
    sg7                     .   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 d dlmZmZ d dlmZ d d	lmZmZmZmZmZmZ d d
lmZ d dlmZmZmZmZmZmZ d dl m!Z!  ed      Z"e"jG                         \  Z$Z%Z&e"jO                         \  Z(Z)Z* e       Z+ e	d      \  Z,Z-Z.Z/d Z0d Z1e"je                  de/e"jL                        Z3de(dz  z  e)z  e*z  Z4 ee4      Z5e)dz  e$z  de(z  e%z  z   de)z  e*z  e&z  z   Z6 ee6      Z7d Z8d Z9d Z:d Z;d Z<d Z=d Z>y)    )
Derivative)Vector)
CoordSys3D)simplify)symbols)S)cossin)Dot)curl
divergencegradientGradient
DivergenceCross)Del)is_conservativeis_solenoidalscalar_potentialdirectional_derivative	laplacianscalar_potential_difference)raisesCza b c qc                  #   t         t        j                  z  t        j                  k(  sJ t         t        j                  z  j                         t        j                  cxk(  rt	        t        j                        k(  sJ  J t         j                  t        j                        t         t        j                  z  k(  sJ t         t        z  j                         t        j                  k(  sJ t         j                  dt        dz  z  t        z  d      t        j                  k(  sJ t         j                  dt        dz  z  t        z        t         dt        dz  z  t        z  z  k(  sJ t        t        z  t        z  t        t        z   t        z   z  } t         | z  j                         t         t        z  t        t        z  z   t        z  t        t        z  t        t        z  z
  t        z  z   t         t        z  t        t        z  z   t        z  z   cxk(  rt	        |       k(  sJ  J t         | z  t         j                  |       k(  sJ t         j                  dt        dz  z  t        z        t        dt        j                        t        dt        j                  dz  z  t        j                        z
  t        j                  z  t        dt        j                         t        dt        j                        z   t        j                  z  z   t        dt        j                         t        dt        j                  dz  z  t        j                        z   t        j                  z  z   k(  sJ t         j                  dt        dz  z  t        z  d      dt        z  t        z  cxk(  r t	        dt        dz  z  t        z        k(  sJ  J t         t        j                  z  t        j                  cxu rt!        t        j                        k(  sJ  J t         t        j                  z  j                         t        j                  u sJ t         j#                  t        j                        t         t        j                  z  k(  sJ t         t        z  j                         t        j                  u sJ t         t        dz  t        z  z  j                         dt        z  cxk(  rt!        t        dz  t        z        k(  sJ  J t         j#                  | d      t        t        z  t        t        z  z   t        t        z  z   cxk(  rt!        |       k(  sJ  J t         | z  t         j#                  |       k(  sJ t         j#                  dt        t        z  t        z  z  t        t        z   t        z   z  d      dt        t        z  t        dz  z  z  dt        t        dz  z  t        z  z  z
  dt        dz  t        z  t        z  z  z
