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Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. (English) Zbl 1304.68223
Watt, Stephen M. (ed.) et al., Intelligent computer mathematics. International conference, CICM 2014, Coimbra, Portugal, July 7–11, 2014. Proceedings. Berlin: Springer (ISBN 978-3-319-08433-6/pbk). Lecture Notes in Computer Science 8543. Lecture Notes in Artificial Intelligence, 45-60 (2014).
Summary: 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.
For the entire collection see [Zbl 1293.68035].

MSC:
68W30 Symbolic computation and algebraic computation
14P10 Semialgebraic sets and related spaces
14Q99 Computational aspects in algebraic geometry
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
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