
    g.M                        d dl Z d dlmZ d dl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 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mZmZ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(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZD d dlEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZM d dlNmOZOmPZP d dlQmRZRmSZS d dlTmUZU d dlVmWZW eOd         ZXd ZYd ZZd Z[d Z\d Z]d Z^d Z_d Z`d Zad Zbd Zcd Zdd  Zed! Zfd" Zgd# Zhd$ Zid% Zjd& Zkd' Zld( Zmd) Znd* Zod+ Zpd, Zqd- Zrd. Zsd/ Ztd0 Zud1 Zvd2 Zwd3 Zxd4 ZydS )5    N)Add)Functiondiff)NumberRational)S)Symbolsymbols)Abs)explog)sqrt)sin)	integrate)amount_of_substancearea
convert_to	find_unitvolume	kilometerjoulemolar_gas_constantvacuum_permittivityelementary_chargevoltohm)amuau
centimetercoulombdayfootgramshourinchkgkmmmeter
millimeterminutequartssecondspeed_of_lightbitbytekibibytemebibytegibibytetebibytepebibyteexbibytekilogramgravitational_constantelectron_rest_mass)	Dimensionchargelengthtimetemperaturepressureenergymass)PREFIXESkilo)PhysicalConstantQuantity)SI)raiseskc                  :    t          t                    dk    sJ d S )Nr8   )strr&        e/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/physics/units/tests/test_quantities.pytest_str_reprrO   #   s    r77j      rM   c                  f    dt           z  dt           z  k    sJ dt           z  dt          z  k    sJ d S )N
   )r(   r-   rL   rM   rN   test_eqrR   '   s0    a42a4<<<<a42a4<<<<<<rM   c                  z   t          d          } |                     t          d          t                     |                     t
                    dt
          z  k    sJ t          j        t
          t          z            dt
          z  t          z  k    sJ t          j        t                    dt          z  k    sJ |                     t                    | k    sJ t          j        t
                    t          k    sJ t          t          z  }t	          |t                    }|t          t          z  k    sJ d S )Nq1  iJxiQ )rF    set_global_relative_scale_factorr   r)   r   r(   r/   r-   r!   r   r.   )qexprconvs      rN   test_convert_torZ   -   s    A&&qww666<<??d1f$$$$$QU++y1}q/@@@@@>!a'''' <<??a$Q''>9999<DdE""D5<rM   c                     t          dd          } |                     dt                     t          dd          }|                    dt                     t          d          } |j        t          t                     t          d          }|                    dt          z  t                     | j        dk    sJ | j        t          k    sJ | j        t          d          k    sJ |j        t          k    sJ |j        dk    sJ |j        t          d          k    sJ |j        d	k    sJ  |j        |j         |k    sJ  |j        |j         j        |j        k    sJ |j        t          k    sJ |j        d
k    sJ d S )Ns10sabbrabbrevrQ   udamr'        rU   )rF   rV   r.   r)   rD   scale_factor	dimensionr>   r_   r	   r=   funcargs)rW   r`   r'   vs       rN   test_Quantity_definitionri   ?   s   w'''A&&r6222U###A&&r5111	$B'B'e444A&&qvu555>R;$8vg&&&&;&    >R8ve}}$$$$?d""""27BG""""27BG!RW,,,,;&    >T!!!!!!rM   c                     t          d          } |                     t          j        t                     | j        t          d          k    sJ | j        t          d          k    sJ t          dd          } |                     t          d          t                     | j        t          d          k    sJ | j        t          d          k    sJ | j        dk    sJ t          | j        t                    sJ t          dd          } |                     dt          z  t                     | j        t          d          k    sJ | j        dk    sJ d S )Nr`   omr^      ikm     )rF   rV   r   Oner)   namer	   r_   rd   
isinstancer   rD   r`   s    rN   test_abbrevrt   Y   s@   A&&que4446VC[[    8vc{{""""T"""A&&qttU3336VC[[    8vd||####>Qanf-----U###A&&qvu5558ve}}$$$$>T!!!!!!rM   c                  |    t          dd          } t          |           dk    sJ t          |           dk    sJ d S )Nunitnamera   r^   )rF   reprrK   rs   s    rN   
