
    sg$                         d dl mZ d dlmZ d dlmZmZ d dlmZ d dl	m
Z
mZ d dlmZ d dlmZ d dlmZ d d	lmZ d d
lmZ d dlmZmZmZmZmZmZmZmZmZ d dl m!Z!m"Z" d Z#d Z$d Z%d Z&y)    )Sum)Mul)oopi)Eq)Dummysymbols)exp)sqrt)sin)Integral)	unchanged)	NormalPoissonvariance
CovarianceVarianceProbabilityExpectationMomentCentralMoment)probabilityexpectationc                  h   t        ddd      } t        ddd      }t        dd      }t        dd      }t        dd	
      }t        d      \  }}}t        | dkD        j	                         t        | dkD        k(  sJ t        | |kD        j	                         t        | |kD        k(  sJ t        | dkD        j                  t              j                         t        | dkD        k(  sJ t        | |kD        j                  t              j                         t        | |kD        k(  sJ t        |       j	                         t        |       k(  sJ t        |       j                  t              j                         t        |       k(  sJ t        | dz        j	                         t        | dz        k(  sJ t        || z        j                  || z  fk(  sJ t        || z        j                         |t        |       z  k(  sJ t        d| z  d|z  z   || z  |z  z         j                         dt        |       z  dt        |      z  z   |t        | |z        z  z   k(  sJ t        d| z  d|z  z   || z  |z  z         j                  d| z  d|z  z   || z  |z  z   fk(  sJ t        t        |             t        t        |             j                         k(  sJ t        d|z  t        |       z  |z  || dz  z  z   || z  |z  z         j                         d|z  t        t        |       |z        z  |t        | dz        z  z   |t        | |z        z  z   k(  sJ t        | |z         j                         t        |       t        |      z   k(  sJ t        | |z   | |z
  z        j                         t        | dz        t        |dz        z
  k(  sJ t        | |z   | |z
  z        j                         j                         dk(  sJ t        | |z   d	      j                         dk(  sJ t        | t        |      z         j                         dk(  sJ t        | t        |      z         j                  d      dt        t        |            z   k(  sJ t        | t        |t        d| z        z         z         j                  d      dt        t        |t        d| z        z               z   k(  sJ t        | t        |t        d| z        z         z         j                         dk(  sJ t        t        d| z              j                         dk(  sJ t        t        d| z              j                  d      t        d| z        k(  sJ t        dt        d| z        z        j                  d      dt        d| z        z  k(  sJ t        | |z   dz        j                         dt        | |dz  z        z  dt        | dz  |z        z  z   t        | dz        z   t        |dz        z   k(  sJ t        | |z
  dz        j                         dt        | |dz  z        z  dt        | dz  |z        z  z
  t        | dz        z   t        |dz        z
  k(  sJ t        | |z
