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    1: \label{Math_Response_Problems}
    2: Math Response is a way to have a problem graded based on an algorithm that is executed inside of a computer algebra system. 
    3: The use of this response type is
    4: generally discouraged, since the responses will not be analyzable by the LON-CAPA statistics tools.
    5: 
    6: Which computer algebra system is to be used is specified in the cas argument of the mathresponse tag; currently, only Maxima is available.
    7: LON-CAPA sets up two arrays inside the computer algebra system: RESPONSE and LONCAPALIST. RESPONSE contains the student input by component, for example, if "3,42,17" is entered, RESPONSE[2] would be 42. LONCAPALIST contains the arguments passed in the args of mathresponse.
    8: 
    9: The answerdisplay is what is displayed when the problem is in "Show Answer" mode.
   10: 
   11: The following example illustrates this.
   12: \begin{verbatim}
   13: <problem>
   14:   <script type="loncapa/perl">
   15: $a1 = random(-6,6,4);
   16: $a2 = random(-6,6,4);
   17: $n1 = random(3,11,2);
   18: $n2 = random(2,10,2);
   19: $function = "$a1*cos($n1*x)+$a2*sin($n2*x)";
   20: $example=&xmlparse('An example would be <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');
   21:   </script>
   22: 
   23: <startouttext />
   24:   Give an example of a function
   25:   <ol>
   26:     <li>
   27:         which is orthogonal to <algebra>$function</algebra> with respect to the
   28:         scalar product
   29:         <m>
   30:            \[<g \mid h> =
   31:                \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]
   32:         </m>
   33:     </li>
   34:     <li>
   35:         whose norm is 1.
   36:     </li>
   37:   </ol>
   38: <endouttext />
   39: 
   40: <mathresponse answerdisplay="$example" cas="maxima" args="$function">
   41:     <answer>
   42: overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
   43: norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
   44: is(overlap=0 and norm=1);
   45:     </answer>
   46:     <textline readonly="no" size="50" />
   47:     <hintgroup showoncorrect="no">
   48:         <mathhint name="ortho" args="$function" cas="maxima">
   49:             <answer>
   50: overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
   51: is(not overlap = 0);
   52:             </answer>
   53:         </mathhint>
   54:         <mathhint name="norm" args="$function" cas="maxima">
   55:             <answer>
   56: norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
   57: is(not norm = 1);
   58:             </answer>
   59:         </mathhint>
   60:         <hintpart on="norm">
   61:            <startouttext />
   62: The function you have provided does not have a norm of one.
   63:            <endouttext />
   64:         </hintpart>
   65:         <hintpart on="ortho">
   66:             <startouttext />
   67: The function you have provided is not orthogonal.
   68:             <endouttext />
   69:         </hintpart>
   70:     </hintgroup>
   71: </mathresponse>
   72: 
   73: 
   74: <postanswerdate>
   75:     <startouttext />
   76:         <p>
   77: Note that with respect to the above norm, <m>$\cos(nx)$</m> is perpendicular
   78: to <m>$\sin(nx)$</m> and perpendicular to <m>$\cos(mx)$</m> for
   79: <m>$n\ne m$</m>.
   80:         </p>
   81:     <endouttext />
   82: </postanswerdate>
   83: </problem>
   84: \end{verbatim}