### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Keywords

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

### Cite this

*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

**Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition.** / England, Matthew; Bradford, Russell J.; Chen, Changbo; Davenport, James H.; Moreno Maza, Mark; Wilson, David.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition

AU - England, Matthew

AU - Bradford, Russell J.

AU - Chen, Changbo

AU - Davenport, James H.

AU - Moreno Maza, Mark

AU - Wilson, David

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - cylindrical algebraic decomposition

KW - truth table invariance

KW - regular chains

KW - triangular decomposition

KW - problem formulation

UR - http://dx.doi.org/10.1007/978-3-319-08434-3_5

UR - http://cicm-conference.org/2014/cicm.php

U2 - 10.1007/978-3-319-08434-3_5

DO - 10.1007/978-3-319-08434-3_5

M3 - Chapter

SN - 9783319084336

T3 - Lecture Notes in Artificial Intelligence

SP - 45

EP - 60

BT - Intelligent Computer Mathematics

A2 - Watt, S. M.

A2 - Davenport, J. H.

A2 - Sexton, A. P.

A2 - Sojka, P.

A2 - Urban, J.

PB - Springer

ER -