LaTeX example (Beamer and TikZ): Algebraic structures

algebra.tex

%-------------------------------------------------------------------------------
\newcommand{\efivebig}{\begin{tikzpicture}[xscale=.8,yscale=.8,line width=2pt] 
\foreach \i in {1,...,5} 
{ \path (\i,1) coordinate (T\i); \path (\i,0) coordinate (B\i); } 
%%%%%%%
\filldraw[fill= black!12,draw=black!12,line width=4pt]  (T1) -- (T5) -- (B5) -- (B1) -- (T1);
\draw[blue] (T3) .. controls +(.1,-.5) and +(-.1,-.5) .. (T4) ;
\draw[blue] (B3) .. controls +(.1,.3) and +(-.1,.3) .. (B4) ;
\draw[blue] (T1) -- (B1);
\draw[blue] (T2) -- (B2);
\draw[blue] (T5) -- (B5);
%%%%%%%
\foreach \i in {1,...,5} 
{ \fill (T\i) circle (4pt); \fill (B\i) circle (4pt); } 
\end{tikzpicture}}

%-------------------------------------------------------------------------------
\newcommand{\bigdiag}{\begin{tikzpicture}[xscale=.8,yscale=.8,line width=2pt] 
\foreach \i in {1,...,5} 
{ \path (\i,1) coordinate (T\i); \path (\i,0) coordinate (B\i); } 
%%%%%%%
\filldraw[fill= black!12,draw=black!12,line width=4pt]  (T1) -- (T5) -- (B5) -- (B1) -- (T1);
\draw[blue] (T1) -- (B5);
\draw[blue] (T2) .. controls +(.1,-.4) and +(-.1,-.5) .. (T5);
\draw[blue] (T3) .. controls +(.1,-.3) and +(-.1,-.3) .. (T4) ;
\draw[blue] (B1) .. controls +(-.1,.5) and +(.1,.5) .. (B2) ;
\draw[blue] (B3) .. controls +(.1,.3) and +(-.1,.3) .. (B4) ;
%%%%%%%
\foreach \i in {1,...,5} 
{ \fill (T\i) circle (4pt); \fill (B\i) circle (4pt); } 
\end{tikzpicture}}


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\begin{frame}[c]{Similar elements}
For any $d$, a $TL_k$ diagram created by the generators, we can always find a generator $e_i$ such that when $e_i$ is multiplied with $d$, the result is $x\cdot d$. 
$$e_i\cdot d=
\begin{array}{c}
\efivebig \\
\bigdiag \\
\end{array} =x\cdot \begin{array}{c}
\bigdiag \\ 
\end{array} =x\cdot d
$$
This means, $\chi(d)=\chi(\frac{1}{x}e_i\cdot d)=\frac{1}{x}\chi(e_i\cdot d)=\frac{1}{x}\chi(d\cdot e_i)$

\end{frame}
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