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 UTC-5, Jotace wrote:
>
> Hi all,
>
> I want (my students) to plot Cornu's spiral, givent in parametric form by
>
> x(t) = integral cos(pi/u^2/2), u going from 0 to t , and y(t) defined
> analogously using the sine function. The integral connot be evaluated
> symbolically, I guess.
>
> The first attempt would be
>
> parametric_plot([integrate(cos(pi*u^2/2),u,0,t),integrate(sin(pi*u^2/2),u,0,t)],(t,-pi,pi))
> which failw (coercion)
>
> The second attempt would be:
>
> parametric_plot([integral_numerical(cos(pi*u^2/2),0,t),integral_numerical(sin(pi*u^2/2),0,t)],(t,-pi,pi))
> which also fails.
>
> I finally did:
> def x(t):
> return integral_numerical(cos(pi*u^2/2),0,t)[0]
>
> def y(t):
> return integral_numerical(sin(pi*u^2/2),0,t)[0]
>
> Points = [(x(t),y(t)) for t in sxrange(-pi,pi,2*pi/200)]
> line(Points).show(figsize=[5, 5],aspect_ratio=1)
>
> This works, but it looks highly inelegant. Also, i cannot expect my
> students to come up with something like this in a first year undergrad
> course.
>
> Is there a way to fix one of the first two options?
>
> Regards,
> JC
>
>
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