×

zbMATH — the first resource for mathematics

Using the Regular Chains library to build cylindrical algebraic decompositions by projecting and lifting. (English) Zbl 1437.14008
Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 458-465 (2014).
Summary: 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.
For the entire collection see [Zbl 1293.65003].

MSC:
14-04 Software, source code, etc. for problems pertaining to algebraic geometry
14Q65 Geometric aspects of numerical algebraic geometry
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
68W30 Symbolic computation and algebraic computation
PDF BibTeX Cite
Full Text: DOI