  k(  sJ t        t        z  t        t        z  z   t        t        z  z   } t         | z  t        t        j                  t        j                        t        t        j                  t        j                        z   t        t        j                  t        j                        z   k(  sJ t         j#                  | d      dcxk(  rt!        |       k(  sJ  J t         | z  t         j#                  |       k(  sJ t%        t         | z  j                               dk(  sJ t         j'                  dd      t        j                  cxk(  rt'        d      k(  sJ  J t         j'                  d      t        d      k(  sJ t        t        j                        j                         t        j                  k(  sJ t        t              t        t        j                  t        j                        t        j                  z  t        t        j                  t        j                        t        j                  z  z   t        t        j                  t        j                        t        j                  z  z   k(  sJ t        t              j                         t        cxk(  rt'        t              k(  sJ  J t        t        t        z  t        z        t        t        j                  t        j                  z  t        j                  z  t        j                        t        j                  z  t        t        j                  t        j                  z  t        j                  z  t        j                        t        j                  z  z   t        t        j                  t        j                  z  t        j                  z  t        j                        t        j                  z  z   k(  sJ t         j'                  t        t        z  t        z  d      t        t        z  t        z  t        t        z  t        z  z   t        t        z  t        z  z   cxk(  r!t'        t        t        z  t        z        k(  sJ  J t        t        t        z  t        z        t         j'                  t        t        z  t        z        k(  sJ t        dt        dz  z        j                         dt        z  t        z  k(  sJ t        t(        t+        t              z  t        z        j                         t(         t+        t              z  t        dz  z  t        z  t(        t-        t              z  t        z  t        z  z   k(  sJ t        j                  t         z  t(              t        j                  u sJ t        j                  t         z  t(              j                         t        j                  u sJ  | t         z  t        j                        j                         t        j                  k(  sJ  | t         z  t        j                        j                         t        j                  u sJ t        t         z  t              j                         dk(  sJ t        t         z  t              j                         dk(  sJ t        t         z  t              j                         dk(  sJ t        t         z  t        t        z  t        z        j                         t        t        z  k(  sJ  | t         z  t              j                         t        k(  sJ  | t         z  t        t        z  t        z        j                         dt        z  t        z  t        z  k(  sJ  | t         z  t        t        z   t        z         t        j                  t        j                  z   t        j                  z   k(  sJ  | t         z  t        t        z   t        z         j                         t        t        z   t        z   k(  sJ  | t         z  |       j                         | k(  sJ t        t         z  |       j                         t        k(  sJ t        t         z  |       j                         t        k(  sJ t        t         z  |       j                         t        k(  sJ  | t         z  t        j                        j                         t        j                  k(  sJ t/        t        t        z  t        z        t        j                  u sJ t/        t        dz        t        d      k(  sJ t/        t        dz  t        dz  z  t        dz  z        dt        dz  z  t        dz  z  dt        dz  z  t        dz  z  z   dt        dz  z  t        dz  z  z   k(  sJ t1        d	d
