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Cylindrical algebraic decomposition (CAD) is an important tool, both forquantifier elimination over the reals and a range of other applications.Traditionally, a CAD is built through a process of projection and lifting tomove the problem within Euclidean spaces of changing dimension. Recently, analternative approach which first decomposes complex space using triangulardecomposition before refining to real space has been introduced and implementedwithin the RegularChains Library of Maple. We here describe a freely availablepackage ProjectionCAD which utilises the routines within the RegularChainsLibrary to build CADs by projection and lifting. We detail how the projectionand lifting algorithms were modified to allow this, discuss the motivation andsurvey the functionality of the package.

Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting