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1.2     ! raeburn     1: \label{Authoring_Daxe_Math}
1.1       raeburn     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}