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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Optimising Problem Formulation for Cylindrical Algebraic Decomposition
verfasst von : Russell Bradford, James H. Davenport, Matthew England, David Wilson
Erschienen in: Intelligent Computer Mathematics
Verlag: Springer Berlin Heidelberg
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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 Gröbner bases to precondition TTICAD and when such formulations constitute the creation of a new problem.