+
    i$R                        R t ^ RIHt ^ RIHt ^ RIHtHt ^ RIH	t	H
t
Ht ^ RIHtHt ^ RIHt ^ RIHtHt ^ RIHtHt ^ R	IHt ^ R
IHt ^ RIHt ^ RIHt ^ RIH t H!t! ^ RI"H#t#H$t$ ^ RI%H&t& ^ RI'H(t( ^ RI)H*t* ^ RI+H,t,H-t-H.t.H/t/ ^ RI0H1t1 ^ RI2H3t3 ^ RI4H5t5H6t6H7t7H8t8H9t9H:t:H;t;H<t<H=t=H>t>  ! R R]54      t? ! R R]?]64      t@ ! R R]9]?4      tA ! R R]?]74      tB ! R R]>4      tC ! R  R!]C]=4      tD ! R" R#]:4      tE ! R$ R%]E];4      tFR& tGR' tHR(# ))zl
Continuous Random Variables Module

See Also
========
sympy.stats.crv_types
sympy.stats.rv
sympy.stats.frv
)Basic)cacheit)Lambda	PoleError)Inanoo)EqNe)S)Dummysymbols)_sympifysympify)	factorial)exp)	Piecewise)
DiracDelta)Integral	integrate)AndOr)PolynomialError)poly)series)	FiniteSetIntersectionIntervalUnion)solveset)reduce_rational_inequalities)
RandomDomainSingleDomainConditionalDomain	is_randomProductDomainPSpaceSinglePSpacerandom_symbolsNamedArgsMixinDistributionc                   .   a  ] tR t^$t o RtRtR tRtV tR# )ContinuousDomainzL
A domain with continuous support

Represented using symbols and Intervals.
Tc                    \        R 4      h)z#Not Implemented for generic Domains)NotImplementedErrorselfs   &o/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/stats/crv.py
as_booleanContinuousDomain.as_boolean,   s    !"GHH     N)	__name__
__module____qualname____firstlineno____doc__is_Continuousr2   __static_attributes____classdictcell____classdict__s   @r1   r,   r,   $   s     
 MI Ir4   r,   c                   4   a  ] tR t^0t o RtRR ltR tRtV tR# )SingleContinuousDomainz^
A univariate domain with continuous support

