122 lines
3.1 KiB
Python
122 lines
3.1 KiB
Python
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from sympy.core import Basic
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from sympy.vector.operators import gradient, divergence, curl
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class Del(Basic):
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"""
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Represents the vector differential operator, usually represented in
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mathematical expressions as the 'nabla' symbol.
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"""
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def __new__(cls):
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obj = super().__new__(cls)
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obj._name = "delop"
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return obj
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def gradient(self, scalar_field, doit=False):
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"""
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Returns the gradient of the given scalar field, as a
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Vector instance.
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Parameters
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==========
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scalar_field : SymPy expression
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The scalar field to calculate the gradient of.
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doit : bool
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If True, the result is returned after calling .doit() on
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each component. Else, the returned expression contains
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Derivative instances
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Examples
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========
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>>> from sympy.vector import CoordSys3D, Del
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>>> C = CoordSys3D('C')
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>>> delop = Del()
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>>> delop.gradient(9)
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0
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>>> delop(C.x*C.y*C.z).doit()
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C.y*C.z*C.i + C.x*C.z*C.j + C.x*C.y*C.k
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"""
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return gradient(scalar_field, doit=doit)
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__call__ = gradient
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__call__.__doc__ = gradient.__doc__
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def dot(self, vect, doit=False):
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"""
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Represents the dot product between this operator and a given
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vector - equal to the divergence of the vector field.
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Parameters
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==========
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vect : Vector
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The vector whose divergence is to be calculated.
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doit : bool
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If True, the result is returned after calling .doit() on
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each component. Else, the returned expression contains
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Derivative instances
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Examples
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========
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>>> from sympy.vector import CoordSys3D, Del
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>>> delop = Del()
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>>> C = CoordSys3D('C')
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>>> delop.dot(C.x*C.i)
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Derivative(C.x, C.x)
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>>> v = C.x*C.y*C.z * (C.i + C.j + C.k)
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>>> (delop & v).doit()
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C.x*C.y + C.x*C.z + C.y*C.z
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"""
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return divergence(vect, doit=doit)
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__and__ = dot
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__and__.__doc__ = dot.__doc__
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def cross(self, vect, doit=False):
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"""
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Represents the cross product between this operator and a given
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vector - equal to the curl of the vector field.
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Parameters
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==========
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vect : Vector
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The vector whose curl is to be calculated.
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doit : bool
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If True, the result is returned after calling .doit() on
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each component. Else, the returned expression contains
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Derivative instances
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Examples
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========
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>>> from sympy.vector import CoordSys3D, Del
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>>> C = CoordSys3D('C')
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>>> delop = Del()
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>>> v = C.x*C.y*C.z * (C.i + C.j + C.k)
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>>> delop.cross(v, doit = True)
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(-C.x*C.y + C.x*C.z)*C.i + (C.x*C.y - C.y*C.z)*C.j +
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(-C.x*C.z + C.y*C.z)*C.k
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>>> (delop ^ C.i).doit()
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0
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"""
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return curl(vect, doit=doit)
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__xor__ = cross
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__xor__.__doc__ = cross.__doc__
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def _sympystr(self, printer):
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return self._name
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