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Optimising problem formulation for cylindrical algebraic decomposition. (English) Zbl 1390.68775
Carette, Jacques (ed.) et al., Intelligent computer mathematics. MKM, Calculemus, DML, and systems and projects 2013, held as part of CICM 2013, Bath, UK, July 8–12, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-39319-8/pbk). Lecture Notes in Computer Science 7961. Lecture Notes in Artificial Intelligence, 19-34 (2013).
Summary: 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.
For the entire collection see [Zbl 1268.68008].

68W30 Symbolic computation and algebraic computation
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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