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\begin_body

\begin_layout Standard
This file shows some possible use cases of computer algebra systems within LyX (currently only for 
\family typewriter
Maxima
\family default
) which might give you an idea what is working.
 It also help us to keep track of things which work (or worked).
 Feel free to send us more examples,
 especially for octave or mathematica.
\end_layout

\begin_layout Section
Maxima
\end_layout

\begin_layout Standard

\series bold
Commands that work fine:
\end_layout

\begin_layout Enumerate
\begin_inset Formula $\log(\%e)=1$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\%i^{2}=-1$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\frac{a*b+2*a*b}{b}+\frac{1}{a}+a*b=a\,b+3\,a+\frac{1}{a}$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\sum^{\infty}_{i=1}\left(\frac{1}{2}\right)^{i}=1$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\prod^{5}_{k=1}k=120$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\frac{37}{3}*2-\sum^{3}_{i=1}i^{i}=-\frac{22}{3}$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\int^{2}_{1}\sin(x)dx=\cos1-\cos2$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
\end_inset


\begin_inset Newline newline
\end_inset


\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Note:

\series default
 One needs to use proper delimiter insets 
\begin_inset Formula $\left(\right)$
\end_inset

 instead of simple '(' ')' characters.
\end_layout

\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\det\left[\begin{array}{ccc}
1 & 6 & 7\\
2 & 5 & 8\\
3 & 4 & 17
\end{array}\right]=-56$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum^{\infty}_{{\mathit{i}_{2}}=0}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $solve\left(x_{1}+y^{3}_{1}=y_{1}+x^{2}_{1},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y^{3}_{1}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y^{3}_{1}-4\,y_{1}+1}+1}{2}\right]$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $expand((x+1)^{2})=x^{2}+2\,x+1$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $factor(x^{2}+2\cdot x+1)=\left(x+1\right)^{2}$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $float(\pi)=3.141592653589793$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $fullratsimp\left(\frac{x^{2}-y^{2}}{x+y}\right)=x-y$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $ratsimp\left(\frac{x^{2}-y^{2}}{x+y}\right)=x-y$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $radcan\left(\frac{e^{x}-1}{e^{x/2}+1}\right)=e^{\frac{x}{2}}-1$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $logcontract(\log(3\cdot x)-2\cdot\log(5\cdot x))=\log\left(\frac{3}{25\,x}\right)$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $trigexpand(\sin(x+y))=\cos x\,\sin y+\sin x\,\cos y$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $trigreduce(\cos x\cdot\sin y+\sin x\cdot\cos y)=\sin\left(y+x\right)$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $trigsimp(2\cdot\sin^{2}x+2\cdot\cos^{2}x)=2$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $trigrat(\sin(3\cdot a)/\sin(a+\pi/3))=\sqrt{3}\,\sin\left(2\,a\right)+\cos\left(2\,a\right)-1$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $powerseries\left(\sin\left(x\right),x,0\right)=\sum^{\infty}_{i_{1}=0}{\frac{\left(-1\right)^{i_{1}}\,x^{2\,i_{1}+1}}{\left(2\,i_{1}+1\right)!}}$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $polarform(1+\%i)=\sqrt{2}\,e^{\frac{i\,\pi}{4}}$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $rectform(e^{\%i\cdot t})=i\,\sin t+\cos t$
\end_inset


\end_layout

\begin_layout Section
Octave
\end_layout

\begin_layout Enumerate
\begin_inset Formula $rand(2,2)=\left(\begin{array}{cc}
0.7397 & 0.5357\\
0.4950 & 0.2038
\end{array}\right)$
\end_inset


\end_layout

\begin_layout Section
Mathematica
\end_layout

\begin_layout Enumerate
\begin_inset Formula $\frac{ab+2ab}{b}+\frac{1}{a}+ab=\frac{1}{a}+ab+\frac{3\,ab}{b}$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\frac{a\,b+2a\,b}{b}+\frac{1}{a}+a\,b=\frac{1}{a}+3\,a+a\,b$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $\frac{a*b+2a*b}{b}+\frac{1}{a}+a*b=\frac{1}{a}+3\,a+a\,b$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $Simplify[\frac{a\,b+2a\,b}{b}+\frac{1}{a}+a\,b]=\frac{1}{a}+a\,\left(3+b\right)$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $Sin[Pi/4]=\frac{1}{{\sqrt{2}}}$
\end_inset

 but 
\begin_inset Formula $Sin[P\,i/4]=\sin(\frac{i\,P}{4})$
\end_inset

,
 even if we could use 
\begin_inset Formula $\sin(\pi/4)=\frac{1}{{\sqrt{2}}}$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $TrigExpand[Cos[\alpha+\beta]]=\cos(\alpha)\,\cos(\beta)-\sin(\alpha)\,\sin(\beta)$
\end_inset


\end_layout

\begin_layout Enumerate
\begin_inset Formula $TrigExpand[\cos\left(\alpha+\beta\right)]=\cos(\alpha)\,\cos(\beta)-\sin(\alpha)\,\sin(\beta)$
\end_inset


\end_layout

\end_body
\end_document
