From: "Luigi Marino" <luigi_marino2 at alice.it>
> It is possible draw the Cornu spiral
> with Maxima by the equations integrals:
> x(t)=int(cos(s^2*%pi/2),s,0,t)
> y(t)=int(sin(s^2*%pi/2),s,0,t) ?
> I have try with integration by series.
It turns out Maxima can compute the integrals symbolically.
Although %i appears in the result, the result evaluates to a
real number for real t. Maxima needs a little encouragement to
get a number instead of an expression containing %i.
One way:
assume (t > 0);
x (t) := ''(integrate (cos (s^2 * %pi/2), s, 0, t));
y (t) := ''(integrate (sin (s^2 * %pi/2), s, 0, t));
plot2d ([parametric, x, y, [t, 0, 4]], [nticks, 100], [plot_realpart, true]);
Another way:
assume (t > 0);
x (t) := expand (''(integrate (cos (s^2 * %pi/2), s, 0, t)));
y (t) := expand (''(integrate (sin (s^2 * %pi/2), s, 0, t)));
plot2d ([parametric, x, y, [t, 0, 4]], [nticks, 100]);
In both cases, '' is two single quotes (not one double quote).
The effect of '' is to evaluate the integral just once, when the
function is defined.
There might be better ways to go about it, I don't know much
about integrals of this kind. By the way, I'm working with a recent
build from CVS which might have some features related to special
functions which are not present in previous releases.
Hope this helps.,
Robert Dodier