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1.1     ! bowersj2    1: 
        !             2: As you may know, it is extremely difficult to determine whether a given expression
        !             3: is exactly equal to another expression in general. For example, is $\sin 2x=2\sin x\cos x$?
        !             4: Symbolically proving it one way or another is impossible in general. Therefore,
        !             5: LON-CAPA uses a sampling system. If your answer and the student's answer
        !             6: agree at the sampling points within your given tolerance factor, the student's
        !             7: answer will be accepted, otherwise it will be rejected.
        !             8: 
        !             9: To specify where to sample the formulas for determining whether the student's
        !            10: answer is correct, you need to put a sampling specification in the \textbf{Sample
        !            11: Points}\index{Sample Points} field. The sampling specifications takes the
        !            12: following format:
        !            13: 
        !            14: \begin{enumerate}
        !            15: \item A comma separated list of the variables you wish to interpret,
        !            16: \item followed by {}``@'' (not in quotes),
        !            17: \item followed by any number of the following two things, separated by semi-colons:
        !            18: 
        !            19: \begin{enumerate}
        !            20: \item a comma separated list of as many numbers as there are variables, which specifies
        !            21: one sampling point, OR
        !            22: \item a comma separated list of as many numbers as there are variables, followed
        !            23: by a colon, followed by another list of as many numbers as there are variables,
        !            24: followed by a \#, followed by an integer.
        !            25: \end{enumerate}
        !            26: \end{enumerate}
        !            27: The first form specifies one point to sample. The second form specifies a
        !            28: range for each variable, and the system will take as many random samples
        !            29: from that range as the number after the \#.
        !            30: 
        !            31: For $2x^{2}+4$, with one variable {}``x'', one could specify
        !            32: 
        !            33: \begin{itemize}
        !            34: \item {}``x@2'', which will sample the answers only at 2. (This is generally
        !            35: a bad idea, as the student could get lucky and match at that point)
        !            36: \item {}``x@1:5\#4'' will takes 4 samples from somewhere between 1 and 5.
        !            37: \item {}``x@1:5\#4;10'' will takes 4 samples from somewhere between 1 and 5,
        !            38: and also sample at 10.
        !            39: \end{itemize}
        !            40: For $2x^{2}+3y^{3}$, which has two variables, one could specify
        !            41: 
        !            42: \begin{itemize}
        !            43: \item {}``x,y@4,5:10,12\#4;0,0'', which take four samples from the box determined
        !            44: by the points (4, 5) and (10, 12), and also sample the point (0, 0).
        !            45: \end{itemize}