Return to HintMathResponse.problem CVS log

Up to [LON-CAPA] / loncom / homework / templates

* Templates for formula and mathresponse
* Adding documentation to the manual
* stringresponse, etc, are not a subsubsection of "Foils" in author manual

 <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>