test_printrx   o   sH    E***A77j    q66ZrM   c                      t          dd          } t          d          }| |k    sJ t          dd          }| |k    sJ t          dd          }| |k    sJ d S )	Nr`   ra   r^   v1v2dsv3dm)rF   )r`   rh   s     rN   test_Quantity_eqr   u   sn    U###AA6666d###A6666d###A666666rM   c                  j   t          d          } t          d          }t          d          }|                     t          d          t                     |                    t          d          t                     |                    t          d          t                     t          | |z   t                    sJ | |                    |           z   dt          j        z   | z  k    sJ t          | |z
  t                    sJ | |                    |           z
  t          j        | z  k    sJ d S )Nr`   rh   wrQ   rb   rl      )	rF   rV   r   r)   r.   rr   r   r   Half)r`   rh   r   s      rN   test_add_subr      s   AAA&&quue444&&qttU333&&qttV444a!eS!!!!!QQZN2222a!eS!!!!!QAF1H,,,,,,rM   c                     t          d          } t          d          }t          d          }|                     dt          t          z             |                    dt          t          z             |                    dt          t          z             |t	          | |z
            z
  }t          j        |           t          t          z  j	        k    sJ t          t          j        |                    }t          j                                        |          t          dt          dik    sJ t          t          t          dz            k    sJ d S )Nv_w1v_w2v_w3r   rl   )rF   rV   r)   r.   r   rG   get_dimensional_exprr=   r>   rq   r;   get_dimension_systemget_dimensional_dependenciesr   )r   r   r   rX   Dqs        rN   test_quantity_absr      s)   FDFDFD))!U6\:::))!U6\:::))!U6\:::#dTk"""D"4((VD[,>>>>>	2*400	1	1B"$$AA"EEbJ     DNN""""""rM   c                  \   t          d          t          d          } t          d                              t          d          t                     |                     t          d          t                                         t          d          t                     d t          t          fd           t          t          fd	           t          t          fd
           t          t          fd           t          t          fd           d S )Nr`   rh   r   rQ   rb   rl   c                 .    t          j        |            d S N)rG   _collect_factor_and_dimension)rX   s    rN   check_unit_consistencyz;test_check_unit_consistency.<locals>.check_unit_consistency   s    
(.....rM   c                         z             S r   rL   r   r`   r   s   rN   <lambda>z-test_check_unit_consistency.<locals>.<lambda>       55a!e<< rM   c                         z
            S r   rL   r   s   rN   r   z-test_check_unit_consistency.<locals>.<lambda>   r   rM   c                         dz             S Nr   rL   r   r`   s   rN   r   z-test_check_unit_consistency.<locals>.<lambda>   r   rM   c                         dz
            S r   rL   r   s   rN   r   z-test_check_unit_consistency.<locals>.<lambda>   r   rM   c                  @      dt          z            z
            S r   )r   r   s   rN   r   z-test_check_unit_consistency.<locals>.<lambda>   s!    55a#a!e**nEE rM   )rF   rV   r   r)   r.   rH   
ValueError)rh   r   r`   r   s    @@@rN   test_check_unit_consistencyr      s+   AAA&&quue444&&qttU333&&qttV444/ / / :<<<<<<===
:<<<<<<===
:<<<<<===
:<<<<<===
:EEEEEEFFFFFrM   c                     t          d          } t          d          }t          d          }t          d          }t          d          }|                     t          d          t                     |                    t          d          t                     |                    t          d          t                     |                    t          d          t          t          z             |                    t          d          t          t          z             d	| z  | d
z  k    sJ | d	z  | k    sJ | |z  }|}||k    sJ ||                    |          k    sJ | d	z  | k    sJ | |z  }|}||k    sJ ||                    |          k    sJ t          d          }|                    t          d          d	t          z             | |z  dk    sJ | dz  d	k    sJ | d	z  | k    sJ t          d          }	t          d          }
|	                    t          d          t          dz             |
                    t          d	d          d	t          z             | dz  |	k    sJ | d
z  |
k    sJ | dz  |	                    |           k    sJ | d
z  |