Represented using a single symbol and interval.
Nc                    Vf   V P                   pV'       g   V# \        V4      \        V P                   4      8w  d   \        R4      h\        WP                  V P
                  33/ VB # )NzValues should be equal)r   	frozenset
ValueErrorr   symbolset)r0   expr	variableskwargss   &&&,r1   compute_expectation*SingleContinuousDomain.compute_expectation6   sX    IKY9T\\#::566{{DHH5@@@r4   c                L    V P                   P                  V P                  4      # N)rF   as_relationalrE   r/   s   &r1   r2   !SingleContinuousDomain.as_boolean@   s    xx%%dkk22r4   r5   rM   	r6   r7   r8   r9   r:   rJ   r2   r<   r=   r>   s   @r1   rA   rA   0   s     
A3 3r4   rA   c                   4   a  ] tR t^Dt o RtRR ltR tRtV tR# )ProductContinuousDomainz=
A collection of independent domains with continuous support
Nc                    Vf   V P                   pV P                   FE  p\        V4      \        VP                   4      ,          pV'       g   K2  VP                  ! W3/ VB pKG  	  V# rM   )r   domainsrC   rJ   )r0   rG   rH   rI   domaindomain_varss   &&&,  r1   rJ   +ProductContinuousDomain.compute_expectationI   sX    IllF#I.6>>1JJK{11$NvN # r4   c                l    \        V P                   Uu. uF  qP                  4       NK  	  up!  # u upi rM   )r   rT   r2   )r0   rU   s   & r1   r2   "ProductContinuousDomain.as_booleanR   s*    t||D|V&&(|DEEDs   1r5   rM   rP   r>   s   @r1   rR   rR   D   s     F Fr4   rR   c                   D   a  ] tR t^Vt o RtRR ltR t]R 4       tRt	V t
R# )ConditionalContinuousDomainzc
A domain with continuous support that has been further restricted by a
condition such as $x > 3$.
Nc                D   Vf   V P                   pV'       g   V# V P                  P                  W4      pVP                  \	        VP
                  4      reV P                  .pV'       Ed   VP                  4       pVP                  '       dW   \        V\        4      '       d   VP                  VP                  4       K^  \        V\        4      '       d   \        R4      hK  VP                  '       Ed   VP                   '       d0   V\#        VP$                  VP&                  ,
          4      ,          pK  VP(                  \+        V P                   4      ,          p	\-        V	4      ^8w  d   \        R4      hV	P                  ! 4       p
\/        V4       Fe  w  rV^ ,          V
8X  g   K  \1        W4      p\3        V^,          V^,          4      pVP5                  V4      pWP6                  VP8                  3Wk&   Kg  	  EK  \;        RV,          4      h\=        V.VO5/ VB # )NzOr not implemented herez-Multivariate Inequalities not yet implementedz+Condition %s is not a relational or Boolean)r   
fulldomainrJ   functionlistlimits	conditionpop
is_Boolean
isinstancer   extendargsr   r.   is_Relationalis_Equalityr   lhsrhsfree_symbolsrF   len	enumerate!reduce_rational_inequalities_wrapr   	intersectleftright	TypeErrorr   )r0   rG   rH   rI   
fullintgrl	integrandr`   
conditionscondr   rE   ilimitcintvllintvlintvls   &&&,            r1   rJ   /ConditionalContinuousDomain.compute_expectation\   s   IK__88I
&//j6G6G1H6nn%
j>>#DdC((%%dii0b))-.GHH *######DHHtxx,?!@@I"//#dll2CCG7|q(1KM M %[[]F$-f$5 8v-%F $&.F &.eAha%AF$*$4$4V$<E)/U[[(IFI %6  ADHJ J 	5F5f55r4   c                ^    \        V P                  P                  4       V P                  4      # rM   )r   r]   r2   ra   r/   s   &r1   r2   &ConditionalContinuousDomain.as_boolean   s     4??--/@@r4   c                    \        V P                  4      ^8X  dL   V P                  P                  \	        V P
                  \        V P                  4      ^ ,          4      ,          # \        R4      h)   z)Set of Conditional Domain not Implemented)rl   r   r]   rF   rn   ra   tupler.   r/   s   &r1   rF   ConditionalContinuousDomain.set   s[    t||!OO''*Kdll 3A 6+8 8 9 &;= =r4   r5   rM   )r6   r7   r8   r9   r:   rJ   r2   propertyrF   r<   r=   r>   s   @r1   r[   r[   V   s*     
-6^A = =r4   r[   c                   &   a  ] tR t^t o R tRtV tR# )ContinuousDistributionc                "    V P                   ! V!  # rM   )pdf)r0   rf   s   &*r1   __call__ContinuousDistribution.__call__   s    xxr4   r5   N)r6   r7   r8   r9   r   r<   r=   r>   s   @r1   r   r      s      r4   r   c                      a  ] tR t^t o Rt]! ]) ]4      tR t]	R 4       t
]R 4       tR tR t]R 4       tR tR	 t]R
 4       tR tR tRR lt]R 4       tR tR tRtV tR# )SingleContinuousDistributionap  Continuous distribution of a single variable.

Explanation
===========

Serves as superclass for Normal/Exponential/UniformDistribution etc....

Represented by parameters for each of the specific classes.  E.g
NormalDistribution is represented by a mean and standard deviation.

Provides methods for pdf, cdf, and sampling.

See Also
========

sympy.stats.crv_types.*
c                d    \        \        \        V4      4      p\        P                  ! V .VO5!  # rM   )r_   mapr   r   __new__)clsrf   s   &*r1   r   $SingleContinuousDistribution.__new__   s'    C&'}}S(4((r4   c                     R # rM   r5   )rf   s   *r1   check"SingleContinuousDistribution.check   s    r4   c                    \        RR\        R7      w  r#V P                  P                  pV P	                  V4      p\        VP                  4       W$V33/ VB p\        WcV8  3R4      p\        W64      # )z1Compute the CDF from the PDF.

