# 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",
deprecated_since_version="1.1",
issue=12866,
).warn()
obj = super(Del, cls).__new__(cls)
obj._name = "delop"
return obj

"""
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()
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

"""

[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__