fieldfunctions.py 文件源码

def gradient(scalar, frame):
    """
    Returns the vector gradient of a scalar field computed wrt the
    coordinate symbols of the given frame.

    Parameters
    ==========

    scalar : sympifiable
        The scalar field to take the gradient of

    frame : ReferenceFrame
        The frame to calculate the gradient in

    Examples
    ========

    >>> from sympy.physics.vector import ReferenceFrame
    >>> from sympy.physics.vector import gradient
    >>> R = ReferenceFrame('R')
    >>> s1 = R[0]*R[1]*R[2]
    >>> gradient(s1, R)
    R_y*R_z*R.x + R_x*R_z*R.y + R_x*R_y*R.z
    >>> s2 = 5*R[0]**2*R[2]
    >>> gradient(s2, R)
    10*R_x*R_z*R.x + 5*R_x**2*R.z

    """

    _check_frame(frame)
    outvec = Vector(0)
    scalar = express(scalar, frame, variables=True)
    for i, x in enumerate(frame):
        outvec += diff(scalar, frame[i]) * x
    return outvec