Returns a Lambda.
x, zTrealr       T)	r   r   rF   startr   r   doitr   r   )r0   rI   xz
left_boundr   cdfs   &,     r1   compute_cdf(SingleContinuousDistribution.compute_cdf   si     vDe4XX^^
 hhqk
QA$6A&A:o.	:a~r4   c                    R # rM   r5   r0   r   s   &&r1   _cdf!SingleContinuousDistribution._cdf       r4   c                    \        V4      ^ 8X  d   V P                  V4      pVe   V# V P                  ! R/ VB ! V4      # zCumulative density function r5   )rl   r   r   )r0   r   rI   r   s   &&, r1   r    SingleContinuousDistribution.cdf   s>    v;!))A,C
)&)!,,r4   c                    \        RR\        R7      w  r#V P                  V4      p\        \	        \
        V,          V,          4      V,          W P                  34      p\        W54      # )zECompute the characteristic function from the PDF.

Returns a Lambda.
x, tTr   )r   r   r   r   r   r   rF   r   )r0   rI   r   tr   cfs   &,    r1   compute_characteristic_function<SingleContinuousDistribution.compute_characteristic_function   sM     vDe4hhqks1Q3q5z#~88}5a}r4   c                    R # rM   r5   r0   r   s   &&r1   _characteristic_function5SingleContinuousDistribution._characteristic_function   r   r4   c                    \        V4      ^ 8X  d   V P                  V4      pVe   V# V P                  ! R/ VB ! V4      # )zCharacteristic function r5   )rl   r   r   )r0   r   rI   r   s   &&, r1   characteristic_function4SingleContinuousDistribution.characteristic_function   sA    v;!..q1B~	33=f=a@@r4   c                    \        RR\        R7      w  r#V P                  V4      p\        \	        W2,          4      V,          W P
                  34      p\        W54      # )zHCompute the moment generating function from the PDF.

Returns a Lambda.
r   Tr   )r   r   r   r   r   rF   r   )r0   rI   r   r   r   mgfs   &,    r1   "compute_moment_generating_function?SingleContinuousDistribution.compute_moment_generating_function   sH     vDe4hhqkAE
S(1hh-8a~r4   c                    R # rM   r5   r   s   &&r1   _moment_generating_function8SingleContinuousDistribution._moment_generating_function   r   r4   c                p    V'       g   V P                  V4      pVe   V# V P                  ! R/ VB ! V4      # )zMoment generating function r5   )r   r   )r0   r   rI   r   s   &&, r1   moment_generating_function7SingleContinuousDistribution.moment_generating_function   s8    66q9?J66@@CCr4   c           	     (   V'       Ed     \        W4      pVP                  '       d   \        P                  # \	        RRR7      pV P                  V4      pVf.   \        WP                  V4      ,          W P                  33/ VB # VP                  4       p\        \        Wv^ V^,           4      P                  4       V4      p	^ p
\        V^,           4       FL  pWP                  W+,          4      V	P                  Wk,          4      ,          \        V4      ,          ,          p
KN  	  V
# \!        WP                  V4      ,          W P                  33/ VB #   \         d1    \        YP                  T4      ,          Y P                  33/ TB u # i ; i)z,Expectation of expression over distribution r   Tr   )r   is_zeror   Zeror   r   r   r   rF   degreer   removeOrangecoeff_monomialr   r   r   )r0   rG   varevaluaterI   pr   r   degtaylorresultks   &&&&,       r1   expectation(SingleContinuousDistribution.expectation  sE   8RO99966M#D)66q9;$THHSM%9C?UfUUhhjfSQa8@@BAFs1uA..sx86;P;PQRQW;XX[def[gggF & D88C=03/LVLL # R !5XXQ&QQRs   ,E AE B!E 8FFc           	         \        RR\        R7      w  r#V P                  P                  pV P	                  V4      p\        WRWB33/ VB p\        Wc,
          W P                  4      p\        V\        Ws^ 8  V^8*  ,          3\        R34      4      # )z6Compute the Quantile from the PDF.

