Projects per year

### 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.

Original language | English |
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Title of host publication | Intelligent Computer Mathematics |

Editors | S. M. Watt, J. H. Davenport, A. P. Sexton, P. Sojka, J. Urban |

Publisher | Springer |

Pages | 45-60 |

Number of pages | 15 |

ISBN (Electronic) | 9783319084343 |

ISBN (Print) | 9783319084336 |

DOIs | |

Publication status | Published - 2014 |

### Publication series

Name | Lecture Notes in Artificial Intelligence |
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Publisher | Springer |

Volume | 8543 |

### Keywords

- cylindrical algebraic decomposition
- truth table invariance
- regular chains
- triangular decomposition
- problem formulation

## Fingerprint Dive into the research topics of 'Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### Real Geometry and Connectedness via Triangular Description

Davenport, J., Bradford, R., England, M. & Wilson, D.

Engineering and Physical Sciences Research Council

1/10/11 → 31/12/15

Project: Research council

## Cite this

England, M., Bradford, R. J., Chen, C., Davenport, J. H., Moreno Maza, M., & Wilson, D. (2014). Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. In S. M. Watt, J. H. Davenport, A. P. Sexton, P. Sojka, & J. Urban (Eds.),

*Intelligent Computer Mathematics*(pp. 45-60). (Lecture Notes in Artificial Intelligence; Vol. 8543). Springer. https://doi.org/10.1007/978-3-319-08434-3_5