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- trying to make the problem code prettier
- addin sample points to HintFormula.problem
- remove tolerance specfication from CAS fomularesponse

<problem>
    <script type="loncapa/perl">
$a1 = random(-6,6,4);
$a2 = random(-6,6,4);
$n1 = random(3,11,2);
$n2 = random(2,10,2);
$function = "$a1*cos($n1*x)+$a2*sin($n2*x)";
$example=&xmlparse('An example would be <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');
    </script>

    <startouttext />
Give an example of a function
<ol>
    <li>which is orthogonal to <algebra>$function</algebra> with respect to the
        scalar product
        <m>\[<g \mid h> = \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>
    </li>
    <li>whose norm is 1.</li>
</ol>
    <endouttext />

    <mathresponse answerdisplay="$example" cas="maxima" args="$function">

        <answer>
overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
is(overlap=0 and norm=1);
        </answer>

        <textline readonly="no" size="50" />

        <hintgroup showoncorrect="no">

            <mathhint name="ortho" args="$function" cas="maxima">

                <answer>
overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
is(not overlap = 0);
                </answer>
            </mathhint>

            <mathhint name="norm" args="$function" cas="maxima">
                <answer>
norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
is(not norm = 1);
                </answer>
            </mathhint>
           
            <hintpart on="norm">
                <startouttext />
The function you have provided does not have a norm of one.
                <endouttext />
            </hintpart>

            <hintpart on="ortho">
                <startouttext />
The function you have provided is not orthogonal.
                <endouttext />
            </hintpart>

        </hintgroup>
    </mathresponse>

    <postanswerdate>

        <startouttext />
<p>
    Note that with respect to the above norm, <m>$\cos(nx)$</m> is
    perpendicular to <m>$\sin(nx)$</m> and perpendicular to <m>$\cos(mx)$</m>
    for <m>$n\ne m$</m>.
</p>
        <endouttext />

    </postanswerdate>
</problem>