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[LON-CAPA] /
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homework /
mathresponse.idea
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Wed Jun 14 18:31:37 2006 UTC (18 years, 3 months ago) by
albertel
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CVS tags:
version_2_2_X,
version_2_2_2,
version_2_2_1,
version_2_2_0,
version_2_1_X,
version_2_1_99_3,
version_2_1_99_2,
version_2_1_99_1,
version_2_1_99_0,
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- adding some design docs
1: <problem>
2:
3: <script type="loncapa/perl">
4: $a1 = random(-5,5,2);
5: $a2 = random(-5,5,2);
6: $n1 = random(1,10,1);
7: $n2 = random(1,10,1);
8: $function = "$a1*cos($n1*x)+$a2*sin($n2*x)";
9: @cas_list = ($function);
10: </script>
11:
12: <startouttext />
13: Give an example of a function which is
14: (1) orthogonal to <algebra>$function</algebra> with respect to the
15: scalar product
16: <m>$$\langle g \mid h \rangle =
17: \frac{1}{\pi} \int_{-\pi}^{\pi} g(x) \cdot h(x)$$</m>
18: and
19: (2) whose norm is 1.
20: <endouttext />
21:
22: <mathresponse cas="maxima" args="@cas_list">
23: <answer>
24: f(x):= LONCAPALIST[1];
25: overlap: integrate(f(x)*RESPONSE[1],x,-%pi,%pi)/%pi;
26: norm: integrate(RESPONSE[1]*RESPONSE[1],x,-%pi,%pi)/%pi;
27: grade: is(overlap=0 and norm=1);
28: [grade];
29: </answer>
30:
31: <textline />
32:
33: <hintgroup showoncorrect="no">
34: <mathhint cas="maxima" args="@cas_list" name="ortho">
35: <answer>
36: f(x):= LONCAPALIST[1];
37: overlap: integrate(f(x)*RESPONSE[1],x,-%pi,%pi)/%pi;
38: [is(overlap != 0)];
39: </answer>
40: </mathhint>
41: <mathhint cas="maxima" args="@cas_list" name="norm">
42: <answer>
43: f(x):= LONCAPALIST[1];
44: norm: integrate(RESPONSE[1]*RESPONSE[1],x,-%pi,%pi)/%pi;
45: [is(norm != 1)];
46: </answer>
47: </mathhint>
48:
49:
50: <hintpart on="norm">
51: <script type="loncapa/perl">
52: $response = &EXT('user.resource.resource.0.submissiom');
53: $norm = &cas('maxima',...); # get the norm
54: $norm_display = &cas_tex_display($norm);
55: </script>
56: <startouttext />
57: The function you have provided is not normal to
58: <algebra>$function</algebra> its norm is
59: <m eval="on">$norm_display</m>
60: <endouttext />
61: </hintpart>
62: <hintpart on="ortho">
63: <startouttext />
64: The function you have provided is not orthognal.
65: <endouttext />
66: </hintpart>
67:
68: </hintgroup>
69: </mathresponse>
70:
71: </problem>
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