U Zʹj!@sddlmZddlmZddlmZddlmZmZddl m Z ddl m Z ddd d d d d gZ ddZddZdd Zdd Zdd Zdd Zdd ZdS))diff)S) integrate)Vectorexpress) _check_frame) _check_vectorcurl divergencegradientis_conservative is_solenoidalscalar_potentialscalar_potential_differencecCst||dkrtdSt||dd}||j}||j}||j}td}|t||dt||d|j7}|t||dt||d|j7}|t||dt||d|j7}|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)rrrdotxyzr)vectframevectxvectyvectzoutvecrb/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/physics/vector/fieldfunctions.pyr s   &&&cCst||dkrtjSt||dd}||j}||j}||j}tj}|t||d7}|t||d7}|t||d7}|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) rrZerorrrrrr)rrrrroutrrrr :s   cCsJt|td}t||dd}t|D]\}}|t||||7}q&|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)Zscalarrrirrrrr es cCs6|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 simplifyfieldrrrrr s cCs4|tdkrdSt|d}t||tjkS)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$r%r r&rr r'rrrr s cCst|std|tdkr"tjSt|t||dd}t|}t| |d|d}t |ddD]>\}}t |||d}| ||}|t|||d7}qh|S)a Returns the scalar potential function of a field in a given frame (without the added integration constant). Parameters ========== field : Vector The vector field whose scalar potential function is to be calculated frame : ReferenceFrame The frame to do the calculation in Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import scalar_potential, gradient >>> R = ReferenceFrame('R') >>> scalar_potential(R.z, R) == R[2] True >>> scalar_field = 2*R[0]**2*R[1]*R[2] >>> grad_field = gradient(scalar_field, R) >>> scalar_potential(grad_field, R) 2*R_x**2*R_y*R_z zField is not conservativerTrrN) r ValueErrorrrr rrr$rrr"r)r(r dimensionsZ temp_functionr#dimZ partial_diffrrrrs c Cst|t|trt||}n|}t|||dd}t|||dd}i}i} t|D],\} } | |||| <| || || <qZ|| ||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 isinstancerrrZpos_fromr"rsubs) r(rZpoint1Zpoint2originZ scalar_fnZ position1Z position2Z subs_dict1Z subs_dict2r#rrrrrs/  N)Zsympy.core.functionrZsympy.core.singletonrZsympy.integrals.integralsrZsympy.physics.vectorrrZsympy.physics.vector.framerZsympy.physics.vector.vectorr__all__r r r r r rrrrrrs"     ,+%2