\section{Expansions}
\label{sec:xml:expansions}
This section defines the polynomial expansions used on each of the defined
geometric composites and variables. Expansion entries specify the number of
modes and the expansion type, or a full list of data of basis type, number of
modes, points type and number of points. The short-hand version has the
following form

\begin{lstlisting}[style=XMLStyle]
<E COMPOSITE="C[0]" NUMMODES="5" FIELDS="u" TYPE="MODIFIED" />
\end{lstlisting}

or, if we have more then one variable we can apply the same basis to all using

\begin{lstlisting}[style=XMLStyle]
<E COMPOSITE="C[0]" NUMMODES="5" FIELDS="u,v,p" TYPE="MODIFIED" />
\end{lstlisting}

The expansion basis can also be specified in detail as a combination of
one-dimensional bases, and thus the user is able to, for example, increase the
quadrature order. For tet elements this takes the form:

\begin{lstlisting}[style=XMLStyle]
<E COMPOSITE="C[0]" 
   BASISTYPE="Modified_A,Modified_B,Modified_C" 
   NUMMODES="3,3,3"
   POINTSTYPE="GaussLobattoLegendre,GaussRadauMAlpha1Beta0,GaussRadauMAlpha2Beta0"
   NUMPOINTS="4,3,3"
   FIELDS="u" />
\end{lstlisting}

and for prism elements:

\begin{lstlisting}[style=XMLStyle]
<E COMPOSITE="C[1]" 
   BASISTYPE="Modified_A,Modified_A,Modified_B" 
   NUMMODES="3,3,3"
   POINTSTYPE="GaussLobattoLegendre,GaussLobattoLegendre,GaussRadauMAlpha1Beta0"
   NUMPOINTS="4,4,3"
   FIELDS="u" />
\end{lstlisting}

The expansions can be defined with a list of \inltt{<E>} elements (e.g., to
represent different polynomial orders for different variables or to address
different composites). The user can define a default expansion field by entering
\inltt{<E>} tags without the \inltt{FIELDS} attribute. The default expansion is
used to define any variables not explicitly listed in the \inltt{<E>} entries.
In the following example, the default expansion is used to define the expansions
for the composites C[0], C[1] and C[2]:

\begin{lstlisting}[style=XMLStyle]
<E COMPOSITE="C[0-2]" NUMMODES="5" TYPE="MODIFIED" />
<E COMPOSITE="C[3]"   NUMMODES="4" TYPE="MODIFIED" FIELDS="u,v"/>
<E COMPOSITE="C[3]"   NUMMODES="3" TYPE="MODIFIED" FIELDS="p"/>
\end{lstlisting}

The expansions of each field should be defined only once for each composite.
