An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination

Authors:
Hidenao Iwane;Hitoshi Yanami;Hirokazu Anai;Kazuhiro Yokoyama
Affiliations:
Fujitsu Laboratories Ltd, Kanagawa, Japan;Fujitsu Laboratories Ltd, Kanagawa, Japan;Fujitsu Laboratories Ltd, Kanagawa, Japan;Rikkyo University, Tokyo, Japan
Venue:
Proceedings of the 2009 conference on Symbolic numeric computation
Year:
2009

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Abstract

Recently quantifier elimination (QE) has been of great interest in many fields of science and engineering. In this paper an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm and its variant specially designed for QE are proposed based on the authors' previous work and our implementation of those is reported. Based on analysing experimental performances, we are improving our design/synthesis of the SNCAD for its practical realization with existing efficient computational techniques and several newly introduced ones. The practicality of the SNCAD is now examined by a number of experimental results including practical engineering problems, which also reveals the quality of the implementation.