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Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
England, Matthew1; Bradford, Russell1; Chen, Changbo2; Davenport, James H.1; Maza, Marc Moreno3; Wilson, David1
2014
摘要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. © 2014 Springer International Publishing.
语种英语
DOI10.1007/978-3-319-08434-3_5
会议(录)名称2014 International Conference on Intelligent Computer Mathematics, CICM 2014
页码45-60
收录类别EI
会议地点Coimbra, Portugal
会议日期July 7, 2014 - July 11, 2014