Huh...
cos(pi/u^2/2), first expression of your problem, has not, indeed, an
explicit solution that sage is able to find.
but, on your following attempts, you reach for the integral of
cos(pi*x^2/2), a horse of a different color (which is the one racing in
Wikipedia pages on Euler spiral) :
The s = var('s') is not necessary (the argument s inside the functions
shadows it).
As for the original question, IMHO there is a learning opportunity here.
Numerical integration is powerful, but it doesn't give you symbolic
answers. Even if you make the integration bound a symbolic variable.
Appreciate the pointers.
Plot statement in prior posting could also be
parametric_plot((g,h),(-pi,pi))
which has a nicer default aspect ratio.
BTW there is sage code for Cornu spiral in the wikipedia article, Euler
spiral http://en.wikipedia.org/wiki/Euler_spiral.
On Wednesday, September
This works on my sage-6.1.1:
s = var('s')
def g(s):
return numerical_integral(cos(pi*x^2/2), 0, s, max_points=100)[0]
def h(s):
return numerical_integral(sin(pi*x^2/2), 0, s, max_points=100)[0]
p = plot((g,h),(-pi,pi),parametric=True)
show(p)
On Tuesday, September 9, 2014 5:17:14 PM