g d      }t1        ddg d      }t/        |j2                  |j4                  z   |j6                  z         d|j2                  z  t-        |j4                        |j2                  dz  t+        |j4                        z  z  z   k(  sJ t/        |j2                  |j4                  z   |j                  z         d|j2                  z  k(  sJ t/        t        t        z  t        z  t        t        z   t        z   z        t        j                  k(  sJ t/        t        t        dz  z  t        z  t        t        z   t        z   z        dt        z  t        z  t        z  dt        z  t        z  t        z  z   dt        z  t        z  t        z  z   k(  sJ y )N   Tdoitr            A	sphericalrthetaphitransformationvariable_namesBcylindricalr&   r'   z)delopr   zeror   r   crossiyjxr/   kr   r   r   Zeror   dotr   r   ar
   r	   r   r   r&   r'   r(   )vr#   r,   s      Z/var/www/html/venv/lib/python3.12/site-packages/sympy/vector/tests/test_field_functions.pytest_del_operatorr=      s    6;;&++---V[[ &&(FKK     ;;v{{#uv{{'::::AI,,,;;qAvaxd;+v{{:::;;qAvax EAadF1H$4444	!AQAQYRTAaCZNacAaCi]*qbdQqSj!^;G     19A&&&KK!Q$q!133*QqssAvXqss";;QSS@ACC  :a#55qss:;ACC  :aQh#<<accABB C B KK!Q$qtK,!A 1a4N     6;;!&&CJv{{,CCCCCCFKK%%'16611199V[[!UV[[%8888AI'''AqDFN  "ac?Z1Q-??????IIadI#qsQqSy1Q3 qM    19		!$$$99Q!AY!a%!),498!A#ad(a1QT6!8n,qAqDF1H~=> > >	!ac	AaCAAIACC-qssACC !#-acc133#78 8 9 899QT9"a8:a=8888819		!$$$UQY$$&'1,,, NN14N(FKK QK    >>!a(((!&&M!V[[000!HACC-qss2QSS!133&'*4QSS!##*>)CD D E D!H??0Xa[00000!A#a%LACCQSS)133.ACCQSS)133./ACCQSS)133.// 0 / NN1Q3q5tN,aCEAaCEMAaCE!QqSUO     1Q<5>>!A#a%0000!AqD&M!QqSU***1SV8a< &&(Bs1vIadNQ3q6!a/0 1 0 KK%#qvv---[[5 !$**,666QY$**,;;;QY%%'166111YN  "a'''YN  "a'''YN  "a'''Y!A$$&!A#---QYN  "a'''QY!A$$&!A#a%'111AIq1uqy!QSS133Y_444QYA	"((*a!eai777QYN  "a'''YN  "a'''YN  "a'''YN  "a'''QY$**,;;; QqSUqvv%%%QT?ad"""QT!Q$Yq!t^$adF1a4K!AqD&A+-!Q$q!t;< < <3{CXYA3}EXYAQSS177]QUU*+qus177|QSS!VCPQPWPWLEX7Y/YYYYQSS177]QSS()QqssU222 QqSUAEAI&'6;;666Qq!tVAXq1uqy)*aCE!Gac!eAg-!Aa78 8 8    c                     dt         z  t        z  t        z  } t         t        z  t        t        z  z   t        t         z  z   }t         dz  t        z  dt        z  z   t        dz  t        z  t
        z  z
  }dt        z  t         t        z  t        z  t
        z  z   }t        | |z  d      }| t        |      z  |t        |       z  z   j                         }t        |      t        |      k(  sJ t        ||z        j                         }|t        |z  z  |t        |z  z  z    |t        z  |      z    |t        z  |      z   j                         }t        |      t        |      k(  sJ t        | |z  z  j                         }| t        |z  z  |t        |       z  z   j                         }t        |      t        |      k(  sJ t        ||z  z  j                         }|t        |z  z  |t        |z  z  z
  j                         }t        |      t        |      k(  sJ t        | |z  z  j                         }t        |       |z  | t        |z  z  z   j                         }t        |      t        |      k(  sJ t        ||z  z  j                         }|t        |z  z  |t        |z  z  z
   |t        z  |      z    |t        z  |      z
  j                         }t        |      t        |      k(  sJ y)z
    Tests the six product rules defined with respect to the Del
    operator

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Del

    r   r   Tr   N)	r6   r4   r/   r3   r5   r7   r0   r   r   )fgur;   lhsrhss         r<   test_product_rulesrE   v   s    	
!AaA	!ac	AaCA	1Q1q!tAvaxA	!ac!eAgA AD
!CuQx<!eAh,&
,
,
.CC=HSM))) A,


COUQY0AIq>(q5y!n./3tv C=HSM))) AaC=


 COU1X/
5
5
7CC=HSM))) AE?
 
 
"COUQY0
6
6
8CC=HSM))) AE?
 
 
"C1XNqEAI/
5
5
7CC=HSM))) AE?
