o 8Va @s@ddlmZddlmZddlmZmZmZGdddeZdS))SymPyDeprecationWarning)Basic)gradient divergencecurlcsleZdZdZdfdd ZdddZeZeje_ddd ZeZeje_dd d Z e Z e je _d d Z Z S)Delz Represents the vector differential operator, usually represented in mathematical expressions as the 'nabla' symbol. Ncs2|durtdddddt|}d|_|S)Nz'delop operator inside coordinate systemzit as instance Del classz1.1iB2)ZfeatureZ useinsteadZdeprecated_since_versionZissueZdelop)rwarnsuper__new___name)clssystemobj __class__:/usr/lib/python3/dist-packages/sympy/vector/deloperator.pyr s z Del.__new__FcC t||dS)a Returns the gradient of the given scalar field, as a Vector instance. Parameters ========== scalar_field : SymPy expression The scalar field to calculate the gradient of. doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, Del >>> C = CoordSys3D('C') >>> delop = Del() >>> delop.gradient(9) 0 >>> delop(C.x*C.y*C.z).doit() C.y*C.z*C.i + C.x*C.z*C.j + C.x*C.y*C.k doit)r)selfZ scalar_fieldrrrrr z Del.gradientcCr)a Represents the dot product between this operator and a given vector - equal to the divergence of the vector field. Parameters ========== vect : Vector The vector whose divergence is to be calculated. doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, Del >>> delop = Del() >>> C = CoordSys3D('C') >>> delop.dot(C.x*C.i) Derivative(C.x, C.x) >>> v = C.x*C.y*C.z * (C.i + C.j + C.k) >>> (delop & v).doit() C.x*C.y + C.x*C.z + C.y*C.z r)rrZvectrrrrdot:rzDel.dotcCr)a4 Represents the cross product between this operator and a given vector - equal to the curl of the vector field. Parameters ========== vect : Vector The vector whose curl is to be calculated. doit : bool If True, the result is returned after calling .doit() on each component. Else, the returned expression contains Derivative instances Examples ======== >>> from sympy.vector import CoordSys3D, Del >>> C = CoordSys3D('C') >>> delop = Del() >>> v = C.x*C.y*C.z * (C.i + C.j + C.k) >>> delop.cross(v, doit = True) (-C.x*C.y + C.x*C.z)*C.i + (C.x*C.y - C.y*C.z)*C.j + (-C.x*C.z + C.y*C.z)*C.k >>> (delop ^ C.i).doit() 0 r)rrrrrcross\s z Del.crosscCs|jSN)r )rZprinterrrr _sympystrsz Del._sympystrr)F) __name__ __module__ __qualname____doc__r r__call__r__and__r__xor__r __classcell__rrrrrs   !rN) Zsympy.utilities.exceptionsrZ sympy.corerZsympy.vector.operatorsrrrrrrrrs