  dz        j                         dt        | |z        z  t        | dz        z   t        |dz        z   k(  sJ t        |      j                  |fk(  sJ t        |      j                         dk(  sJ t        |       j	                         t        |       j                  t              j                         cxk(  rt        |       k(  sJ  J t        | |z         j                  | |z   fk(  sJ t        | |z         j                         t        |       k(  sJ t        | |z        j                  t!        | |      fk(  sJ t#        t        | |z              t        k(  sJ t        || z        j                         |dz  t        |       z  k(  sJ t        | |z         j                         t        |       t        |      z   dt%        | |      z  z   k(  sJ t        | |z   |z   |z         j                         t        |       t        |      z   t        |      z   t        |      z   dt%        | |      z  z   dt%        | |      z  z   dt%        | |      z  z   dt%        ||      z  z   dt%        ||      z  z   dt%        ||      z  z   k(  sJ t        | dz        j	                         t        | dz        k(  sJ t'        t        | dz        sJ t        || dz  z        j                         |dz  t        | dz        z  k(  sJ t        t        |             j                  t        |       fk(  sJ t        t        |             j                         t        t        |             k(  sJ t        |t        |       z        j                         |dz  t        t        |             z  k(  sJ t%        ||      j                  ||fk(  sJ t%        ||      j                         dk(  sJ t%        | |      j                         dk(  sJ t%        ||       j                         dk(  sJ t%        | |      j                  | |fk(  sJ t#        t%        | |            t$        k(  sJ t%        || z  dz   |      j                         |t%        | |      z  k(  sJ t%        | |       j                  | | fk(  sJ t%        | |       j                         t        |       k(  sJ t%        || z  dz   ||z  dz         j                         ||z  t%        | |      z  k(  sJ t%        | |      t%        ||       k(  sJ t%        | |z   ||z         j                         t%        ||       t%        ||      z   t%        | |      z   t%        ||      z   k(  sJ t%        || z  ||z  z   ||z  ||z  z         j                         ||z  t%        ||       z  ||z  t%        ||      z  z   ||z  t%        | |      z  z   ||z  t%        ||      z  z   k(  sJ t%        || dz  z  |t        |      z  z   ||z  |dz  z  ||z  z         j                         ||z  t%        || dz        z  ||z  t%        t        |      |      z  z   ||z  t%        ||dz  z  | dz        z  z   ||z  t%        ||dz  z  t        |            z  z   k(  sJ t%        | | dz        j                         t%        | | dz        k(  sJ t%        | t        |             j                         t%        t        |       |       k(  sJ t%        | dz  t        |       |z        j                         t%        t        |       |z  | dz        k(  sJ t%        ||       j	                         dk(  sJ y )NX      Y   ZWxTrealzy, w, zr   i)evaluate   F)deep	   )r   r   r	   r   evaluate_integralr   rewriter   doitr   r   argsexpandr   r   r   r   typer   r   )r   r   r    r!   r"   ywzs           ^/var/www/html/venv/lib/python3.12/site-packages/sympy/stats/tests/test_symbolic_probability.pytest_literal_probabilityr4      s   sAqAsAqAQAQA$Ai GAq!q1u//1[Q5GGGGq1u//1[Q5GGGGq1u%%h/446+a!e:LLLLq1u%%h/446+a!e:LLLLq>++-Q???q>!!(+002k!nDDDq!t..0K14EEEEqs  QqSF***qs""$+a.(8888qsQqSy1Q3q5()002aA6F;WX>IY6Y\]^ijklmjm^n\n6nnnnqsQqSy1Q3q5()..1Q319qs1u3D2FFFFs1v+c!f"5"<"<">>>>qs3q6z!|a1f,qs1u45<<>!A#kRUVWRXYZRZF[B[AqD 11C245k!A#6F4FCG G G Gq1u$$&;q>KN+JJJJAA'..0K14ETUWXTXHY4YYYYAA'..05573>>>q1ut,113q888q;q>)*//1Q666q;q>)*//U/;q;{[\~C^?