In the last section triplet section subscripts motivated us to define
subranges as a new
kind of range. Likewise, scalar section subscripts drive us to define
a new kind of group. A *restricted group* is defined to be
the subset of processes in some parent group to which a particular
location is mapped. In the current example, the distribution group of
`b` is defined to be the subset of processes in `p` to which
the location `x[0]` is mapped.
The division operator is overloaded to describe these subgroups,
The distribution group of `b` is equivalent to `q`, defined by

The expression in the initializer is called a

In a sense the definition of a restricted group was tacit in the definition
of an abstract location. Without formally defining the idea, we
used it implicitly in section 2.5. In Figure
2.7 of that section the set of processes with
coordinates , and , to which location `x[1]`
is mapped, can be written as

and the set with coordinates and , to which

The intersection of these two--the group containing the single process with coordinates --can be written as

or as

The restricted groups introduced here have a
simple concrete representation. A restricted group can be specified by
its set of effective process dimensions and the identity of the *lead* process in the group--the process with coordinate zero relative
to the dimensions effective in the group. The dimension set can be
specified as a subset of the dimensions of the parent grid using a
simple bitmask. The identity of the lead process can be specified
through a single integer ranking the processes of the parent grid. So
a general HPJava group can be parametrized by a reference to the parent
`Procs` object, plus just two `int` fields. It turns out that
this representation is not only compact; it also lends itself to efficient
computation of the most commonly used operations on groups.

Notice by the way that the inquiry function `dim()` is a member
of the *Procs* class (the process grid class), *not* the
superclass `Group`, which also embraces restricted groups.