Returns a Lambda.
zx, pTr   )
r   r   rF   r   r   r   r   r   r   r   )r0   rI   r   r   r   r   r   quantiles   &,      r1   compute_quantile-SingleContinuousDistribution.compute_quantile  s|     vDe4XX^^
hhqk/:6:CGQ1aHAv!q&.A#Cc4[QRRr4   c                    R # rM   r5   r   s   &&r1   	_quantile&SingleContinuousDistribution._quantile%  r   r4   c                    \        V4      ^ 8X  d   V P                  V4      pVe   V# V P                  ! R/ VB ! V4      # r   )rl   r   r   )r0   r   rI   r   s   &&, r1   r   %SingleContinuousDistribution.quantile(  s@    v;!~~a(H#$$.v.q11r4   r5   NT)r6   r7   r8   r9   r:   r   r   rF   r   staticmethodr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r<   r=   r>   s   @r1   r   r      s     $ B3
C)    -  A  DM, S S2 2r4   r   c                      a  ] tR tRt o RtRtRt]R 4       tRR lt	R t
]R 4       t]R	 4       t]R
 4       t]R 4       tR tR tRR ltRtV tR# )ContinuousPSpacei1  zContinuous Probability Space

Represents the likelihood of an event space defined over a continuum.

Represented with a ContinuousDomain and a PDF (Lambda-Like)
Tc                J    V P                   ! V P                  P                  !  # rM   )densityrU   r   r/   s   &r1   r   ContinuousPSpace.pdf<  s    ||T[[0011r4   Nc                   Vf   V P                   pM\        V4      pTP                  V Uu/ uF  qUVP                  bK  	  up4      p\        R V 4       4      pV P                  P
                  ! V P                  V,          V3/ VB # u upi )Nc              3   8   "   T F  qP                   x  K  	  R # 5irM   rE   ).0rvs   & r1   	<genexpr>7ContinuousPSpace.compute_expectation.<locals>.<genexpr>H  s     ";s99s   )valuesrC   xreplacerE   rU   rJ   r   )r0   rG   rvsr   rI   r   domain_symbolss   &&&&,  r1   rJ   $ContinuousPSpace.compute_expectation@  s}    ;++CC.C}}c:c"))mc:;"";s";;{{..txx$*"(* 	*	 ;s   B	c           	        WP                   9   d   \        \        V P                   4      \        V.4      ,
          4      p\        ;QJ d    . R  V 4       F  NK  	  5M! R  V 4       4      pV P                  P
                  ! V P                  V3/ VB p\        VP                  V4      # \        RRR7      p\        W`P
                  ! \        W,
          4      3/ VB 4      # )c              3   8   "   T F  qP                   x  K  	  R # 5irM   r   )r   rss   & r1   r   3ContinuousPSpace.compute_density.<locals>.<genexpr>R  s     >"IIr   r   Tr   )r   r   rF   rC   rU   rJ   r   r   rE   r   r   )r0   rG   rI   randomsymbolsr   r   r   s   &&,    r1   compute_density ContinuousPSpace.compute_densityM  s    ;;!#dkk"2Yv5F"FGMe>>ee>>>G++11$((GNvNC$++s++#D!a11*TX2FQ&QRRr4   c                R   V P                   P                  P                  '       g   \        R 4      hV P                  ! V3/ VB p\        RR\        R7      w  rEV P                   P                  P                  p\        V! V4      WFV33/ VB p\        WuV8  3R4      p\        WW4      # )z0CDF not well defined on multivariate expressionsr   Tr   r   )rU   rF   is_IntervalrD   r   r   r   r   r   r   r   )r0   rG   rI   dr   r   r   r   s   &&,     r1   r   ContinuousPSpace.compute_cdfY  s    {{***BD D   00vDe4[[__**