^^^^q;q;qs+;';<<=BBBNRS"-k!k!A#>N:N.O"PSQ Q Q Qq;q;qs+;';<<=BBDIII{1Q3'(--/1444{1Q3'(--5-9[1=MMMMqQqS))*//U/;qQqSAQ?QQQQAz"))+qQq!tV1D/D+ad1f%%0&(3AqD(90:<G1<M0N N N NAz"))+qQq!tV1D/D+ad1f%%0&(3AqD(90:<G1<M0N N N NAz"))+r+ac2B/BAqD!0"$/1$506 6 6 6 A;t###A;1$$$A;((*hqk.A.A(.K.P.P.RaV^_`VaaaaaaAE?AE8+++AE?!!#x{222AaC=#a)---1(***AaC=!QT(1+%5555AE?!!#x{Xa['@1ZPQSTEUCU'UUUUAEAIM"))+hqk0IHUVK0WZbcdZe0e'(:a+;';1<>?*QPQBR>R1SUVYcdeghYiUi1j'(:a+;';1<>?*QPQBR>R1SUVYcdeghYiUi1j k k k AqD>++-!Q$???Xq!t$$$AadF""$1Xad^(;;;;CF  SVI---CF""$Q(8888Ac!fH$$&!Q$xA/?*????a  QF***a""$)))a""$)))a""$)))a  QF***
1a !Z///acAgq!((*a
1a0@.@@@@a  QF***a""$333acAgqsQw'..0AaC
1Q4GGGGaz!Q////a!eQU#**,
1a0@:aQRCS0SV`abdeVf0fistuwxiy0yyyyacAaCi1qs+2241Z1=M9MPQRSPST^_`bcTdPd9d01!Jq!4D0D:EGHs:VWYZK[G[:\ ] ] ]a1fqQx'1QTAaC8??Aac*UVXY[\X\J]F]`abc`cdnorstouwxdy`yFy89!JqAvqRSt<T8TGUWXYZWZ[efghiklhlflnqrsnt[uWuGv w w waA%%':aA+>>>>aQ '')ZA-BBBBadCF1H%,,.*SVAXq!t2LLLLa--/1444    c                  V   t        ddd      } t        ddd      }t        dd      }t        dd      }t        d      \  }}}}t        |      j	                  t
              d	k(  sJ t        |       j	                  t
              t        | dz        t        |       dz  z
  k(  sJ t        | |
      j	                  t
              t        | dz  |      t        | |      dz  z
  k(  sJ t        | |      t        | dz        t        |       dz  z
  k7  sJ t        | |z         j	                  t
              t        | |z   dz        t        | |z         dz  z
  k(  sJ t        | |z        j	                  t
              t        | dz  |dz  z        t        | |z        dz  z
  k(  sJ t        ||       j	                  t
              | t        |       z  t        || z        z   k(  sJ t        | |      j	                  t
              t        | |z        t        |       t        |      z  z
  k(  sJ t        | ||
      j	                  t
              t        | |z  |      t        | |      t        ||      z  z
  k(  sJ t        d      \  }}}t        t        | |            }t        t        ||            }	t        |       j	                  t              t        ||z  |t         t        f      k(  sJ t        |      j	                  t              t        ||	z  |d	t        f      k(  sJ t        |       j	                  t              t        |dz  |z  |t         t        f      t        ||z  |t         t        f      dz  z
  k(  sJ t        |      j	                  t              t        |dz  |	z  |d	t        f      t        ||	z  |d	t        f      dz  z
  k(  sJ t        ||       j	                  t              | t        |t        t        | |            z  |t         t        f      z  t        ||z  t        t        | |            z  |t         t        f      z   k(  sJ t        |       j	                  t              t        |       j	                  t              k(  sJ t        |       j	                  t              t        |       j	                  t              k(  sJ t        ||       j	                  t              d	k(  sJ t        ||       j	                  t              d	k(  sJ t        | |
      j	                  t              t        |dz  t        t        | |      |      z  |t         t        f      t        |t        t        | |      |      z  |t         t        f      dz  z
  k(  sJ y )Nr   r   r   r   r   r    r!   z
x, y, w, zr   )	conditionzW, x, z)r   r   r	   r   r+   r   r   r   r   r   r   r   )
