  This article presents the systematic design of a class of relational
numerical abstract domains from non-relational ones. Constructed domains
represent sets of invariants of the form (vj - vi in C), where vj and vi are
two variables, and C lives in an abstraction of P(Z), P(Q), or P(R). We will
call this family of domains weakly relational domains. The underlying concept
allowing this construction is an extension of potential graphs and
shortest-path closure algorithms in exotic-like algebras. Example constructions
are given in order to retrieve well-known domains as well as new ones. Such
domains can then be used in the Abstract Interpretation framework in order to
design various static analyses. Amajor benfit of this construction is its
modularity, allowing to quickly implement new abstract domains from existing
ones.
