@inproceedings{c22f16cefb6a40b98a8e186473aa328c,

title = "Optimising problem formulation for cylindrical algebraic decomposition",

abstract = "Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of variables in the worst case, but the actual computation time can vary greatly. It is possible to offer different formulations for a given problem leading to great differences in tractability. In this paper we suggest a new measure for CAD complexity which takes into account the real geometry of the problem. This leads to new heuristics for choosing: the variable ordering for a CAD problem, a designated equational constraint, and formulations for truth-table invariant CADs (TTICADs). We then consider the possibility of using Gr{\"o}bner bases to precondition TTICAD and when such formulations constitute the creation of a new problem.",

keywords = "cylindrical algebraic decomposition, Gr{\"o}bner bases, problem formulation, symbolic computation",

author = "Russell Bradford and Davenport, {James H.} and Matthew England and David Wilson",

year = "2013",

doi = "10.1007/978-3-642-39320-4_2",

language = "English",

isbn = "9783642393198",

volume = "7961 LNAI",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

pages = "19--34",

editor = "Jacques Carette and David Aspinall and Christoph Lange and Petr Sojka and Wolfgang Windsteiger",

booktitle = "Intelligent Computer Mathematics - MKM, Calculemus, DML, and Systems and Projects 2013 - Held as Part of CICM 2013, Proceedings",

address = "United Kingdom",

note = "Conference on Intelligent Computer Mathematics, CICM 2013, Co-located with the MKM 2013, Calculemus 2013, DML 2013, and Systems and Projects 2013 ; Conference date: 08-07-2013 Through 12-07-2013",

}