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1.1       lira        1: \label{Creating_Math_Response_Problems}
                      2: 
1.2     ! lira        3: Math response problems use a cas system to evaluate the student response. Which computer algebra system is to 
        !             4: be used is specified in the cas argument of the mathresponse tag; both Maxima and R are supported. Maxima and R 
        !             5: are also a powerful stand-alone programs that can be installed on most operating systems. If you are interested 
        !             6: in writing Maxima or R problems, it is a good idea to install a copy on your operating system to access help, 
        !             7: learn syntax, and test your expected responses outside the LON-CAPA environment. 
        !             8: See \texttt{http://maxima.sourceforge.net/} or \texttt{http://www.r-project.org/}.
1.1       lira        9: 
1.2     ! lira       10: LON-CAPA will accept two pre-named arrays inside the answerblock for the computer algebra system: RESPONSE and LONCAPALIST. RESPONSE contains the student input by comman-separated entities, for example, if "3,42,17" is entered by the student, RESPONSE[2] would be 42. LONCAPALIST is built from the arguments passed in an array \texttt{args} which is assigned a array value from the script.
        !            11: 
        !            12: The \texttt{answer} tag contains the Maxima command (and syntax) that are passed to Maxima after the RESPONSE and LONCAPALIST values are substituted. (See example below). The \texttt{answerdisplay} variable contains what is displayed when the problem is in "Show Answer" mode. You will want to include this field so that the students can see the correct answer after the "Show Answer Date" configured when the problem is assigned in the course space. Also note the description in the \texttt{postanswerdate}\index{postanswerdate} tag that is displayed after the answer date.
1.1       lira       13: 
                     14: The following example illustrates this.
                     15: \begin{verbatim}
                     16: <problem>
                     17:   <script type="loncapa/perl">
                     18: $a1 = random(-6,6,4);
                     19: $a2 = random(-6,6,4);
                     20: $n1 = random(3,11,2);
                     21: $n2 = random(2,10,2);
                     22: $function = "$a1*cos($n1*x)+$a2*sin($n2*x)";
1.2     ! lira       23: # reformat next two lines as single line if you copy/paste into a script
        !            24: $example=&xmlparse('An example would be 
        !            25: <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');
1.1       lira       26:   </script>
                     27: 
                     28: <startouttext />
                     29:   Give an example of a function
                     30:   <ol>
                     31:     <li>
                     32:         which is orthogonal to <algebra>$function</algebra> with respect to the
                     33:         scalar product
                     34:         <m>
                     35:            \[<g \mid h> =
                     36:                \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]
                     37:         </m>
                     38:     </li>
                     39:     <li>
                     40:         whose norm is 1.
                     41:     </li>
                     42:   </ol>
                     43: <endouttext />
                     44: 
                     45: <mathresponse answerdisplay="$example" cas="maxima" args="$function">
                     46:     <answer>
                     47: overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
                     48: norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
                     49: is(overlap=0 and norm=1);
                     50:     </answer>
                     51:     <textline readonly="no" size="50" />
                     52:     <hintgroup showoncorrect="no">
                     53:         <mathhint name="ortho" args="$function" cas="maxima">
                     54:             <answer>
                     55: overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
                     56: is(not overlap = 0);
                     57:             </answer>
                     58:         </mathhint>
                     59:         <mathhint name="norm" args="$function" cas="maxima">
                     60:             <answer>
                     61: norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
                     62: is(not norm = 1);
                     63:             </answer>
                     64:         </mathhint>
                     65:         <hintpart on="norm">
                     66:            <startouttext />
                     67: The function you have provided does not have a norm of one.
                     68:            <endouttext />
                     69:         </hintpart>
                     70:         <hintpart on="ortho">
                     71:             <startouttext />
                     72: The function you have provided is not orthogonal.
                     73:             <endouttext />
                     74:         </hintpart>
                     75:     </hintgroup>
                     76: </mathresponse>
                     77: 
                     78: 
                     79: <postanswerdate>
                     80:     <startouttext />
                     81:         <p>
                     82: Note that with respect to the above norm, <m>$\cos(nx)$</m> is perpendicular
                     83: to <m>$\sin(nx)$</m> and perpendicular to <m>$\cos(mx)$</m> for
                     84: <m>$n\ne m$</m>.
                     85:         </p>
                     86:     <endouttext />
                     87: </postanswerdate>
                     88: </problem>
                     89: \end{verbatim}