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Diff for /loncom/homework/templates/HintMathResponse.problem between versions 1.1 and 1.2

version 1.1, 2007/01/22 21:48:55 version 1.2, 2007/01/23 21:16:50
Line 1 Line 1
  <problem>  <problem>
 <script type="loncapa/perl">      <script type="loncapa/perl">
 $a1 = random(-6,6,4);  $a1 = random(-6,6,4);
 $a2 = random(-6,6,4);  $a2 = random(-6,6,4);
 $n1 = random(3,11,2);  $n1 = random(3,11,2);
 $n2 = random(2,10,2);  $n2 = random(2,10,2);
 $function = "$a1*cos($n1*x)+$a2*sin($n2*x)";  $function = "$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>  $example=&xmlparse('An example would be <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');
 <startouttext />      </script>
   
       <startouttext />
 Give an example of a function  Give an example of a function
 <ol>  <ol>
 <li>which is orthogonal to <algebra>$function</algebra> with respect to the      <li>which is orthogonal to <algebra>$function</algebra> with respect to the
 scalar product          scalar product
 <m>\[<g \mid h> =          <m>\[<g \mid h> = \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>
 \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>      </li>
 </li>      <li>whose norm is 1.</li>
 <li>whose norm is 1.</li>  </ol>
 </ol><endouttext />      <endouttext />
 <mathresponse answerdisplay="$example" cas="maxima" args="$function">  
 <answer>overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;      <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;  norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
 is(overlap=0 and norm=1);</answer>  is(overlap=0 and norm=1);
 <textline readonly="no" size="50" />          </answer>
 <hintgroup showoncorrect="no">  
 <mathhint name="ortho" args="$function" cas="maxima">          <textline readonly="no" size="50" />
 <answer>overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;  
 is(not overlap = 0);</answer>          <hintgroup showoncorrect="no">
 </mathhint>  
 <mathhint name="norm" args="$function" cas="maxima">              <mathhint name="ortho" args="$function" cas="maxima">
 <answer>norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;  
 is(not norm = 1);</answer>                  <answer>
 </mathhint> <hintpart on="norm">  overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
 <startouttext />  is(not overlap = 0);
 The function you have provided does not have a norm of one.<endouttext />                  </answer>
 </hintpart>              </mathhint>
 <hintpart on="ortho">  
 <startouttext />              <mathhint name="norm" args="$function" cas="maxima">
 The function you have provided is not orthogonal.<endouttext />                  <answer>
 </hintpart>  norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
 </hintgroup>  is(not norm = 1);
 </mathresponse>                  </answer>
 <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 />              </mathhint>
 </postanswerdate>             
               <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>  </problem>
Removed from v.1.1  
changed lines
  Added in v.1.2

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