### 3.2 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

1<E COMPOSITE="C[0]" NUMMODES="5" FIELDS="u" TYPE="MODIFIED" />

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

1<E COMPOSITE="C[0]" NUMMODES="5" FIELDS="u,v,p" TYPE="MODIFIED" />

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:

1<E COMPOSITE="C[0]"
2   BASISTYPE="Modified_A,Modified_B,Modified_C"
3   NUMMODES="3,3,3"
4   POINTSTYPE="GaussLobattoLegendre,GaussRadauMAlpha1Beta0,GaussRadauMAlpha2Beta0"
5   NUMPOINTS="4,3,3"
6   FIELDS="u" />

and for prism elements:

1<E COMPOSITE="C[1]"
2   BASISTYPE="Modified_A,Modified_A,Modified_B"
3   NUMMODES="3,3,3"
4   POINTSTYPE="GaussLobattoLegendre,GaussLobattoLegendre,GaussRadauMAlpha1Beta0"
5   NUMPOINTS="4,4,3"
6   FIELDS="u" />

The expansions can be defined with a list of `<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 `<E>` tags without the `FIELDS` attribute. The default expansion is used to define any variables not explicitly listed in the `<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]:

1<E COMPOSITE="C[0-2]" NUMMODES="5" TYPE="MODIFIED" />
2<E COMPOSITE="C[3]"   NUMMODES="4" TYPE="MODIFIED" FIELDS="u,v"/>
3<E COMPOSITE="C[3]"   NUMMODES="3" TYPE="MODIFIED" FIELDS="p"/>

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