Initialisation du repository de Beta

venv/lib/python3.12/site-packages/sympy/vector/deloperator.py

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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