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Update quaternion.py #27399

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Update quaternion.py #27399

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26 changes: 26 additions & 0 deletions sympy/algebras/quaternion.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1642,6 +1642,32 @@ def index_vector(self):
"""

return self.norm() * self.axis()
def curl(self, x, y, z):
"""
Computes the curl of the vector field represented by the quaternion.
The quaternion is assumed to represent a 3D vector field, i.e.,
q = xi + yj + zk (where a = 0).

Parameters
----------
x, y, z : symbols
The coordinates of the vector field.

Returns
-------
Quaternion
The quaternion representing the curl of the vector field.
"""
# Extract the components of the quaternion (assuming it's a vector field)
xi, yi, zi = self.b, self.c, self.d # components of i, j, k

# Compute partial derivatives of the components
curl_x = diff(zi, y) - diff(yi, z)
curl_y = diff(xi, z) - diff(zi, x)
curl_z = diff(yi, x) - diff(xi, y)

# Return a quaternion representing the curl (using i, j, k)
return Quaternion(0, curl_x, curl_y, curl_z)

def mensor(self):
"""
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