
    Qi                     B   d dl mZ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 d dlmZmZmZmZ 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 d dlmZ d dlm Z  d dl!m"Z"  ed          \  Z#Z$ edd          Z% edd          Z& edd          Z'd Z(d Z)d Z*dS )    )Inanoopi)EqNe)S)Symbolsymbols)adjoint	conjugatesign	transpose)sqrt)	Piecewise)
DiracDelta	Heaviside)SingularityFunction)signsimp)raises)	unchanged)ArgumentIndexErrorzx ytT)nonzeroj)positivek)negativec                  6   t          d          dk    sJ t          d          dk    sJ t          t                     dk    sJ t          dd          dk    sJ t          t          d          t          t                    k    sJ t          t                    dk    sJ t          t                    dk    sJ t          t
                    dk    sJ t          t                    t          u sJ t          d          j        t           u sJ t          t                    j        t           u sJ t          t          t                              t          t                    k    sJ t          t          t          t          z
                      t          t          t          z
            k    sJ t          t          t                              t          t                    k    sJ t          t          t          t          z
                      t          t          t          z
            k    sJ t          t          t                              t          t                    k    sJ t          t          t          t          z
                      t          t          t          z
            k    sJ t          t                                        t                    t          t          d          k    sJ t          t          d                              t                    t          t          d          k    sJ t          t                                        t                    du sJ t          dt          z                                t                    du sJ t          t          dz                                t                    d	u sJ t          t          t                                                  t                    d	u sJ t          t                                        t                    d	u sJ t          t          t          z                                dt          
          t          t                    t!          t                    z  k    sJ t          t          t          z                                dt          
          t          t                    t!          t                    z  k    sJ t          t          dz  t          z                                dt          
          t          t          dz  t          z            k    sJ t          t                                        dt          
          t          t                    k    sJ t          t          dz
  t          dz
  z  t          dz
  z                                dt          
          t          t          dz
            dz  t          t          dz
            z   t          t          dz
            dz  z   k    sJ t          dt          z            t          t                    k    sJ t          t                    t          t                     k    sJ t          t           d          t          t          d          k    sJ t          t           d          t          t          d           k    sJ t          t"           t          z            t          t"          t          z            k    sJ t          t          t          z
            t          t          t          z
            k    sJ t%          t          t          t          z
            t          t          t          z
            z
            dk    sJ t          t          t          z                                dt          
          t          t                    t!          t                    z  k    sJ t          t          t          z                                dt          
          t          t                    t!          t                    z  k    sJ t          t          dz  t          z                                dt          
          t          t          dz  t          z            k    sJ t          t                                        dt          
          t          t                    k    sJ t          t          dz
  t          dz
  z  t          dz
  z                                d          t          t          dz
            dz  t          t          dz
            z   t          t          dz
            dz  z   k    sJ t'          t(          d            t'          t*          d            t'          t*          d            t'          t*          d            d S )N   r   gffffff@         T   F)
diracdeltawrt)r%   c                  P    t          t                                        d          S Nr#   )r   xfdiff     /var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/sympy/functions/special/tests/test_delta_functions.py<lambda>z!test_DiracDelta.<locals>.<lambda>P   s    z!}}':':1'='= r,   c                  ,    t          t          d          S )N)r   r)   r+   r,   r-   r.   z!test_DiracDelta.<locals>.<lambda>Q   s    z!R00 r,   c                  *    t          t                    S Nr   r   r+   r,   r-   r.   z!test_DiracDelta.<locals>.<lambda>R   s    z!}} r,   c                  6    t          ddt          z  z             S Nr#   r$   r3   r+   r,   r-   r.   z!test_DiracDelta.<locals>.<lambda>S   s    z!ac'22 r,   )r   r   r)   ir   r   r   funcr   yr   r   diff	is_simpler   expandabsr   r   r   r   
ValueErrorr+   r,   r-   test_DiracDeltar>      s   a==Ac??arc??aaq    az!}},,,,a==Aa==Aa==Ac??c!!!!a==++++a==++++ :a==!!Z]]2222:a!e$$%%AE):):::::Z]]##z!}}4444ZA&&'':a!e+<+<<<<<Z]]##z!}}4444ZA&&'':a!e+<+<<<<<a==a  Jq!$4$44444a  ##z!Q'7'77777a==""1%%----ac??$$Q''4////ad%%a((E1111d1gg((++u4444a==""1%%....ac??!!Tq!99Z]]3q66=QQQQQac??!!Tq!99Z]]3q66=QQQQQad1f$$!$<<
1a4PQ6@R@RRRRRa==4Q77:a==HHHHq1uq1uoq1u-..5515MM1q5!jQ///*QU2C2CA2EEG G G G ac??jmm++++a==JrNN****qb!
1a 0 00000qb!Aq!1!1 11111rc!e
2a4 0 00000a!e
1q5 1 11111Jq1u%%
1q5(9(99::a????ac??!!Tq!99Z]]3q66=QQQQQac??!!Tq!99Z]]3q66=QQQQQad1f$$!$<<
1a4PQ6@R@RRRRRa==4Q77:a==HHHHq1uq1uoq1u-..555FFq1ua*QU"3"33jQ6G6G6IIK K K K ==>>>
:00111
:,,---
:2233333r,   c                     t          d          dk    sJ t          d          dk    sJ t          d          t          j        k    sJ t          dt                    t          k    sJ t	          t           t          t
                    sJ t          dt
                    t
          k    sJ t          t          d          } t          t          t          j                  }t          t          d          }| j        | j        cxk    rt          dfk    sn J |j        |j        cxk    rt          dfk    sn J |j        t          t          j        fk    sJ |j        t          fk    sJ t          t          t                              t          t                    k    sJ t          t          t          t          z
                      t          t          t          z
            k    sJ t          t          t                              t          t                    k    sJ t          t          t          t          z
                      t          t          t          z
            k    sJ t          t          t                              t          t                    k    sJ t          t          t          t          z
                      t          t          t          z
            k    sJ t          t                                        t                    t          t                    k    sJ t          t          t          z             j        du sJ t          t          t          z            j        du sJ t!          t"          d            t!          t$          d            t!          t$          d            d S )Nr   r    Tc                  P    t          t                                        d          S r(   )r   r)   r*   r+   r,   r-   r.   z test_heaviside.<locals>.<lambda>s   s    y||'9'9!'<'< r,   c                  *    t          t                    S r2   r   r   r+   r,   r-   r.   z test_heaviside.<locals>.<lambda>t   s    y|| r,   c                  6    t          ddt          z  z             S r5   rC   r+   r,   r-   r.   z test_heaviside.<locals>.<lambda>u   s    yQqS11 r,   )r   r	   Halfr)   r   r   argspargsr   r8   r   r   r9   r   r   is_Functionr   r   r=   )h0h12h1s      r-   test_heavisiderL   V   s   R==AQ<<1Q<<16!!!!Q??aYq#&&&&&Q####
Aq//B
Aqv