                    |           k    sJ d S )Nr`   rh   tutrQ   rb   rl      r   r   lp1r   u2u3d   )rF   rV   r   r)   r.   r   r   )r`   rh   r   r   r{   rz   ut1ut2r   r   r   s              rN   test_mul_divr      s   AAA	$B	#B&&quue444&&qttU333&&qttV444''"uV|<<<''!eFl;;;q5AGq5A::::	
QB	
B 8888r"""""" q5A::::
a%C
C #::::#..%%%%%% 5//C((1qw777s7b====a419999a419999 
$B	$B''#q999''B5AAA6R<<<<7b====6R]]1%%%%%%7bmmA&&&&&&&&rM   c                  &   t          dt          z  t          z  t          z  t          z  d          dk    sJ t          t
          t          z  t                    t          dd          k    sJ t          t          t          t          z  t                                        d                    dk    sJ dt          z  t          z  t          z  } t          t          | t          t          z            t                    } |                                 t          dd	          k    sJ t!          t          dz            t          k    sJ t!          t                    dz  t          k    sJ t#          d
          } t%          | t          z  t          z  | dt          z  dt          z  f          dt          z  t          z  k    sJ | t          z  t          z                      | dt          z  dt          z  f          dt          z  t          z  k    sJ d S )Nrb   r   i  i  i'  rl   z6.0e+23l   !|8. l   eJ r      )r   r(   r-   r!   r'   r"   r)   r   rK   r#   r   nr   r/   r+   simplifyr   r	   r   )r   s    rN   
test_unitsr      s   qs1us{b(!,,3333dUlE**htU.C.CCCCC z%)U++--a0011Y>>>> 
2	&(A:a00%88A::<<8K<<<<<< 1::????GGa<1sAQqSUQ!QqSM**bd1f4444E!G1Q3!}--Aa777777rM   c                      t          dt          z  t          dz  z  t                    dk    sJ t          dt          z  t          dz  z  t                    dk    sJ d S )N   rn      )r   r,   r%   r)   r*   rL   rM   rN   test_issue_quartr     sX    a%i$!)+U33s::::a%i$!)+Z88C??????rM   c                      t          t          t                    dt          z  k    sJ t          t          t                    dt          z  k    sJ d S )Ngy9goR:)r   r:   r8   r#   rL   rM   rN   test_electron_rest_massr   
  sL    ((337G7PPPPP(%004DU4JJJJJJJrM   c                  4    t           t          k     j        sJ d S r   )r(   r-   is_RelationalrL   rM   rN   test_issue_5565r     s    E      rM   c                  :   t          d          g dk    sJ t          t                    g dk    sJ t          t                    g dk    sJ t          t                    g dk    sJ t          t          dz            g dk    sJ t          t          dz            g dk    sJ t          t          dz            g dk    sJ t          t          d	z            g d
k    sJ t          d          g dk    sJ t          t
                    g dk    sJ d S )Nr    )r    coulombscoulomb_constant)Cr    r   planck_charger   )1r(   r   cmr~   ftr'   lymimmnmpmumydnmifeetr"   r%   mileyardr)   milesyardsinchesmetersmicronmicronsangstrom	angstroms	decimeterr   	lightyear	nanometer	picometerr   
decimeters
kilometers
lightyears
micrometerr*   
nanometers
picometerscentimetersmicrometersmillimetersnautical_mileplanck_lengthnautical_milesastronomical_unitastronomical_unitsr   )Ddioptreoptical_powerrl   )hahectareplanck_arearn   )LlcLcldLdlmLmlliterr,   litersquarts	deciliter
centiliter
deciliters
millilitercentilitersmillilitersplanck_volumevoltage)Vrh   r   voltsplanck_voltage)gr   Dar&   memgugr   mmuamusgrammmusr#   poundtonnedaltonpoundsr8   	kilograms	microgram	milligram
metric_ton
micrograms
milligramsplanck_massmilli_mass_unitatomic_mass_unitr:   atomic_mass_constant)r   r    r<   r%   r=   r#   rL   rM   rN   test_find_unitr    s   Y#N#N#NNNNNW!c!c!cccccV b b bbbbbT?? E E E E E E E T2X"C"C"CCCCCVRZ  $E$E$EEEEETQY#C#C#CCCCCTQY $7 $7 $7 7 7 7 7 Y#P#P#PPPPPU  N  N  N N N N N N NrM   c                  j   t          d          } t          | t          z  |           t          k    sJ t          | dz  t          dz  z  |           d| dz  z  t          dz  z  k    sJ t          t          t                    dk    sJ t          t          dz  t                    dt          z  k    sJ d S )Nxrn   rl   r   )r
   r   r)   )r  s    rN   test_Quantity_derivativer  -  s    A%u$$$$1UAXq!!Qq!tVE1H_4444u""""q%  AeG++++++rM   c            	         t          d          } t          d          }t          j        | t          t          dz  z  t
