  Cylindrical algebraic decompositions (CADs) are a key tool for solving
problems in real algebraic geometry and beyond. We recently presented a new CAD
algorithm combining two advances: truth-table invariance, making the CAD
invariant with respect to the truth of logical formulae rather than the signs
of polynomials; and CAD construction by regular chains technology, where first
a complex decomposition is constructed by refining a tree incrementally by
constraint. We here consider how best to formulate problems for input to this
algorithm. We focus on a choice (not relevant for other CAD algorithms) about
the order in which constraints are presented. We develop new heuristics to help
make this choice and thus allow the best use of the algorithm in practice. We
also consider other choices of problem formulation for CAD, as discussed in
CICM 2013, revisiting these in the context of the new algorithm.
