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version 1.5, 2007/01/22 21:49:26
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As you may know, it is extremely difficult to determine whether a given expression |
As you may know, it is extremely difficult to determine whether a given expression |
is exactly equal to another expression in general. For example, is $\sin 2x=2\sin x\cos x$? |
is exactly equal to another expression in general. For example, is $\sin 2x=2\sin x\cos x$? |
Symbolically proving it one way or another is impossible in general. Therefore, |
LON-CAPA has two ways of finding out if it is: |
LON-CAPA uses a sampling system. If your answer and the student's answer |
\begin{itemize} |
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\item algebraically, using a symbolic algebra system |
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\item numerically, using sampling points |
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\end{itemize} |
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You need to determine which way is the safest in a given situation. |
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If you don't specify sampling points, the symbolic algebra system is used. |
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If you do specify sampling points, LON-CAPA uses them. |
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If your answer and the student's answer |
agree at the sampling points within your given tolerance factor, the student's |
agree at the sampling points within your given tolerance factor, the student's |
answer will be accepted. If the student's answer does not agree at the sampling points within your given tolerance factor, it will be rejected. |
answer will be accepted. If the student's answer does not agree at the sampling points within your given tolerance factor, it will be rejected. |
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