4.C] Write the code to find the curl of \vec{F} = xy^2\hat{i} + 2x^2yz \hat{j} - 3yz^2 \hat{k}
Answer:
from sympy.physics.vector import ReferenceFrame, curl
from sympy import var, symbols, display
# Declare variables
x, y, z = var('x y z')
# Define reference frame
v = ReferenceFrame('v')
# Define vector field F
F = v[0]*v[1]**2*v.x + 2*v[0]**2*v[1]*v[2]*v.y - 3*v[1]*v[2]**2*v.z
# Compute the curl of F
C = curl(F, v)
# Substitute v[0], v[1], v[2] with x, y, z in F
F = F.subs([(v[0], x), (v[1], y), (v[2], z)])
print('Given vector field F =')
display(F)
# Substitute v[0], v[1], v[2] with x, y, z in the curl result
C = C.subs([(v[0], x), (v[1], y), (v[2], z)])
print('Curl of F =')
display(C)