Return to Math_Response_Problems.tex CVS log

Up to [LON-CAPA] / loncom / html / adm / help / tex

Annotation of loncom/html/adm/help/tex/Math_Response_Problems.tex, revision 1.1

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>
        !            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}$</m>');</script>
        !            21: <startouttext />
        !            22: Give an example of a function
        !            23: <ol>
        !            24: <li>which is orthogonal to <algebra>$function</algebra> with respect to the
        !            25: scalar product
        !            26: <m>\[<g \mid h> =
        !            27: \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>
        !            28: </li>
        !            29: <li>whose norm is 1.</li>
        !            30: </ol><endouttext />
        !            31: <mathresponse answerdisplay="$example" cas="maxima" args="$function">
        !            32: <answer>overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
        !            33: norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
        !            34: is(overlap=0 and norm=1);</answer>
        !            35: <textline readonly="no" size="50" />
        !            36: <hintgroup showoncorrect="no">
        !            37: <mathhint name="ortho" args="$function" cas="maxima">
        !            38: <answer>overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
        !            39: is(not overlap = 0);</answer>
        !            40: </mathhint>
        !            41: <mathhint name="norm" args="$function" cas="maxima">
        !            42: <answer>norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
        !            43: is(not norm = 1);</answer>
        !            44: </mathhint> <hintpart on="norm">
        !            45: <startouttext />
        !            46: The function you have provided does not have a norm of one.<endouttext />
        !            47: </hintpart>
        !            48: <hintpart on="ortho">
        !            49: <startouttext />
        !            50: The function you have provided is not orthogonal.<endouttext />
        !            51: </hintpart>
        !            52: </hintgroup>
        !            53: </mathresponse>
        !            54: <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 />
        !            55: </postanswerdate>
        !            56: </problem>
        !            57: \end{verbatim}