Give an example of a function which is
(1) orthogonal to $function with respect to the
scalar product
$$\langle g \mid h \rangle =
\frac{1}{\pi} \int_{-\pi}^{\pi} g(x) \cdot h(x)$$
and
(2) whose norm is 1.
f(x):= LONCAPALIST[1];
overlap: integrate(f(x)*RESPONSE[1],x,-%pi,%pi)/%pi;
norm: integrate(RESPONSE[1]*RESPONSE[1],x,-%pi,%pi)/%pi;
grade: is(overlap=0 and norm=1);
[grade];
f(x):= LONCAPALIST[1];
overlap: integrate(f(x)*RESPONSE[1],x,-%pi,%pi)/%pi;
[is(overlap != 0)];
f(x):= LONCAPALIST[1];
norm: integrate(RESPONSE[1]*RESPONSE[1],x,-%pi,%pi)/%pi;
[is(norm != 1)];
The function you have provided is not normal to
$function its norm is
$norm_display
The function you have provided is not orthognal.