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Annotation of loncom/html/adm/help/tex/Math_Response_Problems.tex, revision 1.2

1.1       www         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>
1.2     ! albertel   14:   <script type="loncapa/perl">
1.1       www        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)";
1.2     ! albertel   20: $example=&xmlparse('An example would be <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');
        !            21:   </script>
        !            22: 
1.1       www        23: <startouttext />
1.2     ! albertel   24:   Give an example of a function
        !            25:   <ol>
        !            26:     <li>
        !            27:         which is orthogonal to <algebra>$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: 
1.1       www        40: <mathresponse answerdisplay="$example" cas="maxima" args="$function">
1.2     ! albertel   41:     <answer>
        !            42: overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
1.1       www        43: norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
1.2     ! albertel   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>
1.1       www        71: </mathresponse>
1.2     ! albertel   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 />
1.1       www        82: </postanswerdate>
                     83: </problem>
                     84: \end{verbatim}