#LyX 1.3 created this file. For more info see http://www.lyx.org/
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\layout Title

Maxima + Lyx - an example document
\layout Standard

The fun begins - there is apparently a way to send commands to Maxima from
 Lyx.
 It's somewhat different from the TeXmacs functionality, but does seem to
 be functional at least on a basic level.
 Let's start with a basic example.
 First, type Alt-m m or Alt-m d to get a mathematical input, and enter a
 basic Maxima expression (we will use Alt-m d here):
\layout Standard


\begin_inset Formula \[
integrate\left(\frac{x}{1+x^{3}}+1,x\right)\]

\end_inset 


\layout Standard

Now, the fun part.
 There should be a menu entry Maxima under Edit
\begin_inset Formula $\rightarrow$
\end_inset 

Math
\begin_inset Formula $\rightarrow$
\end_inset 

Use Computer Algebra System.
 Note the Math submenu will only be active if your cursor is located in
 the expression you want to evaluate.
 If we select Maxima we get the following result:
\layout Standard


\begin_inset Formula \begin{eqnarray*}
integrate\left(\frac{x}{1+x^{3}}+1,x\right) & = & \frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\, x-1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log\left(x+1\right)}{3}+x\end{eqnarray*}

\end_inset 


\layout Standard

Note also that Lyx is able to translate the formatted input into something
 Maxima can understand.
 So far this ability is unique to this interface.
 It even extends to basic operators - for example, if we want to evaluate
 a formatted input of the form:
\begin_inset Formula \[
\int\left(\sin\left(x\right)+\frac{1}{1+x^{2}}\right)dx\]

\end_inset 

Lyx and Maxima can make sense of it:
\layout Standard


\begin_inset Formula \begin{eqnarray*}
\int\left(\sin\left(x\right)+\frac{1}{1+x^{2}}\right)dx & = & \arctan x-\cos x\end{eqnarray*}

\end_inset 

The previous case also works perfectly.
 Parenthesis seem to be optional:
\layout Standard


\begin_inset Formula \begin{eqnarray*}
\int\frac{x}{1+x^{3}}+1\, dx & = & \frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\, x-1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log\left(x+1\right)}{3}+x\end{eqnarray*}

\end_inset 


\layout Standard

Or, in another example, if we want to evaluate 
\begin_inset Formula $\sum_{i=1}^{\infty}\left(\frac{1}{3}\right)^{i}$
\end_inset 

 :
\begin_inset Formula \begin{eqnarray*}
\sum_{i=1}^{\infty}\left(\frac{1}{3}\right)^{i} & = & \frac{1}{2}\end{eqnarray*}

\end_inset 

It seems to handle rather complex outputs cleanly as well:
\layout Standard


\begin_inset Formula \begin{eqnarray*}
powerseries\left(\log\left(\frac{\sin\left(x\right)}{x}\right),x,0\right) & = & \frac{\sum_{I_{1}=1}^{\infty}{\frac{\left(-1\right)^{I_{1}}\,2^{2\, I_{1}}\, BERN\left(2\, I_{1}\right)\, x^{2\, I_{1}}}{I_{1}\,\left(2\, I_{1}\right)!}}}{2}\end{eqnarray*}

\end_inset 


\layout Standard

Unfortunately, plotting is not integrated as yet.
\the_end