 
 
"C	?Q%!)_,AIq>&QYN+,0DF C=HSM)))r>   Pr   r"      c                     t        t        j                        du sJ t        t              du sJ t        dt        z  dt        z  z   dt
        z  z         du sJ t        t        t        z  t        z  t        t        z  t        z  z   t        t        z  t
        z  z         du sJ t        t        t        z        du sJ t        t              du sJ t        t              du sJ t        dt        z  t        z  t        z  t        z  dt        dz  z  t        z  t        z  z         du sJ t        t        t        j                  z  t        j                  t
        z  z         du sJ y )NTr   r"   r   F)r   r   r1   r3   r5   r7   r4   r/   r6   
grad_field
curl_fieldrF    r>   r<   test_conservativerL      s2   6;;'4///1%%%1q51q5=1q501T999AaCEAaCEMAaCE12  1q5!U***:&$...:&%///AaCE!GAI!Q$q
23  1QSS5133q5=)T111r>   c                  <   t        t        j                        du sJ t        t              du sJ t        dt        z  dt        z  z   dt
        z  z         du sJ t        t        t        z  t        z  t        t        z  t        z  z   t        t        z  t
        z  z         du sJ t        t        t        z        du sJ t        t              du sJ t        t              du sJ t        dt        z  dz   t
        z        du sJ t        t        t              t        z  t        t              t        z  z   t        t              t        j
                  z  z         du sJ t        t        t        j                  z  t        j                  t
        z  z         du sJ y )NTr   r"   r   F)r   r   r1   r3   r5   r7   r4   r/   r6   rI   rJ   r	   qr
   rF   rK   r>   r<   test_solenoidalrP      sK   %---t###QQQ./4777!A#a%!A#a%-!A#a%/0  Q5((($---$,,,"Q$(A&$...QCF1H,s1vaccz9:dBBB133Q'4///r>   c                     t        t        j                  t        j                  z  t        j                  z  dt        j
                  z  dt        j                  z  z   t        j                  z         t        j                  t        j                  z  dt        j                  z  t        j                  z  z   dt        j                  z  t        j                  z  z   k(  sJ t        dt        j                  dz  z  t        j                  z  dt        j
                  z  dt        j                  z  z   t        j                  z         dt        j                  dz  z  dt        j                  z  t        j                  z  z   k(  sJ t        dt        j                  dz  z  t        j                  z  dt        j                  z        t        j                  u sJ t        ddg dg d	
      } | j                         \  }}}| j                         \  }}}t        |dz  |z  |      d|z  |z  k(  sJ t        d|dz  z  |z  d|z  d|z  z   |z         d|dz  z  d|z  |z  z   k(  sJ y )Nr"   r   rG   r      Dr$   r%   )e_re_thetae_phi)r+   vector_names)r   r   r6   r4   r/   r3   r5   r7   r   r8   r   base_scalarsbase_vectors)rS   r&   r'   r(   rT   rU   rV   s          r<   test_directional_derivativerZ      s   !!##acc'!##+ququ}qss/BCqss133wQRSTSVSVQVWXWZWZQZGZ]^_`_b_b]bcdcfcf]fGffff!!ACCF(133,!##!##0CD!##q&SUVWVYVYSYZ[Z]Z]S]H]]]]!!ACCF(133,!##6!&&@@@34I ;	=ANN$MAuc..*C%!!Q$s(C0AaCG;;;!!AqD&*aeai.?%.GHAaQRdFUWXYUYZ]U]L]]]]r>   c                     t        t        j                  t              dk(  sJ t        t        t              t
        k(  sJ t        t        t              t        k(  sJ t        t        t              t        k(  sJ t        t        t        z  t        z  t
        t        z  t        z  z   t
        t        z  t        z  z   t              t
        t        z  t        z  k(  sJ t        t        t              t        k(  sJ t        t        t        j                  z  t        j
                  t        z  z   t              t
        t        z  t        t              z  t        t        z  t        t              z  z   k(  sJ t        t        t        j                  z  t        j
                  t        z  z   t              t        j
                  t        j                  z  k(  sJ t!        t"        d        y )Nr   c                  8    t        t        t        z  t              S )N)r   r6   r5   r   rK   r>   r<   <lambda>z'test_scalar_potential.<locals>.<lambda>   s    /!Q7 r>   )r   r   r1   r   r3   r6   r5   r4   r7   r/   rI   scalar_fieldrF   r	   rO   r
   r   
