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1.1     ! raeburn     1: \label{Authorinag_Daxe_Math}
        !             2: 
        !             3: \textbf{LON-CAPA math syntax}
        !             4: 
        !             5: As usual, the \texttt{$<$m$>$} element can be used for math with a LaTeX syntax. It can be inserted with the \texttt{\$} button in the toolbar or the \texttt{ctrl-T} shortcut.
        !             6: 
        !             7: Daxe also supports a new LON-CAPA element: the \texttt{$<$lm$>$} element, which allows for a simpler syntax for math. To use the \texttt{$<$lm$>$} element to insert a math expression use the √x button or the \texttt{ctrl-E} shortcut. In the future this syntax may also be used to evaluate \texttt{$<$formularesponse$>$}, but for now its use in \texttt{$<$formularresponse$>$} is limited to the real-time preview of the expression entered in the answer textbox.
        !             8: 
        !             9: Below is a description of the syntax used by \texttt{$<$lm$>$} for displaying math (there is more to this syntax when it is used for evaluation, which is not described here).
        !            10: 
        !            11: Since it can be used for evaluation, it describes mathematical operations rather than appearance (as opposed to LaTeX, which describes how the math should \emph{appear}). Display is the same when the math operations are the same, for instance \texttt{2*(x)} will be displayed just like \texttt{2x}. One advantage to that system is that math will be displayed in a consistent way; disadvantages are that display cannot be chosen precisely, and also the \texttt{$<$lm$>$} element will only be available on servers running LON-CAPA 2.12 (and for now, only at MSU where a modified 2.11.4 with some 2.12 features included, pre-release, has been deployed).
        !            12: \begin{description}
        !            13:         \item[\textmd{\normalsize\textit{Spaces}}]
        !            14: 
        !            15: Spaces are always ignored.
        !            16:         \item[\textmd{\normalsize\textit{Decimal separators and function parameter separators}}]
        !            17: 
        !            18: To keep compatible with previous \texttt{$<$formularesponse$>$} syntax, only \texttt{``.''} can be used as a decimal separator, and \texttt{``,''} is used to separate function and vector/matrix parameters.
        !            19:         \item[\textmd{\normalsize\textit{Variables and constants}}]
        !            20: 
        !            21: Variable names and constant names are used directly, without any special character before. They are displayed in italics.
        !            22:         \item[\textmd{\normalsize\textit{Units}}]
        !            23: 
        !            24: Unit names are used directly. They are displayed with a straight font. LON-CAPA has a list of known units and a list of known constants to differentiate them in units mode.
        !            25:         \item[\textmd{\normalsize\textit{Parenthesis}}]
        !            26: 
        !            27: Parenthesis can be used to specify evaluation order. They are only displayed when necessary.
        !            28:         \item[\textmd{\normalsize\textit{Operators}}]
        !            29: \begin{itemize}
        !            30:         \item arithmetic: \texttt{+ - * / \^{} }
        !            31: \\
        !            32:         \item factorial: \texttt{!}
        !            33:         \item relational: \texttt{= \# $<$ $<$= $>$= $>$}
        !            34:         \item units: \texttt{`}
        !            35: \\ Example: \texttt{2`m + 3`m = 5`m}
        !            36:         \item scalar product for vectors, multiplication for matrices: \texttt{.}
        !            37: \end{itemize}
        !            38:         \item[\textmd{\normalsize\textit{Implicit operators}}]
        !            39: 
        !            40: \texttt{*} and \texttt{`} are implicit.
        !            41: 
        !            42: The parser will try to guess which operator is missing whenever possible. The choice between \texttt{*} and \texttt{`} depends on the mode for interpreting equations.
        !            43: 
        !            44: Example: \texttt{2c+3m/s} is understood in unit mode to be \texttt{2*c + 3`(m/s)}. In symbolic mode, it would be interpreted \texttt{2*c + (3*m)/s} (\texttt{m} and \texttt{s} being variables).
        !            45:         \item[\textmd{\normalsize\textit{Functions}}]
        !            46: 
        !            47: Functions use the syntax \texttt{f(a,b)}.
        !            48: \begin{itemize}
        !            49:         \item basic:
        !            50: \begin{verbatim}
        !            51: sqrt(x), abs(x), exp(x)=e^x, factorial(x)=x!\end{verbatim}
        !            52:         \item binomial (displayed like a vector):
        !            53: \begin{verbatim}
        !            54: binomial(n,p)=n!/(p!*(n-p)!)\end{verbatim}
        !            55:         \item sum and product (requiring symbolic mode):
        !            56: \begin{verbatim}
        !            57: sum(f(x),x,x1,x2), product(f(x),x,x1,x2)\end{verbatim}
        !            58:         \item differential, integral, limit:
        !            59: \begin{verbatim}
        !            60: diff(expr, x, n), integrate(expr, x, a, b), limit(expr, x, val, plus/minus)\end{verbatim}
        !            61: \end{itemize}
        !            62:         \item[\textmd{\normalsize\textit{Vectors and matrices}}]
        !            63: 
        !            64: Vectors and matrices are defined with square brackets. A matrix is made of a list of row vectors.
        !            65: \begin{itemize}
        !            66:         \item vectors: \texttt{[1,2,3]}
        !            67:         \item matrices: \texttt{[[1,2],[3,4]]}
        !            68: \end{itemize}
        !            69:         \item[\textmd{\normalsize\textit{Sets}}]
        !            70: 
        !            71: Sets are defined with curly brackets: \texttt{\{1,2,3\}}
        !            72: 
        !            73: Operators:
        !            74: \begin{itemize}
        !            75:         \item union: \texttt{union(\{1,2\},\{1,3\}) = \{1,2,3\}}
        !            76:         \item intersection: \texttt{intersection(\{1,2\},\{1,3\}) = \{1\}}
        !            77: \end{itemize}
        !            78: \end{description}