
    sg                         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 d dlmZmZ d dlmZ d d	lmZ d d
lmZmZmZmZmZmZmZmZmZ d dlmZm Z m!Z!m"Z"m#Z#m$Z$  ed      Z%d Z&d Z'd Z(d Z)y)    )pi)S)sqrt)cossin)raises)
CoordSys3D)ParametricIntegralvector_integrate)ParametricRegion)ImplicitRegion)	xyzuvrtthetaphi)PointSegmentCurveCirclePolygonPlaneCc            	      0   t        dt        t              z  dt        t              z  ft        t         dz  t        dz  f      } t        t        j                  t        j                  dz  z  |       t        d      dz  k(  sJ t        t        t        dz  t        dz  ft        ddf      }dt        j                  dz  z  t        j                  z  t        j                  z  t        j                  z  dt        j                  z  t        j                  z  z   dt        j                  z  t        j                  z  t        j                  z  z
  }t        ||      dk(  sJ t        dt        z  dz
  ddt        z  z
  t        ft        ddf      }t        t        j                  t        j                  z  t        j                  z  t        j                  t        j                  z  t        j                  z  z
  |      dk(  sJ t        dt        j                  dz  z  t        dt        ft        ddf            dk(  sJ t        t        t              t        t              dt        z  ft        ddt        z  f      }t        t        j                  t        j                  z  t        j                  z  |      d	t        d
      z  t        z  k(  sJ t        j                  t        j                  z  t        j                  t        j                  z  z   t        j                  t        j                  z  z   }t        |t        t        t              t        t              t        dz  ft        dt        f            dt        z  dz  t        dz  dz  z   k(  sJ y )N      i          r         
   )r   r   r   r   r   r
   r   r   r   r   r   r   ijkr   )
halfcirclecurvefield1linehelixfield2s         T/var/www/html/venv/lib/python3.12/site-packages/sympy/vector/tests/test_integrals.pytest_parametric_lineintegralsr2      s|   !1SZ<3u:">ArRSt@TUJacc!##q&j*54BBBaAq!t_q!Qi8EqssAvXacc\!##acc!AaccE!##I-!##acc	!##=Ffe,111QqS1Wa!A#gq1Aq!9=Dacc!##gacckACCGACCK7>!CCCaQh(8!Q!Q(KLPQQQQc!fc!fac2Q1R4LAEacc!##gacck51RR[^CCCSSWqss133wQSS(Ff&6AA17MPQSTVXz&Z[_abd_def_fikmninopip_pppp    c            	         t        dt        t              z  t        t              z  dt        t              z  t        t              z  dt        t              z  ft        ddt
        z  ft        dt
        dz  f      } t        t        j                  |       dt
        z  k(  sJ t        t        d      t        t              z  t        d      t        t              z  t        ft        ddft        ddt
        z  f      }t        t        j                  |      dk(  sJ t        t        t        t              z  t        t        t              z  t        ft        ddt
        z  ft        ddf      }t        t        j                  t        j                  z  t        j                  t        j                  z  z   t        j                  dz  t        j                   z  z   |      t
        dz  k(  sJ t        t        t        ft        ddft        ddd	t        z  z
  f      }t        t        t        ft        ddd	t        z  z
  ft        ddf      }t        d
t        j                  z  t        j                   z  |      t        d
t        j                  z  t        j                   z  |      k(  sJ t        t        j                  |      dt        j                  z  k(  sJ y )Nr    r   r$   r"      r#   r   r&   r!   g333333/)r   r   r   r   r   r   r
   r   r   r   r   r   r   r   r(   r)   r*   )
semispherecylindercone	triangle1	triangle2s        r1    test_parametric_surfaceintegralsr;   !   s   !1SX:c%j#8!CH*SZ:OQRSVWZS[Q["\"Aqt,sAr!tn>Jacc:.!B$666aU!3T!WSZ5G KaQRTUYY^`acdegcgXhiHacc8,111Qs1vXqQx3aAbD\Aq!9MDacc!##gACC/!##q&*<dCr!tKKK !Q!QQ2!84DEI !Q!QQqS)9Aq!9EIeACCimY7;MeTUTWTWiXYX[X[m]f;ggggacc9-ACC777r3   c            
         t        t        t        t        ft        ddft        ddft        ddf      } t	        d|       dk(  sJ t        t
        t        t              z  t        t              z  t
        t        t              z  t        t              z  t
        t        t              z  ft
        ddft        ddt        z  ft        dt        f      }t        t
        t        t              z  t        t              z  t
        t        t              z  t        t              z  t
        t        t              z  ft
