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 10, 2014 4:56:05 AM UTC-5, Volker Braun wrote: > > 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. > > > > On Wednesday, September 10, 2014 6:09:06 AM UTC+1, Hal Snyder wrote: >> >> 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 >>> >>> -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
