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

Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition