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from sympy.core import Basic
from sympy.vector.operators import gradient, divergence, curl
class Del(Basic):
"""
Represents the vector differential operator, usually represented in
mathematical expressions as the 'nabla' symbol.
"""
def __new__(cls):
obj = super().__new__(cls)
obj._name = "delop"
return obj
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__
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__
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 _sympystr(self, printer):
return self._name
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