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An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination. (English) Zbl 1291.68433
Summary: With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm for QE incorporating several new devices, which we call “quick tests”. The simple quick tests are run beforehand to detect an unnecessary procedure that might be skipped without violating the correctness of results and they thus considerably reduce the computing time. The effectiveness of the SNCAD algorithm is examined in a number of experiments including practical engineering problems, which also reveal the quality of the implementation. Experimental results show that our implementation has significantly improved efficiency compared with our previous work.

MSC:
68W30 Symbolic computation and algebraic computation
03C10 Quantifier elimination, model completeness and related topics
Software:
AQCS; QEPCAD; RAGlib
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