sympy/stats/tests/test_error_prop.pytest_variance_propr"   	   si   gGA!g&&FCVQAQKE\!_%E\!_%EaA	u}	u}		5=5(	!QuW	Ua4Z%1*$	!Ua4Z	eqDj5A:%q!t+Ac!A#hAaC!E'#ac("QBqD	1a4:c"Q$q&k)	8A;
E KKMC/zz "    c                     [        S5      u  pn[        S5      =u  p4n[        U 5      n[        U5      n[        U5      n[        U5      n	[        U5      n
[        U
5      n[        Xh5      n[        Xj5      n[        X5      nX-   Xy-   SU-  -   Xa-   Xy-   SU-  -   X-   U-   Xy-   U-   SU-  -   SU-  -   SU-  -   SU -  SU-  X-  XqS-  -  XS-  -  -   SU-  X-  -  -   SU -  XpS-  -  [	        U 5      U[	        SU -  5      -  [	        SU -  5      SU-  [	        SU -  5      -  [	        U * U-  5      US-  U-  [	        SU-  U -  5      -  0	nUR                  5        H  u  nn[        UUSS9nUU:X  a  M   e   g )	Nr   r   r   r   r   r   T)r   include_covar)r   r   r   r	   r   r   r   )r   r   r   r   r   r   r   r   br   cr   	covar_x_y	covar_x_z	covar_y_zr   r   r   r    s                      r!   test_variance_prop_with_covarr+   "   s   gGA!g&&FCVQAQKEQAQKEQAQKE1 I1 I1 I	u}q{*	u}q{*		5=5(Y;!"9-/0{;	!QuW	Ua4Z%1*$q{AC'88	!Ua4ZAc!A#hAaC!E'#ac("QBqD	1a4:c"Q$q&k)
E KKMSCdCczz "r#   N)sympy.core.functionr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   sympy.stats.error_propr    sympy.stats.symbolic_probabilityr   r   r	   r"   r+    r#   r!   <module>r2      s%    ( % 6 0 2r#   