利用正则链库通过投影和提升构造柱形代数分解
Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting
摘要：
柱形代数分解（CAD）是实数上量词消去的一个重要工具，也是一系列其他应用的一个重要工具。传统上，CAD是通过投影和提升的过程来构建的，以在改变维度的欧几里得空间内移动问题。最近，Maple的RegularChains Library中引入并实现了一种替代方法，该方法首先使用三角分解来分解复杂空间，然后再细化到真实空间。我们在这里描述了一个免费的软件包ProjectionCAD，它利用RegularChains Library中的例程通过投影和提升来构建CAD。我们详细介绍了如何修改投影和提升算法，以允许这一点，讨论的动机和调查的功能包。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