          z  t          z             t          j        |t          t          z  t
          z  t          dz  t          z  z             | |z   sJ | |z   }t          t          j	        |                    }t          j
                                        |          t          dt          dt
          dt          dik    sJ d S )NrT   q2rl   r   r   )rF   rG   set_quantity_dimensionr=   r@   r?   r>   rA   r;   r   r   r   rB   )rT   r  rW   r   s       rN   test_quantity_postprocessingr   5  s    	$B	$Bb&1"4["@"EFFFb&/+"=vqy~"NOOO7NNN
RA	2*1--	.	.B"$$AA"EEaQb	J      rM   c                     dt          d          ft          j        d          k    sJ dt          ft          j        t          t
          z             k    sJ dt          t          z  ft          j        t          t          z  dt
          z  dt          z  z  z             k    sJ t          d          \  } }| |dz  z   t          ft          j        | t          z  |t          z  z             k    sJ t          d	          }t          j        |t          t          z             t!          |           }dt          t          z  ft          j        t#          |                    k    sJ t          d
          }t          d          }|                    t'          dd          t          t          z             |                    dt          t          z             t)          |dz  |z
            }t'          dd          t          t          z  ft          j        |          k    sJ t'          dd          t          z  t          z  |z  dz
  }dt'          dd          z    t          d          ft          j        |          k    sJ |||z  z  }t'          dd          t'          dd          z  t          t          z  t'          dd          z  ft          j        |          k    sJ d S )Nro   r   i  rl   $   rQ   zx yr   cHr   r   rn   rb   r   i  )r;   rG   r   r=   r)   r'   r>   r.   r$   r
   r(   r   rF   r  r   r   r   r   rV   r   r   )r  yr#  pHr   r   rX   s          rN   test_factor_and_dimensionr&  G  s   )A,,2#CD#I#IIIII&>R=ebjIIIIIIvd{r?fr"ubg& (  ( ( ( ( ( 5>>DAq#Iv""B	!a
l# #     
$Bb"5f"<===
b''Bv))*b.NB/ /     FDFD))(1a..%,GGG))!U6\:::tAv}DQNNF4K(
(../ / / / Aq>>& &t+d2DXa^^#$ill3
(../ / / / $t)Da^^hq!nn,vd{Xa^^.KL
(../ / / / / /rM   c                  6   t          d          } t          d          }t          d          }|                     dt                     |                    dt                     |                    dt                     t          d          }t          d          }t          d          } |||                              ||          }|                     |||          | ||||i          }t          j
        |          t          j
        | |z  |z            cxk    r&t          d	          t          d
          dz  z  k    sn J t          j        |          t          j        | |z  |z            cxk    rdt          t          dz  z  fk    sn J d S )Nr   r   t1r"  r   r  r$  fr=   r>   rl   rQ   )rF   rV   r'   r$   r.   r	   r   r   subsrG   r   r   r=   r>   )r   r   r(  r  r$  r)  dfdxdl_dts           rN   #test_dimensional_expr_of_derivativer-  l  s   AA	$B&&r2...&&q$///''6222sAsAA1Q77<<1DIIqqAww1aB/00E"5))
A
+++ + + +x**+ + + + + + +E22
(Q44   	VD!G^       rM   c                     t          d          } t          d          }|                     dt          t          z             |                    dt          t          z             t	          j        t          |                     t          t	          j        |                     k    sJ t	          j        t          | |z                      dk    sJ d S )Nr   r   r   )rF   rV   r)   r.   rG   r   r   )r   r   s     rN   'test_get_dimensional_expr_with_functionr/    s    FDFD))!U6\:::))!U6\:::"3t99--B#D))**+ + + +"3tDy>>22a777777rM   c                     t          t          t                    dt          z  k    sJ t          t          t                    dt          z  k    sJ t          t          t                    dt          z  k    sJ t          t
          t                    dt          z  k    sJ t          t          t                    dt          z  k    sJ t          t          t                    dt          z  k    sJ t          j         t                    dt          z  k    sJ t          j         t                    dt          z  k    sJ d	t          z  t          z  } t          | t                    d
