[BACK]Return to HintMathResponse.problem CVS log [TXT] [DIR] Up to [LON-CAPA] / loncom / homework / templates

Diff for /loncom/homework/templates/HintMathResponse.problem between versions 1.1 and 1.5

version 1.1, 2007/01/22 21:48:55 version 1.5, 2010/06/11 19:50:12
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>');
   </script>
   
 <startouttext />  <startouttext />
 Give an example of a function  Give an example of a function
 <ol>  <ol>
 <li>which is orthogonal to <algebra>$function</algebra> with respect to the      <li>which is orthogonal to<br />
 scalar product  <center> <algebra>$function</algebra></center>
 <m>\[<g \mid h> =  <br />
 \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>   with respect to the scalar product
 </li>          <m>\[<g \mid h> = \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>
 <li>whose norm is 1.</li>      </li>
 </ol><endouttext />      <li>whose norm is 1.</li>
   </ol>
   <endouttext />
   
 <mathresponse answerdisplay="$example" cas="maxima" args="$function">  <mathresponse answerdisplay="$example" cas="maxima" args="$function">
 <answer>overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;      <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="$function" cas="maxima">      <textline readonly="no" size="50" />
 <answer>overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;  
 is(not overlap = 0);</answer>      <hintgroup showoncorrect="no">
 </mathhint>          <mathhint name="ortho" args="$function" cas="maxima">
 <mathhint name="norm" args="$function" cas="maxima">              <answer>
 <answer>norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;  overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
 is(not norm = 1);</answer>  is(not overlap = 0);
 </mathhint> <hintpart on="norm">              </answer>
 <startouttext />          </mathhint>
 The function you have provided does not have a norm of one.<endouttext />  
 </hintpart>          <mathhint name="norm" args="$function" cas="maxima">
 <hintpart on="ortho">              <answer>
 <startouttext />  norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
 The function you have provided is not orthogonal.<endouttext />  is(not norm = 1);
 </hintpart>              </answer>
 </hintgroup>          </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>  </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>
       <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>  </postanswerdate>
   
 </problem>  </problem>
Removed from v.1.1  
changed lines
  Added in v.1.5

FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>