  Dependent symmetries, symmetries that depend on the situation of the
subsystem in a larger closed system, are explored by looking at simple
examples. This is a new kind of symmetry in the open quantum dynamics of a
subsystem
  Each symmetry implies a particular form for the results of the open dynamics.
The forms exhibit the symmetries very simply. It is shown directly, without
assuming anything about the symmetry, that the dynamics produces the form, but
knowing the symmetry and the form it implies can reduce what needs to be done
to work out the dynamics; pieces can be deduced from the symmetry rather that
calculated from the dynamics.
  Symmetries can be related to constants of the motion in new ways. A quantity
might be a dependent constant of the motion, constant only for particular
situations of the subsystem in the larger system. In particular, a generator of
dependent symmetries could represent a quantity that is a dependent constant of
the motion for the same situations as for the symmetries. The examples present
a variety of possibilities. Sometimes a generator of dependent symmetries does
represent a dependent constant of the motion. Sometimes it does not. Sometimes
no quantity is a dependent constant of the motion. Sometimes every quantity is.