t          z  t          z  k    sJ t          | t                    dt          z  t          z  k    sJ t          | t          t          g          dt          z  t          z  k    sJ d S )Ni   i   i   @l        l           l            i       rQ   i (  iX  i `	 )r   r2   r1   r3   r4   r5   r6   r7   r0   r$   r+   )as    rN   test_binary_informationr3    s~   h%%d2222h%%5555h%%5555h%%5555h%%5555h%%5555s##vcz1111?31S5((((
8DAa%*T/1111a  CL$77777a$((F4K,>>>>>>>rM   c                  2   t          d          } t          d          }t          d          }|                    d|            |                    t          j        dz  |           t          d          }t          d          }t          d          }|                    t          j        dz  |           |                    d	|           t	          ||z  t
          z  ||t          g          t          j        dz  d
z  dz  |z  |z  t          z  k    sJ d S )N
good_gradekilo_good_gradecenti_good_graderc   i charity_pointsmilli_charity_pointsmissions   ix rQ   )rF   rV   r   rp   r   r*   r   )r5  r6  r7  r8  r9  r:  s         rN   -test_conversion_with_2_nonstandard_dimensionsr<    s(   ,''J011O 23344T:FFF55aeEk?SSS.//N#$:;;
##H99!%*nUUU--c>BBB,,Z7	8Z0  
(	#b	(+;	;H	DZ	OP P P P P PrM   c                     t          d          \  } }}| |z  }| t          t          dz  z  t          dz  z  |t          i}|                    |          t          dz  t          dz  z  k    sJ ||z  }|t
          t          dz  z  t          dz  z  |t          i}|                    |          t
          t          z  t          dz  z  k    sJ d S )Nzenergy mass forcerl   )r
   r8   r)   r.   r*  r9   )rA   rB   forceexpr1unitsexpr2s         rN   test_eval_subsrB    s    !"566FD%4KEXeQh&vqy0$AE::eq 22222$JE)(A+5eQh>XNE::e 6x ?q HHHHHHHrM   c                  
   t          t                    t          d          z
                                  t          t          dz            k    sJ t          t                    t          t                    z
                                  t          d           k    sJ t	          dd          } t          t                    t          |           z
                                  t          t          | z            k    sJ d S )Nrl   r   pT)positive)r   r%   r   r"   r
   )rD  s    rN   test_issue_14932rF    s    IIA((**c$q&kk9999IID		!++--#b''9999d###AIIA((**c$q&kk999999rM   c                  8   ddl m} m} ddlm} t          |           j        J t          |           j        J t          |           j        J t          |           j	        J t          |           j
        J t          |           j        J  |t          |           t          |                    J t          d          }| |z   }|j        rt          |j                  | |hk    sJ | dz   }|j        rt          |j                  | dhk    sJ d S )Nr   )r"   r%   )Eqr  r   )sympy.physics.unitsr"   r%   sympy.core.relationalrH  r   is_zerois_positiveis_nonnegativeis_negativeis_algebraicis_rationalr	   is_Addsetrg   )r"   r%   rH  r  es        rN   test_issue_14547rT    s;    /.......((((((t99$$$t99 (((t99#+++t99 (((t99!)))t99 (((2c$iiT##///sAqA80AFay0000qA80AFay000000rM   c                  X   t          j        d           t          d          } t          j        | t
                     t          j        | d           t          d          }t          j        |t
                     t          j        |d           | |z  }t          j        |           d S )Nerrorr~   r   bad_exp)warningssimplefilterrF   rG   r  r=   set_quantity_scale_factorr   )r~   rW  rX   s      rN   test_issue_22164r[    s    '"""	$Bb&))) Q'''y!!Ggv... !,,,=D $T*****rM   c                      ddl m} m}m} ddlm} |                     |          d|z  k    sJ |                    t                    t          dik    sJ |j
        dk    sJ d S )Nr   )r  r  r  )	dimsys_SIi@B rl   g/K ;)rI  r  r  r  sympy.physics.units.systems.sir]  r   r   r   r=   rd   )r  r  r  r]  s       rN   test_issue_22819r_    s    3333333333888888D!!WT\111111$77FA;FFFF?2222222rM   c                     ddl m}  ddlm} t	          d          }t	          d          }t          j        ||           t          j        ||           |                    dt                     |                    dt                     dt          |dz  |dz  z            z   }t          j
