Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
arXiv:1404.6371 · doi:10.1007/978-3-319-08434-3_5
Abstract
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.
References in corpus (1)
Cited by in corpus (6)
- Improving the use of equational constraints in cylindrical algebraic decomposition
- Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting
- Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
- Using the distribution of cells by dimension in a cylindrical algebraic decomposition
- An implementation of Sub-CAD in Maple
- Formulating problems for real algebraic geometry