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.
|Title of host publication||Mathematical Software – ICMS 2014|
|Subtitle of host publication||4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings|
|Editors||H. Hong, C. Yap|
|Number of pages||8|
|Publication status||Published - 2014|
|Name||Lecture Notes in Computer Science|
England, M., Wilson, D., Bradford, R., & Davenport, J. H. (2014). Using the regular chains library to build cylindrical algebraic decompositions by projecting and lifting. In H. Hong, & C. Yap (Eds.), Mathematical Software – ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings (pp. 458-465). (Lecture Notes in Computer Science; Vol. 8592). Springer. https://doi.org/10.1007/978-3-662-44199-2_69