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

Abstract

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

References in corpus (2)

• Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
• An implementation of CAD in Maple utilising McCallum projection

Cited by in corpus (4)

• Improving the use of equational constraints in cylindrical algebraic decomposition
• Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition
• Using the distribution of cells by dimension in a cylindrical algebraic decomposition
• An implementation of Sub-CAD in Maple