ValueErrorrK   r>   r<   test_scalar_potentialr`      s3   FKK+q000Aq!Q&&&Aq!Q&&&Aq!Q&&&AaCEAaCEMAaCE1151Q>>>J*l:::AaccEACCEM1-1SVac#a&j1HHHHAaccEACCEM1-QSS888
:78r>   c                  F   t         j                  j                  ddt        z  dt        z  z   dt
        z  z         } t         j                  j                  ddt        z  dt        z  z   dt
        z  z         }t         j                  j                  d	t        t        z  t        t        z  z   t        t
        z  z         }t        j                  j                  d
t        j                  t        j                  z  t        j                  t        j                  z  z   t        j                  t        j
                  z  z         }t        t        j                  t         | |      dk(  sJ t        t        t         t         j                  |      t        k(  sJ t        t        t         t         j                  |      t        k(  sJ t        t        t         | |      dk(  sJ t        t        t        z  t        z  t        t        z  t        z  z   t        t        z  t
        z  z   t         | |      t        t        z  t        z  dz
  k(  sJ dt        j                  z  t        j                  t        t               z  t        j                  t#        t               z  z   z  t        j                  t#        t               z  t        j                  t        t               z  z
  dz  z  }t        t        t        t        j                  |      j%                         |j%                         k(  sJ y )NP1r    r   r"   P2r   rG      RPPPr   i  )r   origin
locate_newr3   r5   r7   r6   r4   r/   rF   r   r   r8   r^   rI   r
   rO   r	   r   )point1point2genericpointCgenericpointPpotential_diff_Ps        r<    test_scalar_potential_differencern      s5   XX  qsQqSy1Q37FXX  qsQqSy1Q37FHH''acAaCi!A#o>MHH''acc!##gACC.?!##acc'.IJM&qvvq&&AQFFF'a(57   (
Aqxx(57   'z1ffELLL'!A!A()!A)./0&(57 aCEAI   !##qss3q6zACCAJ67SVacc#a&j0145'
Aqxx(577?xz%%'( ) (r>   c                     t        ddg d      } t        ddg d      }t        d| j                  z  d	| j                  z  z         d| j                  z  d	| j                  z  | j
                  z  z   k(  sJ t        d| j                  z  | j                  z  d	| j                  z  z         d| j                  z  | j                  z  d	| j                  z  | j
                  z  z   dt        | j                        z  | j                  z  z   k(  sJ t        d
| j                  z  d
| j                  z  z   d
| j                  z  z         t        j                  k(  sJ t        | j                  | j                  z  | j                  z        | j                  | j                  z  | j                  z  | j                  | j
                  z  z   | j                  t        | j                        z  | j                  z  z   k(  sJ t        | j                  | j                  z  | j                  | j
                  z  z   | j                  | j                  z  z         t        | j                        | j                  z  t        | j                        | j                  z  | j                  z  z   t        | j                        | j                  dz  z  z  dz   dt        | j                        | j                  z  z  z   k(  sJ t        d| j                  z  | j                  z  | j                  z  | j                  | j
                  z  z   | j                  | j                  z  | j                  z  | j                  z  z         t        | j                        | j                  z  t        | j                        | j                  z  | j                  z  z   t        | j                        | j                  dz  z  z  d| j                  z  z   | j                  t        | j                        z  z   k(  sJ t        t        j                        d
k(  sJ t        d
| j                  z  d
| j
                  z  z   d
| j                  z  z         d
k(  sJ t        | j                  | j                  z  | j                  | j
                  z  z   | j                  | j                  z  z         t        | j                        | j                  z  t        | j                        | j                  z  z  | j                  z  | j                   | j                  z  | j
                  z  z   | j                  | j                  z  | j                  z  z   k(  sJ t        | j                  | j
