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VTS and Lazard Projection CAD in Quantifier Elimination with Maple

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VTS and Lazard Projection CAD in Quantifier Elimination with Maple
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31
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CC Attribution - NonCommercial - NoDerivatives 3.0 Germany:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Production Year2020
Production PlaceBath, UK

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Traditionally, VTS (Virtual Term Substitution) and CAD (Cylindrical Algebraic Decomposition) are the two main algorithms for Quantifier Elimination over the reals (QE) with differing limitations and benefits. We discuss QuantifierElimination, a package in Maple implementing VTS and CAD in a poly-algorithmic sense to attempt to minimise the limitations of both, including an amalgamation of contemporary ideas about CAD including equational constraints & the Lazard projection, providing features in demand for the Real Algebraic Geometry community. Further ideas expand on how best to use CAD following from VTS, including in an incremental sense in the context of QE.
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