        |          d| z   t          d          fk    sJ d S )Nr   E)rA   r`   rh   r   rl   )sympy.core.numbersrb  rI  rA   rF   rG   r  rV   r   r   r   r;   )rb  rA   r`   rh   rX   s        rN   test_issue_20288rd    s    $$$$$$******AAa(((a(((&&q%000&&q%000s1a419~~D+D11a!eYq\\5JJJJJJJrM   c                     ddl m}  ddlm}m}m}m}m}m} t          d          }t          d          }t          d          }	t          j        ||           t          j        ||           t          j        |	|           |                    d|           |                    d|           |	                    d|           |	||z  z  }
t          j        |
          d         }t          j                                        |          sJ dt!          |
          z   }t          j        |          d| z   t#          d          fk    sJ d S )Nr   ra  )	impedancecapacitancer>   r   faradr.   Rr   Tr   )rc  rb  rI  rf  rg  r>   r   rh  r.   rF   rG   r  rV   r   r   is_dimensionlessr   r;   )rb  rf  rg  r>   r   rh  r.   ri  r   rj  rX   dimexp_exprs                rN   test_issue_24062rn    se   $$$$$$TTTTTTTTTTTTTTTTAAAa+++a---a&&&&&q#...&&q%000&&q&111A;D

*4
0
0
3C"$$55c:::::3t99}H+H55!a%19NNNNNNNrM   c                     ddl m} m}m}m}m} t          d          }t          j        ||           t          j	        |d|z  |z             t          d          }t          j        ||           t          j	        |d|z  |dz  z             t          d          }t          j        ||            t          j	        |d|z             ||z  |z   }t          j
        |           d S )Nr   )r>   velocityaccelerationr.   r)   V1r   A1rl   T1)rI  r>   rp  rq  r.   r)   rF   rG   r  rZ  r   )	r>   rp  rq  r.   r)   rr  rs  rt  rX   s	            rN   test_issue_24211ru    s    OOOOOOOOOOOOOO	$Bb(+++ QY%7888	$Bb,/// QY%:;;;	$Bb$''' QZ000b52:D$T*****rM   c                     t           j        rJ t          j        rJ t          j        rJ t          j        rJ t
          j        rJ t          j        rJ t          j        sJ t          j        sJ t          j        sJ t          j        sJ d S r   )r)   is_prefixedr   r!   r.   r   r   r   r   r8   r6   rL   rM   rN   test_prefixed_propertyrx  #  s            !!!!!!!!    rM   c                  >   ddl m}  t          |           D ]}t          | |          }t	          |t
                    s(|                    d          rEt	          |t                    sJ | dt          |                       |j	        sJ | d            t          t          t          t          t          fD ]G}t	          |t                    sJ | dt          |                       |j	        sJ | d            Ht          j	        rJ t           j	        rJ d S )Nr   )definitions	_constantz" must be PhysicalConstant, but is z4 is not marked as physics constant when it should be)rI  rz  dirgetattrrr   rF   endswithrE   typeis_physical_constantr9   r   r   r/   r   r)   r   )rz  rq   quantityconsts       rN   test_physics_constantr  /  s\   //////K   p p;--(H-- 	==%% 	ph(899zzh;z;zjnowjxjx;z;zzzz0ooT2o2o2oooo(*<>QSactu j j%!122mmu4m4m`dej`k`k4m4mmmm)iie+i+i+iiiii))))))))))rM   )zrX  sympy.core.addr   sympy.core.functionr   r   rc  r   r   sympy.core.singletonr   sympy.core.symbolr	   r
   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   sympy.integrals.integralsr   rI  r   r   r   r   r   r   r   r   r   r   r   r   sympy.physics.units.definitionsr   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   5sympy.physics.units.definitions.dimension_definitionsr;   r<   r=   r>   r?   r@   rA   rB   sympy.physics.units.prefixesrC   rD   sympy.physics.units.quantitiesrE   rF   sympy.physics.units.systemsrG   sympy.testing.pytestrH   rI   rO   rR   rZ   ri   rt   rx   r   r   r   r   r   r   r   r   r   r  r  r   r&  r-  r/  r3  r<  rB  rF  rT  r[  r_  rd  rn  ru  rx  r  rL   rM   rN   <module>r     s|          0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 " " " " " " / / / / / / / / 4 4 4 4 4 4 = = = = = = = = 9 9 9 9 9 9 8 8 8 8 8 8 / / / / / /& & & & & & & & & & & & & & & & & & & & & & & & & & & &: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :                    8 7 7 7 7 7 7 7 E E E E E E E E * * * * * * ' ' ' ' ' 'SM! ! !       $" " "4" " ",       - - -# # #,G G G&6' 6' 6'r8 8 8,@ @ @K K K! ! !N N N6, , ,  $"/ "/ "/J  (8 8 8? ? ?$P P P*I I I: : :1 1 1,+ + + 3 3 3
K 
K 
KO O O(+ + +"
  
  
 * * * * *rM   