                  z  | j                  | j                  z  z         t        | j                        | j                  z  t        | j                        | j                  z  z  | j                  z  | j                   | j                  z  | j
                  z  z   d| j                  z  z   k(  sJ t        d
|j                  z  d
|j                  z  z   d
|j                  z  z         t        j                  k(  sJ t        |j                  |j                  z  |j                  z        |j                  |j                  z  |j                  z  |j                  |j
                  z  z   |j                  |j                  z  |j                  z  z   k(  sJ t        d|j                  z        d|j                  z  k(  sJ t        d|j                  z        d|j                  z  |j
                  z  k(  sJ t        d	|j                  z        d	|j                  z  k(  sJ t        |j                  |j                  z  |j                  |j
                  z  z   |j                  |j                  z  z         dd|j                  z  z   k(  sJ t        |j                  |j
                  z  |j                  |j                  z  z         dk(  sJ t        |j                  |j
                  z  |j                  |j                  z  z         d|j                  z  k(  sJ t        d|j                  z  d|j                  z  |j
                  z  z   d	|j                  z  z         t        j                  k(  sJ y )Nr#   r$   r%   r)   r,   r-   r.   r"   r   r   r   r    	   )r   r   r&   r'   r3   r5   r(   r
   r7   r   r1   r   r	   r   r/   )r#   r,   s     r<   .test_differential_operators_curvilinear_systemrq      s   3{CXYA3}EXYAAaccEAaggI%&!ACC%!ACC%)*;;;;AaccE!%%K!AGG)+,!%%aeACCi0G1SQRQXQX\>[\[^[^J^0^^^^AaccEAaggI%ag-.&++===ACCK%&!''!%%-*;aeeACCi*G177SVWXW^W^S_K_abadadJd*ddddaccACCi!''ACC-/!%%!##+=>Ls177|ACC/77#agg,qssAv:MNQRRUVX[\]\c\cXdefehehXhUiij j jaeAEEk!##o3acc!''k!%%6G6KKLLs177|ACC/77#agg,qssAv:MNQRSTSXSXQXX[\[b[bcfghgngnco[oop p pfkk"a'''aeaemae+,111ACC!''!##+%acc	12LAGGQSS 011336155&*acc9IIAGGTUTWTWKXYX[X[O[\ \ \ACC!%%)#$QWWaee);S\!##=M)NPQPSPS(SXYX]X]W]^_^a^aWacdcfcfVf(fijklknknin(nnnn AaccEAaggI%ae+,;;;ACCKO$ACC!##acc'(AACCKPQPSPSO(SSSSAaccE?ae###AaggI!ACC%!##+---AaccE?ae###acc!##g+acc!##g56!ae)CCCacc!##gACC'(A---ACC!##acc'!"ae+++!##!##acc	!AaccE)*fkk999r>   c            
      0   t        d      } t        d      }t        d      }t        | j                  |j                  z        |j                  | j                  z  | j                  |j
                  z  z   k(  sJ t        dt        t              z  | j                  z  |j                  z  | j                  | j                  t        t              |j                  z   z   z  z         | j                  d|j                  z  t        t              z  z   | j                  z  | j                  |j                  z   t        t              z   | j
                  z  z   d| j                  z  t        t              z  | j                  z   |j                  z  z   k(  sJ t        | j                  |j                  z        t        | j                  |j                  z        k(  sJ t        t        | j                  |j                  z              t        t        | j                  |j                  z              k(  sJ t        dt        t              z  | j                  z  |j                  z  | j                  z  | j                  z  |j                  |j                  z  z   t        | j                  | j                  z         |j                  z  z         d| j                  z  | j                  z  |j                  z  t        t              z  |j                  t        | j                  | j                  z         z  z
  | j                  z  d| j                  z  | j                  z  |j                  z  t        t              z  |j                  t        | j                  | j                  z         z  z
  | j
                  z  z   d| j                  z  | j                  z  |j                  z  t        t              z  | j                  z  z   d| j                  z  | j                  z  | j                  z  t        t              z  |j                  z  z   |j                  |j