C
Aq//B7bh((((1a&((((((7bh((((1a&((((((816{""""99Q<<  IaLL00009QU##$$	!a%(8(88888Yq\\""ill2222Yq1u%%&&)AE*:*:::::Yq\\""ill2222Yq1u%%&&)AE*:*:::::Q<<Q:a==0000QU'4////QqS>>%----
<<===
:++,,,
:1122222r,   c                     t          dd          t          d          }} t          |                               t                    t          d| dk     ft          d          t	          | d          fd          k    sJ t          |                              t                    t          d|dk     ft          d          t	          |d          fd          k    sJ t          | |                              t                    t          d| dk     f|t	          | d          fd          k    sJ t          | d                              t                    t          d| dk    fd          k    sJ t          | d                              t                    t          d| dk     fd          k    sJ t          | t
                                        t                    t          d| dk     ft
          t	          | d          fd          k    sJ t          |                               t                    t          | t          d                                        t                    cxk    rt          t          |           d	z  t          d          d	z  z   t	          t          d          t          d          d	z            ft          t          |           d	z  t          d          d	z  z   t          | d          ft          d          df          df          k    sn J t          |                              t                    t          |          k    sJ t          | t          j	                                      t                    t          |           dz   d	z  k    sJ t          | |                              t                    t          t          |           d	z  t          d          d	z  z   t	          |t          d          d	z            ft          t          |           d	z  t          d          d	z  z   t          | d          f|df          df          k    sJ t          |                              t                    t          t          d          t	          |d          fd
          k    sJ t          |d                              t                    t          |d          k    sJ t          | dz
                                t                    t          t          d          t	          | dz
  d          fd
          k    sJ | t          | dz
            z                      t                    | t          | dd          z  k    sJ d| z  |z  t          |d                              t                    z  d| z  |z  t          |dd          z  k    sJ t          d                              t                    t          ddd          k    sJ t          dd                              t                    t          ddd          k    sJ t          |                               t                    t          | dd          k    sJ d| z  |z  t          |dz                                 t                    z  d| z  |z  t          |dd          z  k    sJ | dz
  dz  t          | dz
            z                      t                    | dz
  dz  t          | dd          z  k    sJ t          d                              t                    t          j	        k    sJ d S )Nr)   T)realr8   r   )r    Tr    )H0r#   )r   Tr!   
   r0   r$   )r
   r   rewriter   r   r   r   r	   r   rE   r   r   )r)   r8   s     r-   test_rewriterS   x   s   #D!!!6#;;qAQ<<	**1a!e*y||R1XX6	BBD D D DQ<<	**1a!e*y||R1XX6	BBD D D DQ??""9--1a!e*q"Q((mY779 9 9 9Q??""9--1a1f+y))+ + + +Q??""9--1a!e*i((* * * *Q$$Y//1a!e*sBq!HHoy99; ; ; ; Q<<%%!	!%%%--d33
 
