Source code for sympy.vector.deloperator

from sympy.utilities.exceptions import SymPyDeprecationWarning
from sympy.core import Basic
from sympy.vector.vector import Vector
from sympy.vector.operators import gradient, divergence, curl


[docs]class Del(Basic): """ Represents the vector differential operator, usually represented in mathematical expressions as the 'nabla' symbol. """ def __new__(cls, system=None): if system is not None: SymPyDeprecationWarning( feature="delop operator inside coordinate system", useinstead="it as instance Del class", deprecated_since_version="1.1", issue=12866, ).warn() obj = super(Del, cls).__new__(cls) obj._name = "delop" return obj
[docs] def gradient(self, scalar_field, doit=False): """ 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 """
return gradient(scalar_field, doit=doit) __call__ = gradient __call__.__doc__ = gradient.__doc__
[docs] def dot(self, vect, doit=False): """ 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 """
return divergence(vect, doit=doit) __and__ = dot __and__.__doc__ = dot.__doc__
[docs] def cross(self, vect, doit=False): """ 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 """
return curl(vect, doit=doit) __xor__ = cross __xor__.__doc__ = cross.__doc__ def __str__(self, printer=None): return self._name __repr__ = __str__
_sympystr = __str__