% LISTS
\def\bit{\begin{itemize}}
\def\eit{  \end{itemize}}

\def\ben{\begin{enumerate}}
\def\een{  \end{enumerate}}

\def\itt{\item}

% SEPARATORS
\def\lp{\left(}
\def\rp{\right)}

\def\lb{\left[}
\def\rb{\right]}

%\def\ll{\left|}
%\def\rl{\right|}

\def\lc{\left\{}
\def\rc{\right\}}

% EQUATIONS
\def\beq{\begin{equation}}
\def\eeq{  \end{equation}}
\def\req#1{equation~(\ref{eqn:#1})}
\def\reqs#1{equations~(\ref{eqn:#1})}
\def\reqo#1{(\ref{eqn:#1})}

\def\bea{\begin{array}}
\def\eea{  \end{array}}
\def\beqa{\begin{eqnarray}}
\def\eeqa{  \end{eqnarray}}

\def\beqt{\tiny   \begin{eqnarray}}
\def\eeqt{\nonumber \end{eqnarray} \normalsize}

% VECTORS
\def\iv{\vec{i}} % x unit vector
\def\jv{\vec{j}} % y unit vector

\def\abs#1{\left| #1 \right|}	% vector modulus
\def\vdp#1#2{\lp#1\cdot#2\rp}   % dot product

% SIDE-BY-SIDE objects
\def\sidetwo#1#2{     \matrix{ {#1} & {#2}               \cr}}
\def\sidethree#1#2#3{ \matrix{ {#1} & {#2} & {#3}        \cr}}
\def\sidefour#1#2#3#4{\matrix{ {#1} & {#2} & {#3} & {#4} \cr}}

% OVER-UNDER objects
\def\overtwo#1#2{     \matrix{ {#1} \cr {#2}                   \cr}}
\def\overthree#1#2#3{ \matrix{ {#1} \cr {#2} \cr {#3}          \cr}}
\def\overfour#1#2#3#4{\matrix{ {#1} \cr {#2} \cr {#3} \cr {#4} \cr}}