 
 
!WWQY1aIaLL!A$$q&!9!9:aQqTT!V#R1XX.1t0DF FGKM	
 	

 
 
 
 
 
 Q<<%%15555Q''--$q''!)Q>>>>Q??""4((!WWQY1aAqttAv/aQqTT!V#R1XX.D	; ;<@B	
 	

 
 
 
 a==  ++y*Q--Aq9RT]/^/^^^^^a##I..*Q2B2BBBBBa!e$$Y//:a=="QUA,,/;;= = = = jR   ))*=>>!DWXY[]_aDbDbBbbbbbQ3q5Aq!!))*=>>>!A#a%H[\]_`bdHeHeBeeeeea==  !4559LQPQSU9V9VVVVVa##$788<OPQSTVX<Y<YYYYYQ<< 3448KAqRS8T8TTTTTQ3q51q5!!))*=>>>!A#a%H[\]_acdHeHeBeeeeeUQJyQ'''001DEE!a%RSTghiklnoTpTpIpppppQ<< 344>>>>>>r,   N)+sympy.core.numbersr   r   r   r   sympy.core.relationalr   r   sympy.core.singletonr	   sympy.core.symbolr
   r   $sympy.functions.elementary.complexesr   r   r   r   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   'sympy.functions.special.delta_functionsr   r   -sympy.functions.special.singularity_functionsr   sympy.simplify.simplifyr   sympy.testing.pytestr   sympy.core.exprr   sympy.core.functionr   r)   r8   r6   r   r   r>   rL   rS   r+   r,   r-   <module>ra      s   / / / / / / / / / / / / * * * * * * * * " " " " " " / / / / / / / / V V V V V V V V V V V V 9 9 9 9 9 9 : : : : : : K K K K K K K K M M M M M M , , , , , , ( ' ' ' ' ' % % % % % % 2 2 2 2 2 2 wu~~1GCGC$GC$:4 :4 :4z3 3 3D-? -? -? -? -?r,   