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.