You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
122 lines
3.1 KiB
122 lines
3.1 KiB
5 months ago
|
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
|