 !qa0;F;:o.	:a~r4   c                J   V P                   P                  P                  '       g   \        R 4      hV P                  ! V3/ VB p\        RR\        R7      w  rE\        \        \        V,          V,          4      V! V4      ,          V\        ) \        33/ VB p\        WV4      # )zCCharacteristic function of multivariate expressions not implementedr   Tr   )rU   rF   r   r.   r   r   r   r   r   r   r   r   )r0   rG   rI   r   r   r   r   s   &&,    r1   r   0ContinuousPSpace.compute_characteristic_functioni  s~    {{***%&kll  00vDe4s1Q3q5z!A$RC??a}r4   c                2   V P                   P                  P                  '       g   \        R 4      hV P                  ! V3/ VB p\        RR\        R7      w  rE\        \        WT,          4      V! V4      ,          V\        ) \        33/ VB p\        WV4      # )zFMoment generating function of multivariate expressions not implementedr   Tr   )rU   rF   r   r.   r   r   r   r   r   r   r   )r0   rG   rI   r   r   r   r   s   &&,    r1   r   3ContinuousPSpace.compute_moment_generating_functions  sy    {{***%&noo  00vDe4AE
QqT)AsB<B6Ba~r4   c                   V P                   P                  P                  '       g   \        R 4      hV P                  ! V3/ VB p\        RRR7      p\        RRR7      p\        V! V4      V,
          W@P                  4      p\        WV4      # )z5Quantile not well defined on multivariate expressionsr   Tr   r   )positive)rU   rF   r   rD   r   r   r   r   )r0   rG   rI   r   r   r   r   s   &&,    r1   r   !ContinuousPSpace.compute_quantile}  sz    {{***GI I T,V,#D!#%AaD1Ha2a""r4   c                  aaa \        R RR7      oRp\        V\        4      '       d1   \        VP                  ^ ,          VP                  ^,          4      pRp V P                  V4      pV P                   Uu. uF!  qUP                  VP                  8X  g   K  VNK#  	  up^ ,          pV P                  ! V3/ SB oVP                  \        P                  J g!   \        VP                  \        4      '       d)   V'       g   \        P                  # \        P                  # \        VP                  \        4      '       d,   \!        VVV3R lVP                  P                   4       4      # \#        S! S4      SVP                  33/ SB # u upi   \$         d    ^ RIHp TP*                  TP,                  ,
          p\/        T4      '       g   T P(                  pTP,                  p	MT! T3/ SB p^ p	\        T\0        4      '       g$   ^ RIHp
 T
! YP6                  P                  R7      p\9        ST4      pTP;                  TP=                  TP>                  T	4      4      pT'       g   Tu # \        P                  T,
          u # i ; i)r   Tr   Fc              3   ~   <"   T F2  p\        V\        4      '       g   K  \        S! S4      SV33/ SB x  K4  	  R # 5irM   )rd   r   r   )r   subsetrI   r   r   s   & r1   r   /ContinuousPSpace.probability.<locals>.<genexpr>  s>      F$ BH(268(D =Xc!fq&k<V<$s   ==)r   )ContinuousDistributionHandmade)rF   ) r   rd   r
   r	   rf   wherer   rE   r   rF   r   EmptySetr   r   Oner   sumr   r.   sympy.stats.rvr   ri   rj   r$   r   sympy.stats.crv_typesr  rU   SingleContinuousPSpaceprobability	__class__value)r0   ra   rI   cond_invrU   r   r   rG   denscompr  spacer   r   r   s   &&l          @@r1   r  ContinuousPSpace.probability  s   #D!i$$9>>!,innQ.?@IH 	>ZZ	*F#{{I{ii6==.H""{I!LB&&r4V4CzzQZZ':fjj)+L+L%-qvv81558&**e,, FZZ__F F F CFQ

