g!ddlmZddlmZddlmZddlmZmZddl m Z ddl m Z gdZ dZd Zd Zd Zd Zd ZdZdS))diff)S) integrate)Vectorexpress) _check_frame) _check_vector)curl divergencegradientis_conservative is_solenoidalscalar_potentialscalar_potential_differencec|t||dkrtdSt||d}||j}||j}||j}td}|t||dt||dz |jzz }|t||dt||dz |jzz }|t||dt||dz |jzz }|S)aP 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 rT variables)r rrdotxyzr)vectframevectxvectyvectzoutvecs _/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/physics/vector/fieldfunctions.pyr r s:$ qyyayy 4$ / / /D HHUW  E HHUW  E HHUW  E AYYF tE58$$tE58'<'<<GGF tE58$$tE58'<'<<GGF tE58$$tE58'<'<<GGF Mct||dkr tjSt||d}||j}||j}||j}tj}|t||dz }|t||dz }|t||dz }|S)ab 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 rTrrr) r rZerorrrrrr)rrrrrouts r r r :s:$ qyyv 4$ / / /D HHUW  E HHUW  E HHUW  E &C4uQx  C4uQx  C4uQx  C Jr!ct|td}t||d}t|D]!\}}|t ||||zz }"|S)a 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 rTr)rrr enumerater)scalarrrirs r r r esp: AYYF VUd 3 3 3F%  --1$vuQx((1,, Mr!c|tdkrdSt|d}t||tdkS)a 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 rT)rlistseparater simplifyfieldrs r r r s]2 q t !! " "1 %E u   & & ( (F1II 55r!c|tdkrdSt|d}t||t juS)a 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 rT)rr*r+r r,rr#r-s r rrsY2 q t !! " "1 %E eU # # , , . .!& 88r!ct|std|tdkr tjSt |t ||d}t|}t| |d|d}t|ddD]R\}}t|||dz}| ||z }|t|||dzz }S|S)a 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 zField is not conservativerTrrN) r ValueErrorrrr#rrr*rrr&r)r.r dimensions temp_functionr(dim partial_diffs r rrs> 5 ! !64555 q v  E5D 1 1 1EeJeii 1 66aAAMJqrrN++??3M5Q<88 yy~~ 4 <q1u>>> r!ct|t|trt||}n|}t |||d}t |||d}i}i} t |D]A\} } | |||| <| || || <B|| ||z S)a* Returns the scalar potential difference between two points in a certain frame, wrt a given field. If a scalar field is provided, its values at the two points are considered. If a conservative vector field is provided, the values of its scalar potential function at the two points are used. Returns (potential at position 2) - (potential at position 1) Parameters ========== field : Vector/sympyfiable The field to calculate wrt frame : ReferenceFrame The frame to do the calculations in point1 : Point The initial Point in given frame position2 : Point The second Point in the given frame origin : Point The Point to use as reference point for position vector calculation Examples ======== >>> 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 Tr) r isinstancerrrpos_fromr&rsubs) r.rpoint1point2origin scalar_fn position1 position2 subs_dict1 subs_dict2r(rs r rrs^%  $UE22  //$GGGI//$GGGIJJ%  001 uuY// 58 uuY// 58 >>* % % z(B(B BBr!N)sympy.core.functionrsympy.core.singletonrsympy.integrals.integralsrsympy.physics.vectorrrsympy.physics.vector.framersympy.physics.vector.vectorr __all__r r r r rrrr!r rJs$$$$$$""""""//////00000000333333555555 * * * )))X(((V"""J666>999>///d?C?C?C?C?Cr!