ó ”¼™\c@s°ddlmZmZmZddlmZmZddlmZddl m Z ddddd d d gZ d „Z d „Z d„Zd„Zd„Zd„Zd„ZdS(i’’’’(tdifft integratetS(tVectortexpress(t _check_frame(t _check_vectortcurlt divergencetgradienttis_conservativet is_solenoidaltscalar_potentialtscalar_potential_differencecCst|ƒ|dkr tdƒSt||dtƒ}|j|jƒ}|j|jƒ}|j|jƒ}tdƒ}|t||dƒt||dƒ|j7}|t||dƒt||dƒ|j7}|t||dƒt||dƒ|j7}|S(sP Returns the curl of a vector field computed wrt the coordinate symbols of the given frame. Parameters ========== vect : Vector The vector operand frame : ReferenceFrame The reference frame to calculate the curl in Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import curl >>> R = ReferenceFrame('R') >>> v1 = R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z >>> curl(v1, R) 0 >>> v2 = R[0]*R[1]*R[2]*R.x >>> curl(v2, R) R_x*R_y*R.y - R_x*R_z*R.z it variablesii( RRRtTruetdottxtytzR(tvecttframetvectxtvectytvectztoutvec((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyR s    ///cCsĄt|ƒ|dkr tdƒSt||dtƒ}|j|jƒ}|j|jƒ}|j|jƒ}tdƒ}|t||dƒ7}|t||dƒ7}|t||dƒ7}|S(sb Returns the divergence of a vector field computed wrt the coordinate symbols of the given frame. Parameters ========== vect : Vector The vector operand frame : ReferenceFrame The reference frame to calculate the divergence in Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import divergence >>> R = ReferenceFrame('R') >>> v1 = R[0]*R[1]*R[2] * (R.x+R.y+R.z) >>> divergence(v1, R) R_x*R_y + R_x*R_z + R_y*R_z >>> v2 = 2*R[1]*R[2]*R.y >>> divergence(v2, R) 2*R_z iRii( RRRRRRRRR(RRRRRtout((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyR8s    cCsgt|ƒtdƒ}t||dtƒ}x5t|ƒD]'\}}|t|||ƒ|7}q8W|S(s… Returns the vector gradient of a scalar field computed wrt the coordinate symbols of the given frame. Parameters ========== scalar : sympifiable The scalar field to take the gradient of frame : ReferenceFrame The frame to calculate the gradient in Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import gradient >>> R = ReferenceFrame('R') >>> s1 = R[0]*R[1]*R[2] >>> gradient(s1, R) R_y*R_z*R.x + R_x*R_z*R.y + R_x*R_y*R.z >>> s2 = 5*R[0]**2*R[2] >>> gradient(s2, R) 10*R_x*R_z*R.x + 5*R_x**2*R.z iR(RRRRt enumerateR(tscalarRRtiR((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyR cs   cCsK|tdƒkrtSt|jƒƒd}t||ƒjƒtdƒkS(sĄ Checks if a field is conservative. Parameters ========== field : Vector The field to check for conservative property Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import is_conservative >>> R = ReferenceFrame('R') >>> is_conservative(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) True >>> is_conservative(R[2] * R.y) False i(RRtlisttseparateRtsimplify(tfieldR((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyR ˆscCsK|tdƒkrtSt|jƒƒd}t||ƒjƒtdƒkS(s¶ Checks if a field is solenoidal. Parameters ========== field : Vector The field to check for solenoidal property Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import is_solenoidal >>> R = ReferenceFrame('R') >>> is_solenoidal(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) True >>> is_solenoidal(R[1] * R.y) False i(RRRRRR R(R!R((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyR ØscCsłt|ƒstdƒ‚n|tdƒkr7tdƒSt|ƒt||dtƒ}g|D] }|^q]}t|j|dƒ|dƒ}xct |dƒD]Q\}}t |||dƒ}|j|ƒ|}|t|||dƒ7}q W|S(sŹ Returns the scalar potential function of a field in a given frame (without the added integration constant). Parameters ========== field : Vector The vector field whose scalar potential function is to be calculated frame : ReferenceFrame The frame to do the calculation in Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import scalar_potential, gradient >>> R = ReferenceFrame('R') >>> scalar_potential(R.z, R) == R[2] True >>> scalar_field = 2*R[0]**2*R[1]*R[2] >>> grad_field = gradient(scalar_field, R) >>> scalar_potential(grad_field, R) 2*R_x**2*R_y*R_z sField is not conservativeiRi( R t ValueErrorRRRRRRRRR(R!RRt dimensionst temp_functionRtdimt partial_diff((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyR Čs    c CsŽt|ƒt|tƒr+t||ƒ}n|}t|j|ƒ|dtƒ}t|j|ƒ|dtƒ}i}i} xHt|ƒD]:\} } | j|ƒ||| <| j|ƒ| || >> from sympy.physics.vector import ReferenceFrame, Point >>> from sympy.physics.vector import scalar_potential_difference >>> R = ReferenceFrame('R') >>> O = Point('O') >>> P = O.locatenew('P', R[0]*R.x + R[1]*R.y + R[2]*R.z) >>> vectfield = 4*R[0]*R[1]*R.x + 2*R[0]**2*R.y >>> scalar_potential_difference(vectfield, R, O, P, O) 2*R_x**2*R_y >>> Q = O.locatenew('O', 3*R.x + R.y + 2*R.z) >>> scalar_potential_difference(vectfield, R, P, Q, O) -2*R_x**2*R_y + 18 R( Rt isinstanceRR Rtpos_fromRRRtsubs( R!Rtpoint1tpoint2torigint scalar_fnt position1t position2t subs_dict1t subs_dict2RR((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyR śs/ N(tsympyRRRtsympy.physics.vectorRRtsympy.physics.vector.frameRtsympy.physics.vector.vectorRt__all__RRR R R R R (((sBlib/python2.7/site-packages/sympy/physics/vector/fieldfunctions.pyts   , + % 2