        ddft        dt        ft        ddt        z  f      }t	        t        j                  dz  t        j                  dz  z   |      dt        z  dz  k(  sJ t	        t        j                  dz  t        j                  dz  z   |      dt        z  dz  k(  sJ t        t        t        t        ft        ddft        ddt        z  dz  dz   ft        dd	dt        z  z
  dt        z  z
  f      }t        t        t        t        ft        ddft        dd	dt        z  z
  dt        z  z
  ft        ddt        z  dz  dz   f      }t	        t        j                  t        j                  z  t        j                  z   d
t        j                  z  z
  |      t	        t        j                  t        j                  z  t        j                  z   d
t        j                  z  z
  |      k(  sJ t	        dt        j                  z  |      dk(  sJ y )Nr   r#   r    i       r"   r5   d   i)r   r   r   r   r
   r   r   r   r   r   r   r   r(   r)   r*   )cubesolidsphere1solidsphere2region_under_plane1region_under_plane2s        r1   test_parametric_volumeintegralsrF   2   s   Q1I1ay1a)aAYGDa&!+++#Qs3xZE
%:Ac#hJs5z<QSTUXY\U]S]$^1Iq!B$'7#q"GL#Qs3xZE
%:Ac#hJs5z<QSTUXY\U]S]$^1IQ|eQ"5EGLacc1fqssAvo|<R
JJJacc1fqssAvo|<Br	III*Aq!9q!Qi!Q1QQR
AS%&1qs7QqS=$9;*Aq!9q!Qi!QAaCRSTURUAV%&2a46A:$68 acc!##gmc!##g57JK133qss7QSS=3qss724GHI I Iae%89R???r3   c            	      	   t        t        t        t              z  t        t	        t              z  ft        ddft        dt
        f      } t        t        j                  dz  |       dt
        z  k(  sJ t        t        j                  t        t        t        dz  ft        ddf            dt        d      z  dz  d	t        d	      z  dz  z   k(  sJ t        t        j                  dz  t        j                  z  t        j                  ddft        j                  d
df      dt        j                  z  dz  k(  sJ t        t        dd      t        dd            }t        dt        j                  z  |      t        d      dz  k(  sJ t        t        ddd      t        ddd            }t        t        j                  t        j                   z  |      dk(  sJ t#        t	        t              t        t              ft        ddf      }t        dt        j                  z  |      dt        j                  z  k(  sJ t%        t        dd      d      }t        t        j                  t        j                  z  |      dt
        z  k(  sJ t%        t        dd      t        dd      t        dd            }t        d|      |j&                  k(  sJ t)        ddd      }t        t        j                  t        j                   z  dt        j                  z  t        j*                  z  z
  |      dk(  sJ g d\  }}}	}
t)        |||	|
      }t        dt        j                  z  |      dt        j                  z  dt        d      z  t        j                  z  z
  k(  sJ t        dd      }t        t        j                   t        j                  z  t        j                  z
  |      t-        t        j                  t        j                   z  t        d            k(  sJ t/        t        t        ft        dz  t        dz  z   dz
        }t        d|      dt
        z  k(  sJ t/        t        t        ft        dz
  dz  t        dz
  dz  z   dz
        }t        d|      dt
        z  k(  sJ t1        t        ddd      t        ddd      t        ddd            t3        t4        fd        y )!Nr?   r    r   r   r"   i      %   i  r#   i	      ir!   r&   r5   H   r   r   r#   r   )r#   r#      )rO   rP   )r!   r#   )r   r#   ii_   )r    r"   -      c                      t        t        j                  t        j                  z  t        j                  z  t        j
                  z          S )N)r   r   r   r   r(   r*   )pls   r1   <lambda>z'test_vector_integrate.<locals>.<lambda>j   s,    /ACCacc0A2F r3   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r(   r   r   circumferencer   r)   r
   r   r   r   
ValueError)halfdiscs1s2r,   c1c2trianglep1p2p3p4polypointc3c4rV   s                  @r1   test_vector_integraterh   G   s   3u:q#e*} =2qzESTVX>ZHACCFH-2555ACC!11ad)aAY!GHCPTUWPXLY[O^`aefhai^ijl^lLllllQSS!VACCZ!##q!qssBlCs133wqyPPP	q!eAqk	*BCGR(AcF1H444	q!Qq!Q	0BACCGR(B...3q63q6"Q1I.EAaccE5)RV333	aQ	BACCGR(BrE111	aU1a[%1+	6BAr"b&6&6666vvv.HACCGbfQSSj0(;q@@@5NBB2r2r"DCGT*d133hDHQSS.HHHH!QKEACCGaccM515GACCQabhQi5jjjj	A1q!ta	0BB#s2v---	AQ
a!eaZ 7! ;	<BAr"ad***	uQ1~uQ1~uQ1~	>B
:FGr3   N)*sympy.core.numbersr   sympy.core.singletonr   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   sympy.testing.pytestr   sympy.vector.coordsysrectr	   sympy.vector.integralsr
   r   sympy.vector.parametricregionr   sympy.vector.implicitregionr   	sympy.abcr   r   r   r   r   r   r   r   r   sympy.geometryr   r   r   r   r   r   r   r2   r;   rF   rh    r3   r1   <module>ru      sO    ! " 9 ? ' 0 G : 6 5 5 5 H HsOq$8"@*#Hr3   