r   r   r    r!   r"   r0   r1   r2   pxpzs
             r3   test_probability_rewriter:   c   sE   sAqAsAqAQAQA&JAq!QA;{+q000A;{+{16/B[QR^WXEX/XXXXA#++K8KQPQ<RU`abdeUfjkUk<kkkkAq>[A.Q1BBBBBAE?"";/;A!|3L{[\_`[`OaefOf3ffffAE?"";/;qAvQ3OR]^_bc^cRdhiRi3iiiia##K0QB{1~4ETUVWTWHX4XXXXa##K0K!4D{ST~VabcVdGd4ddddaa(00=QQRUTUAVYdefhiYjmxyz|}m~Y~A~~~~i GAq!	R1X	B	R1X	Bq>!!+.(1R4!bS"2NNNNq>!!+.#adQ2J2GGGGA;{+x1R!bS"/NQYZ[\^Z^abegdgik`lQmopQp/ppppA;{+s1a47Q2J/G#aPRdUVXY[]T^J_abJb/bbbba##K02hqR1X..RC==1[Y[\]_`YaMbIbefikhkmodp@qqr r r A;s#x{':':8'DDDDq>!!#&+a.*@*@*JJJJa##C(A---a##H-222A#++K8HQT+VXYZ\]V^`aJbEbefikhkmodp<q<DQ{SUVWYZS[]^G_E_bcfhehjlam<npq<q=r r r rr5   c            
         t        dd      } t        dd      }t        d      }t        d| |      }t        |dd	      }|j                  t              t	        |d	z
  dz        k(  sJ |j                  t
              t        |d	z
  dz  t        t        ||            z  |t         t        f      k(  sJ t        d
      }t        t        d	      |d	z
  dz  z  t        || z
  d	z   d	|d	z  z  z        z  d	t        t              z  |z  z  |t         t        f      }|j                  t              j                  |      sJ |j                         | dz  d| dz  z  z
  d| d	z  z  |d	z  z  z   d| d	z  z  z   d| z  |d	z  z  z
  d| z  z
  d|dz  z  z   d|d	z  z  z   dz   k(  sJ t        d	d      }|j                         dk(  sJ y )NmuTr#   sigmapositiver"   r   r   r   k   r                r&   )r	   r   r   r+   r   r   r   r   r   r   r   r
   r   dummy_eqr,   )r<   r=   r"   r   Mr@   expris          r3   test_symbolic_MomentrI      s   	D	!BGd+EAsBAq!QA99[![!a%!%<<<<99[!Xq1uqjR1X9N.N%&RL&2 2 2 2c
AT!Wa!eaZ'a/. -%(
-$ )% %&'Rj&68:;bS"GE99X''...668A"a%!BE'%(*::2q5b5>*,.rE245eQhJ?ACE1HMOQR S S Sq!A668tr5   c                     t        dd      } t        dd      }t        d      }t        d| |      }t        |d      }|j                  t              t	        |t	        |      z
  dz        k(  sJ |j                  t
              t        |t        |t        d      z  |t         t        f      z
  dz  t        t        ||            z  |t         t        f      k(  sJ t        d	      }t        t        d
      |t        t        d
      |z  t        || z
  d
z   d
|d
z  z  z        z  d
t        t              z  |z  z  |t         t        f      z
  dz  z  t        || z
  d
z   d
|d
z  z  z        z  d
t        t              z  |z  z  |t         t        f      }|j                  t              j                  |      sJ |j                         j                         d|dz  z  k(  sJ t!        dd      }|j                         dk(  sJ y )Nr<   Tr#   r=   r>   r"   r   rB   r@   r      r&   i5  )r	   r   r   r+   r   r   r   r   r   r   r   r
   r   rF   r,   simplifyr   )r<   r=   r"   r   CMr@   rH   s          r3   test_symbolic_CentralMomentrN      s'   	D	!BGd+EAsBA	q!	B::k"k1{1~3E2I&JJJJ::k"hHQ{4?P=PRL5" 1"$%0&&1"Q(&;0<>?"b\'K K K Kc
AT!Wa(4719S1
<; :%(
: 6 ,Rj.,023bS"#? ?ABC CCF
JI H%(
H DRj.023bS"?E ::h((///7792eQh;...	1B779r5   N)'sympy.concrete.summationsr   sympy.core.mulr   sympy.core.numbersr   r   sympy.core.relationalr   sympy.core.symbolr   r	   &sympy.functions.elementary.exponentialr
   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   sympy.integrals.integralsr   sympy.core.exprr   sympy.statsr   r   r   r   r   r   r   r   r   sympy.stats.rvr   r   r4   r:   rI   rN    r5   r3   <module>r\      sP    )  ' $ . 6 9 8 . %J J J 3P5f&rR&r5   