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Sage version 6.5 app on Mac OS 10.95. Following code tries to evaluate the total curvature of a certain space curve. The answer should be given as a complete elliptic integral of the second kind (which I then hoped to numerically evaluate for a range of values of r). But I get "Error executing code in Maxima".

r,t = var('r,t') assume(r > 0) X = vector((r * cos(t) - (1/3)* r^3 * cos(3t), - r * sin(t) - (1/3) *r^3 * sin(3t), r^2 cos(2t))) Xtheta = X.diff(t) AbsXtheta = abs(Xtheta) T = (1/AbsXtheta) * Xtheta ## unit tangent kappa = abs(T.diff(t)) kappa = kappa.expand().trig_simplify().canonicalize_radical() print(kappa) Curvature = integral(kappa,t,0,2*pi)

Sage version 6.5 app on Mac OS 10.95. Following code tries to evaluate the total curvature of a certain space curve. The answer should be given as a complete elliptic integral of the second kind (which I then hoped to numerically evaluate for a range of values of r). But I get "Error executing code in Maxima".

r,t = var('r,t')
assume(r > 0)
X = vector((r * cos(t) - (1/3)* r^3 * cos(3t), cos(3*t),               - r * sin(t) - (1/3) *r^3 * sin(3t),
sin(3*t),
             r^2 cos(2t)))
*cos(2*t)))
Xtheta = X.diff(t)
AbsXtheta = abs(Xtheta)
T = (1/AbsXtheta) * Xtheta    ## unit tangent
kappa = abs(T.diff(t))
kappa = kappa.expand().trig_simplify().canonicalize_radical()
print(kappa)
Curvature = integral(kappa,t,0,2*pi) 
integral(kappa,t,0,2*pi)