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Consistent problem templates:
- New line after each tag (not for texts in foils)
- One empty row after each end tag and before new start tag for second level tags
- No indentation for second level tags, e.g. <script>
- Four white spaces as indentation for each further sub level
    Exceptions:
        -Content (mostly text) in separate line(s): no indentation
        - Concept groups: same indentation as foilgroup
          (allows to insert code from problems without concept groups without changing the indentation and vice versa)
- No new line at end of template
- Removed new lines from within the middle of default texts
- Added one blank each after "<m>$" and before "$</m>" to ensure no misinterpretation neither by human nor by machine (e.g. "<m>$x" is not "<m>$ $x")
- Replaced deprecated font tag in <instructorcomment> by CSS
- Removed dos line endings
- dos2unix conversion
  (ClickImageExample.problem, RandomLabelExample.problem, SimpleMatching.problem)

<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>