O>v>> J # 	>.==9==0DT??|| }}t.v.d$:;;P5dP*1d3E&&y':':5;;'MNF!)6=quuv~=	>sK   F 9FF A"F F F #A
F .F F CJ1J
Jc                R   \        \        V4      4      p\        V4      ^8X  d"   VP                  V P                  4      '       g   \        R4      h\        V4      ^ ,          p\        W4      pVP                  V P                  P                  4      p\        VP                  V4      # )r   z2Multiple continuous random variables not supported)rC   r(   rl   issubsetr   r.   r   rn   ro   rU   rF   rA   rE   )r0   ra   r   r   intervals   &&   r1   r  ContinuousPSpace.where  s    y12CA#,,t{{";";%DF F3Z]4YC%%dkkoo6%bii::r4   c           	        TP                  V P                   Uu/ uF  qDVP                  bK  	  up4      p\        V P                  V4      pV'       d   V P
                   Uu/ uF  qD\        \        V4      4      bK  	  ppVP                  ! V P                  3/ VB pV P                  VP                  V4      ,          p\        \        VP
                  4      V4      p	\        VX	4      # u upi u upi rM   )r   r   rE   r[   rU   r   r   strrJ   r   r   r   r   )
r0   ra   	normalizerI   r   rU   replacementnormr   r   s
   &&&,      r1   conditional_space"ContinuousPSpace.conditional_space  s    &&'L"BII'LM	,T[[)D :>F2c"g.KF--dhhA&AD((T]];77C U6>>2C8G00 (M Gs   C+"C0r5   NFr   )r6   r7   r8   r9   r:   r;   is_realr   r   rJ   r   r   r   r   r   r   r  r  r  r<   r=   r>   s   @r1   r   r   1  s      MG2 2*
S       # #'>R;1 1r4   r   c                   v   a  ] tR tRt o Rt]R 4       t]R 4       tRR ltRR lt	R t
R	 tR
 tR tR tRtV tR# )r  i  z
A continuous probability space over a single univariate variable.

These consist of a Symbol and a SingleContinuousDistribution

This class is normally accessed through the various random variable
functions, Normal, Exponential, Uniform, etc....
c                .    V P                   P                  # rM   )distributionrF   r/   s   &r1   rF   SingleContinuousPSpace.set  s      $$$r4   c                T    \        \        V P                  4      V P                  4      # rM   )rA   r   rE   rF   r/   s   &r1   rU   SingleContinuousPSpace.domain  s    %gdkk&:DHHEEr4   Nc                T    V P                   V P                  P                  WVR7      /# )zX
Internal sample method.

Returns dictionary mapping RandomSymbol to realization value.
)libraryseed)r  r$  sample)r0   sizer)  r*  s   &&&&r1   r+  SingleContinuousPSpace.sample  s*     

D--44TQU4VWWr4   c                   T;'       g    V P                   3pV P                   V9  d   V# \        V4      pTP                  V Uu/ uF  qUVP                  bK  	  up4      pV P                   P                  p V P                  P
                  ! W3R V/VB # u upi   \         d,    \        YP                  ,          Y`P                  33/ TB u # i ; i)r   )
r  r   r   rE   r$  r   r   r   r   rF   )r0   rG   r   r   rI   r   r   s   &&&&,  r1   rJ   *SingleContinuousPSpace.compute_expectation  s    ""djj]::S K~}}c:c"))mc:;JJ	F$$00V8VvVV	 ;
  	FD88Oa]EfEE	Fs   B8B 3CCc                    WP                   8X  d4   \        R RR7      p\        W0P                  P                  ! V3/ VB 4      # \
        P                  ! W3/ VB # )r   Tr   )r  r   r   r$  r   r   r   )r0   rG   rI   r   s   &&, r1   r   "SingleContinuousPSpace.compute_cdf  sO    ::c%A!..221??@@#//EfEEr4   c                    WP                   8X  d4   \        R RR7      p\        W0P                  P                  ! V3/ VB 4      # \
        P                  ! W3/ VB # r   Tr   )r  r   r   r$  r   r   r   r0   rG   rI   r   s   &&, r1   r   6SingleContinuousPSpace.compute_characteristic_function   sP    ::c%A!..FFqSFSTT#CCDYRXYYr4   c                    WP                   8X  d4   \        R RR7      p\        W0P                  P                  ! V3/ VB 4      # \
        P                  ! W3/ VB # r3  )r  r   r   r$  r   r   r   r4  s   &&, r1   r   9SingleContinuousPSpace.compute_moment_generating_function  sP    ::c%A!..II!VvVWW#FFt\U[\\r4   c                X  aa WP                   8X  d   V P                  # \        R RR7      o\        VS,
          V P                   \        P
                  4      p\        V\        4      '       dS   \        VP                  4      ^8X  d9   VP                  ^ ,          \        P
                  J d   VP                  ^,          pVP                  '       g   \        RV: RV P                   : 24      hV P                  V P                   4      o\        VV3R lV 4       4      p\        SV4      # )yTr   zCan not solve z for c              3   r   <"   T F,  pS! V4      \        VP                  S4      4      ,          x  K.  	  R # 5irM   )absdiff)r   gfxr9  s   & r1   r   9SingleContinuousPSpace.compute_density.<locals>.<genexpr>  s)     4AAQVVAY''s   47)r  r   r   r   r   Realsrd   r   rl   rf   is_FiniteSetrD   r   r	  r   )r0   rG   rI   gsfyr>  r9  s   &&,  @@r1   r   &SingleContinuousPSpace.compute_density  s    ::<<#D!dQh

