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Annotation of loncom/homework/templates/HintMathResponse.problem, revision 1.3

1.2       albertel    1: <problem>
                      2:     <script type="loncapa/perl">
1.3     ! albertel    3: $a1 = &random(-6,6,4);
        !             4: $a2 = &random(-6,6,4);
        !             5: $n1 = &random(3,11,2);
        !             6: $n2 = &random(2,10,2);
1.1       www         7: $function = "$a1*cos($n1*x)+$a2*sin($n2*x)";
1.2       albertel    8: $example=&xmlparse('An example would be <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');
                      9:     </script>
                     10: 
                     11:     <startouttext />
1.1       www        12: Give an example of a function
                     13: <ol>
1.2       albertel   14:     <li>which is orthogonal to <algebra>$function</algebra> with respect to the
                     15:         scalar product
                     16:         <m>\[<g \mid h> = \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>
                     17:     </li>
                     18:     <li>whose norm is 1.</li>
                     19: </ol>
                     20:     <endouttext />
                     21: 
                     22:     <mathresponse answerdisplay="$example" cas="maxima" args="$function">
                     23: 
                     24:         <answer>
                     25: overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
1.1       www        26: norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
1.2       albertel   27: is(overlap=0 and norm=1);
                     28:         </answer>
                     29: 
                     30:         <textline readonly="no" size="50" />
                     31: 
                     32:         <hintgroup showoncorrect="no">
                     33: 
                     34:             <mathhint name="ortho" args="$function" cas="maxima">
                     35: 
                     36:                 <answer>
                     37: overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
                     38: is(not overlap = 0);
                     39:                 </answer>
                     40:             </mathhint>
                     41: 
                     42:             <mathhint name="norm" args="$function" cas="maxima">
                     43:                 <answer>
                     44: norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
                     45: is(not norm = 1);
                     46:                 </answer>
                     47:             </mathhint>
                     48:            
                     49:             <hintpart on="norm">
                     50:                 <startouttext />
                     51: The function you have provided does not have a norm of one.
                     52:                 <endouttext />
                     53:             </hintpart>
                     54: 
                     55:             <hintpart on="ortho">
                     56:                 <startouttext />
                     57: The function you have provided is not orthogonal.
                     58:                 <endouttext />
                     59:             </hintpart>
                     60: 
                     61:         </hintgroup>
                     62:     </mathresponse>
                     63: 
                     64:     <postanswerdate>
                     65: 
                     66:         <startouttext />
                     67: <p>
                     68:     Note that with respect to the above norm, <m>$\cos(nx)$</m> is
                     69:     perpendicular to <m>$\sin(nx)$</m> and perpendicular to <m>$\cos(mx)$</m>
                     70:     for <m>$n\ne m$</m>.
                     71: </p>
                     72:         <endouttext />
                     73: 
                     74:     </postanswerdate>
1.1       www        75: </problem>