On Dec. 8 Robert Dodier wrote:
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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]);
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Thank you for reminding me of this construct, which also works
with draw2d. However things fall apart if you go past about
t = 4.8, due to a current bug in the evaluation of erf(z).
(%i1) (display2d:false,assume(t>0))$
(%i2) x (t) := ''(integrate (cos (s^2 * %pi/2), s, 0, t))$
(%i3) y (t) := ''(integrate (sin (s^2 * %pi/2), s, 0, t))$
(%i4) showtime:true$
(%i5) load(draw)$
note that draw2d doesn't need any special switches to get
this plot
(%i6) draw2d( explicit(x(t),t,0,3) )$
Evaluation took 3.0500 seconds (3.0500 elapsed)
(%i7) draw2d( explicit(y(t),t,0,3) )$
Evaluation took 2.5800 seconds (2.5800 elapsed)
(%i8) draw2d( parametric(x(t),y(t),t,0,3),nticks=100)$
Evaluation took 2.2200 seconds (2.2200 elapsed)
the draw2d parametric plot looks much cruder than your
plot2d( parametric(..) ) plot. Maybe someone knows how
to smooth this out.
Here we show the blow up by looking at the
real and imaginary parts of what should be
a real function (to within floating point errors).
(%i9) xfr(t) := realpart(float(x(t)))$
Evaluation took 0.0000 seconds (0.0000 elapsed)
(%i10) map('xfr,[1,2,3,4,5,6,7]);
(%o10) [0.77989340037682,0.48825340607534,0.60572078930926,0.49842588395517,
0.92294250203326,5394606.134146459,1.1458348613507996E+16]
(%i11) xfi(t) := imagpart(float(x(t)))$
(%i12) map('xfi,[1,2,3,4,5,6,7]);
(%o12) [-8.3266726846886741E-17,5.6898930012039273E-15,
-8.6821105860224179E-12,3.772560090431476E-7,0.53728316249859,
Ted Woollett
2.1605661208583072E+7,-3.4913409426819615E+15]