                  z  z   |j                  t        | j                  | j                  z         z   |j                  z  z   k(  sJ t        | j                  | j                  z  | j
                  | j                  z  z   | j                  | j                  z  z   |j                  |j                  z  z   |j
                  |j                  z  z   |j                  |j                  z  z   |j                  |j                  z  z   |j
                  |j                  z  z   |j                  |j                  z  z         t        d      k(  sJ t        d| j                  z  | j                  z  | j                  z  |j
                  |j                  z  |j                  z  z   d| j
                  z  | j                  z  | j                  z  z         d| j                  z  |j                  t        |j
                  |j                        z  z   k(  sJ t        dt        t              z  | j                  z  |j                  z  |j                  z  |j                  z        d| j                  z  |j                  z  t        t              z  t        |j                  |j                        z  d| j                  z  |j                  z  t        t              z  z   d|j                  z  |j                  z  t        t              z  t        |j                  | j                        z  z   k(  sJ t        | j                  |j                  z  |j                  z  t        | j                  | j                  z  | j                  |j
                  z        z        | j                  |j                  z  |j                  z  t!        t        | j                  | j                  z  | j                  |j
                  z              z  |j                  |j                  z  t        t        | j                  | j                  z  | j                  |j
                  z        | j                        z  z   | j                  |j                  z  t        t        | j                  | j                  z  | j                  |j
                  z        |j                        z  z   | j                  |j                  z  t        t        | j                  | j                  z  | j                  |j
                  z        |j                        z  z   k(  sJ t        | j                  |j                  z  |j                  z  | j                  | j                  z  |j                  |j                  z  z   z        d| j                  z  |j                  z  |j                  z  | j                  dz  |j                  z  t        | j                  |j                        z  z   | j                  dz  |j                  z  t        | j                  |j                        z  z   |j                  dz  |j                  z  t        |j                  | j                        z  z   | j                  |j                  dz  z  t        |j                  |j                        z  z   k(  sJ y )	Nr:   bcr"   rp   rd   r   r   )r   r   r6   r4   r3   r5   r	   rO   r   r/   r
   r7   r   r   r   r   r   )r:   rs   rt   s      r<   test_mixed_coordinatesru     s   3A3A3AACCGACC!##acc' 1111Ac!fHQSSL$QSS!##s1vaccz*:%;;<CC!ACC%A,#qssQSSy3q6'9133&>>!ACC%A,QRQTQTBTVWVYVYAYYZ Z Z
 ACCH!##qss(!3333CACCL!Xc!##acc'l%;;;;Ac!fHQSSL$QSS(,acc!##g5ACCGQSS8HHIaccE!##IaccM#a& 133s1339~#55qss:accE!##IaccM#a& 133s1339~#55qss:;>?eACCimCPQF>RTUTWTW=WXaccE!##IaccM#a& !##%&()ACC03433QSS133Y3G2LMM M M
 acc!##gacc!##goacc!##g-ACC7ACC?ACCG!##acc'QRSRURUVWVYVYRYYZ[Z]Z]^_^a^aZaabfghifjjjjaeACCimacc!##gacck1AaccE!##IaccMABaccEACCACC%%& & &aAhqssl133&qss*133./	!##acc	#a&QSS!##&133qss3q6)99AaccE!##Ic!f<LSQRQTQTVWVYVY]<ZZ[ [ [acc!##gacck%ACCQSS"99:33qss7133;z%ACCQSS"9::33qss73uQSSWacc!##g.44533qss73uQSSWacc!##g.445 33qss73uQSSWacc!##g.4455 5 5
 acc!##gacck133qss7QSSW#456!##acc	!##Qqss
3qssACC=()Qqss
3qssACC=() Qqss
3qssACC=() ACCF
3qssACC=(	)) ) )r>   N)?sympy.core.functionr   sympy.vector.vectorr   sympy.vector.coordsysrectr   sympy.simplifyr   sympy.core.symbolr   
sympy.corer   (sympy.functions.elementary.trigonometricr	   r
   r   sympy.vector.operatorsr   r   r   r   r   r   sympy.vector.deloperatorr   sympy.vector.functionsr   r   r   r   r   r   sympy.testing.pytestr   r   rY   r3   r5   r7   rX   r6   r4   r/   r0   r:   rs   rt   rO   r=   rE   orient_new_axisrF   r^   rI   vector_fieldrJ   rL   rP   rZ   r`   rn   rq   ru   rK   r>   r<   <module>r      s   * & 0 # %  ? # Z Z (L L (sO
..
1a
..
1aY
1a\8~0*f c1acc"Avaxzl#
!tAv!A~!Aa',
20
^	9)0:B#)r>   