+ j!^RIHt^RIHt^RIHt^RIHtHt^RI H t ^RI H t .ROt RtRtR tR tR tR tR tR#))diff)S) integrate)Vectorexpress) _check_frame) _check_vectorc\V4V^8Xd \^4#\WRR7pVPVP4pVPVP 4pVPVP 4p\^4pV\WA^,4\W1^,4, VP,, pV\W!^,4\WA^,4, VP ,, pV\W1^,4\W!^,4, VP ,, pV#)a 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 T variables)r rrdotxyzr)vectframevectxvectyvectzoutvecs&& d/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/physics/vector/fieldfunctions.pycurlrs:$ qyay 4$ /D HHUWW E HHUWW E HHUWW E AYF tE8$tE8'<<GGF tE8$tE8'<<GGF tE8$tE8'<<GGF Mc\V4V^8Xd\P#\WRR7pVP VP 4pVP VP 4pVP VP4p\PpV\W!^,4, pV\W1^,4, pV\WA^,4, pV#)a Returns the divergence of a vector field computed wrt the coordinate symbols of the given frame. Parameters ========== vect : Vector The vector operand frame : ReferenceFrame The reference frame to calculate the divergence in Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import divergence >>> R = ReferenceFrame('R') >>> v1 = R[0]*R[1]*R[2] * (R.x+R.y+R.z) >>> divergence(v1, R) R_x*R_y + R_x*R_z + R_y*R_z >>> v2 = 2*R[1]*R[2]*R.y >>> divergence(v2, R) 2*R_z Tr ) r rZerorr rrrr)rrrrrouts&& r divergencer:s:$ qyvv 4$ /D HHUWW E HHUWW E HHUWW E &&C4Qx  C4Qx  C4Qx  C Jrc\V4\^4p\WRR7p\V4F%wr4V\ WV,4V,, pK' V#)a5 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 Tr )rrr enumerater)scalarrrirs&& rgradientr"esO: AYF Vd 3F% $vQx(1,,! MrcV\^48XdR#\VP44^,p\W4P 4\^48H#)a Checks if a field is conservative. Parameters ========== field : Vector The field to check for conservative property Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import is_conservative >>> R = ReferenceFrame('R') >>> is_conservative(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) True >>> is_conservative(R[2] * R.y) False T)rlistseparatersimplifyfieldrs& ris_conservativer)sF2 q  ! "1 %E   & & (F1I 55rcV\^48XdR#\VP44^,p\W4P 4\ P J#)az Checks if a field is solenoidal. Parameters ========== field : Vector The field to check for solenoidal property Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.vector import is_solenoidal >>> R = ReferenceFrame('R') >>> is_solenoidal(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) True >>> is_solenoidal(R[1] * R.y) False T)rr$r%rr&rrr's& r is_solenoidalr+sF2 q  ! "1 %E e # , , .!&& 88rc\V4'g \R4hV\^48Xd\P#\ V4\ WRR7p\V4p\VPV^,4V^,4p\VR,4FVwrE\W1V^,,4pVPV4V, pV\WaV^,,4, pKX V#)av 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 conservativeTr :NN) r) ValueErrorrrrrrr$rr rr)r(r dimensions temp_functionr!dim partial_diffs&& rscalar_potentialr3s> 5 ! !455 q vv  ED 1EeJeii 1 6aAMJrN+MQ<8 yy~ 4 > , rc\V4\V\4'd \W4pMTp\ VP V4VRR7p\ VP V4VRR7p/p/p \ V4F9wrV PV4WV ,&V PV4WV ,&K; VPV 4VPV4, #)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 isinstancerr3rpos_fromrr subs) r(rpoint1point2origin scalar_fn position1 position2 subs_dict1 subs_dict2r!rs &&&&& rscalar_potential_differencer@s^%  $U2  /$GI/$GIJJ%  uuY/ 8 uuY/ 8! >>* % z(B BBrN)rrr"r)r+r3r@)sympy.core.functionrsympy.core.singletonrsympy.integrals.integralsrsympy.physics.vectorrrsympy.physics.vector.framersympy.physics.vector.vectorr __all__rrr"r)r+r3r@rrrIsF$"/035 * )X(V"J6>9>/d?Cr