  In this paper we consider the classification of singularities (Du Val) and
real structures (Wall) of weak Del Pezzo surfaces from an algorithmic point of
view.
  It is well known that the singularities of weak Del Pezzo surfaces correspond
to root subsystems. We present an algorithm which computes the classification
of these root subsystems. We represent equivalence classes of root subsystems
by unique labels. These labels allow us to construct examples of weak Del Pezzo
surfaces with the corresponding singularity configuration.
  Equivalence classes of real structures of weak Del Pezzo surfaces are also
represented by root subsystems. We present an algorithm which computes the
classification of real structures. This leads to an alternative proof of the
known classification for Del Pezzo surfaces and extends this classification to
singular weak Del Pezzo surfaces.
  As an application we classify families of real conics on cyclides.
