# Maple code (classic style) to find analytic expression for normal
# vectors from parametric surface equation

with(linalg);

# define the ellipse function 
p := [ax * cos(u) * cos(v), ay * sin(u) * cos(v), az * sin(v) ];

# find the cross product of the direction derivatives in the u and v directions
n := simplify(crossprod(diff(p,u), diff(p,v)));

# Now, looking at the above result, divide by the quantity that is
# constant to each component (this is important, as there are times
# when it might be zero...)
n := simplify(evalm(n / cos(v)));