AGG4b,''277|q RWWQZ177%:WWQZ$

KLL!!$**-444a}r4   c                    WP                   8X  d4   \        R RR7      p\        W0P                  P                  ! V3/ VB 4      # \
        P                  ! W3/ VB # )r   Tr   )r  r   r   r$  r   r   r   )r0   rG   rI   r   s   &&, r1   r   'SingleContinuousPSpace.compute_quantile  sO    ::c%A!..77DVDEE#44TJ6JJr4   r5   )r5   scipyNr   )r6   r7   r8   r9   r:   r   rF   rU   r+  rJ   r   r   r   r   r   r<   r=   r>   s   @r1   r  r    sc      % % F FXFFZ]"K Kr4   r  c                 l     \        W3/ VB #   \         d    \        R T ^ ,          ,          4      hi ; i)z!Reduction of condition failed %s
)r    r   rD   )ru   r   rI   s   &&,r1   _reduce_inequalitiesrI  '  s>    O+JFvFF O=
1MNNOs    %3c                    V P                   '       d   \        V ..VR R7      # \        V \        4      '       d2   \	        V P
                   Uu. uF  p\        V..VR R7      NK  	  up!  # \        V \        4      '       dP   V P
                   Uu. uF  p\        V..VR R7      NK  	  ppV^ ,          pV F  pVP                  ! V4      pK  	  V# R# u upi u upi )F)
relationalN)rg   rI  rd   r   r   rf   r   ro   )ra   r   arg	intervalsr   rw   s   &&    r1   rn   rn   .  s    #i[M35II)R   ~~'% ,cUGSUK%' ( 	()S!! ~~'% *C5'35I% 	 'aLAAA  "''s   CCN)Ir:   sympy.core.basicr   sympy.core.cacher   sympy.core.functionr   r   sympy.core.numbersr   r   r   sympy.core.relationalr	   r
   sympy.core.singletonr   sympy.core.symbolr   r   sympy.core.sympifyr   r   (sympy.functions.combinatorial.factorialsr   &sympy.functions.elementary.exponentialr   $sympy.functions.elementary.piecewiser   'sympy.functions.special.delta_functionsr   sympy.integrals.integralsr   r   sympy.logic.boolalgr   r   sympy.polys.polyerrorsr   sympy.polys.polytoolsr   sympy.series.seriesr   sympy.sets.setsr   r   r   r   sympy.solvers.solvesetr   sympy.solvers.inequalitiesr    r
  r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r,   rA   rR   r[   r   r   r   r  rI  rn   r5   r4   r1   <module>rb     s    # $ 1 + + * " . 0 > 6 : > ; ) 2 & & F F + C[ [ [	I| 	I3-| 3(Fm-= F$?="24E ?=D\ 
Q2#9> Q2h]1v ]1@TK-| TKlOr4   