3. Constants terms:

In fact, this operator signature permits testing not only the emptiness but also other attributes of the HQSet. We remark that some constants such as CONSTANT_EMPTY, CONSTANT_UNIVERSE, UNDEFINED are introduced. In the polyhedral case, they respectively represent an empty set, e.g. with only the constraint $0==1$, all the space ($R^n$), with no constraint, and an undefined HQSet object.

The undefined HQSet object is not available in PPL, Octagon and New POLKA but only in $C^3$. In $C^3$, there is a distinction between the pointer to an undefined constraint system and a standard ANSI C pointer. It is because sometimes programmers want to know whether the returned object is an empty or undefined constraint system .