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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}
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