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Annotation of loncom/homework/templates/HintMathResponse.problem, revision 1.1

1.1     ! www         1:  <problem>
        !             2: <script type="loncapa/perl">
        !             3: $a1 = random(-6,6,4);
        !             4: $a2 = random(-6,6,4);
        !             5: $n1 = random(3,11,2);
        !             6: $n2 = random(2,10,2);
        !             7: $function = "$a1*cos($n1*x)+$a2*sin($n2*x)";
        !             8: $example=&xmlparse('An example would be <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');</script>
        !             9: <startouttext />
        !            10: Give an example of a function
        !            11: <ol>
        !            12: <li>which is orthogonal to <algebra>$function</algebra> with respect to the
        !            13: scalar product
        !            14: <m>\[<g \mid h> =
        !            15: \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>
        !            16: </li>
        !            17: <li>whose norm is 1.</li>
        !            18: </ol><endouttext />
        !            19: <mathresponse answerdisplay="$example" cas="maxima" args="$function">
        !            20: <answer>overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
        !            21: norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
        !            22: is(overlap=0 and norm=1);</answer>
        !            23: <textline readonly="no" size="50" />
        !            24: <hintgroup showoncorrect="no">
        !            25: <mathhint name="ortho" args="$function" cas="maxima">
        !            26: <answer>overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
        !            27: is(not overlap = 0);</answer>
        !            28: </mathhint>
        !            29: <mathhint name="norm" args="$function" cas="maxima">
        !            30: <answer>norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
        !            31: is(not norm = 1);</answer>
        !            32: </mathhint> <hintpart on="norm">
        !            33: <startouttext />
        !            34: The function you have provided does not have a norm of one.<endouttext />
        !            35: </hintpart>
        !            36: <hintpart on="ortho">
        !            37: <startouttext />
        !            38: The function you have provided is not orthogonal.<endouttext />
        !            39: </hintpart>
        !            40: </hintgroup>
        !            41: </mathresponse>
        !            42: <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 />
        !            43: </postanswerdate>
        !            44: </problem>