
    g                         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)dS )    )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            	      >   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 d S )N      i          r         
   )r   r   r   r   r   r
   r   r   r   r   r   r   ijkr   )
halfcirclecurvefield1linehelixfield2s         ]/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/vector/tests/test_integrals.pytest_parametric_lineintegralsr2      s   !1SZZ<3u::">ArRSt@TUUJac!#q&j*554BBBBaAq!t_q!Qi88EqsAvXac\!#ac!AacE!#I-!#ac	!#=Ffe,,1111QqS1Wa!A#gq1Aq!9==Dac!#gackACGACK7>>!CCCCaQh(8!Q!Q(K(KLLPQQQQQc!ffc!ffac2Q1R4LAAEac!#gack511RR[^CCCCSWqs13wQS(Ff&6AA17MPQSTVXz&Z&Z[[_abd_def_fikmninopip_ppppppp    c            	      F   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 d S )Nr    r   r$   r"      r#   r   r&   r!   g333333/)r   r   r   r   r   r   r
   r   r   r   r   r   r   r   r(   r)   r*   )
semispherecylindercone	triangle1	triangle2s        r1    test_parametric_surfaceintegralsr;   !   s?   !1SXX:c%jj#8!CHH*SZZ:OQRSVWZS[S[Q["\"Aqt,sAr!tn> >Jac:..!B$6666aU!3T!WWSZZ5G KaQRTUYY^`acdegcgXhiiHac8,,1111Qs1vvXqQx3aAbD\Aq!9MMDac!#gAC/!#q&*<dCCr!tKKKK !Q!QQ2!84DEEI !Q!QQqS)9Aq!9EEIeACimY77;MeTUTWiXYX[m]f;g;gggggac9--AC777777r3   c            
      H   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 d S )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GGDa&&!++++#Qs3xxZE

%:Ac#hhJs5zz<QSTUXY\U]U]S]$^1Iq!B$'7#q"G GL#Qs3xxZE

%:Ac#hhJs5zz<QSTUXY\U]U]S]$^1IQ|eQ"5EG GLac1fqsAvo|<<R
JJJJac1fqsAvo|<<Br	I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 8 ac!#gmc!#g57JKK13qs7QS=3qs724GHHI I I Iae%89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            d S )!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'    /ACac0A2F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>ZZHACFH--25555AC!11ad)aAY!G!GHHCPTUWPXPXLY[O^`aefhaiai^ijl^lLlllllQS!VACZ!#q!qsBlCCs13wqyPPPP	q!eAqkk	*	*BCGR((AcFF1H4444	q!Qq!Q	0	0BACGR((B....3q663q66"Q1I..EAacE5))RV3333	aQ		BACGR((BrE1111	aU1a[[%1++	6	6BAr""b&66666vvv..HACGbfQSj0(;;q@@@@555NBB2r2r""DCGT**d13hDHHQS.HHHHH!QKKEACGacM5115GACQabhQiQi5j5jjjjj	A1q!ta	0	0BB##s2v----	AQ
a!eaZ 7! ;	<	<BAr""ad****	uQ1~~uQ1~~uQ1~~	>	>B
:FFFFGGGG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      s   ! ! ! ! ! ! " " " " " " 9 9 9 9 9 9 ? ? ? ? ? ? ? ? ' ' ' ' ' ' 0 0 0 0 0 0 G G G G G G G G : : : : : : 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 H H H H H H H H H H H H H H H HJsOOq q q$8 8 8"@ @ @*#H #H #H #H #Hr3   