利用McCallum投影在Maple中实现CAD
An implementation of CAD in Maple utilising McCallum projection
摘要：
柱形代数分解（CAD）是研究半代数集的重要工具。最初由柯林斯在20世纪70年代引入用于量词消去，它已经在代数几何和其他领域找到了许多应用。1988年，McCallum提出了一种改进的算法CADW，大大提高了CAD的实用性。2009年，西安大略大学的一个团队提出了一种新的、完全独立的CAD算法，该算法被实现并包含在计算机代数系统Maple中。作为巴斯研究CAD及其应用的更广泛项目的一部分，Collins和McCallum的CAD算法已经在Maple中实现。本报告详细介绍了这些实现，并将其与Qepcad和Ontario算法进行了比较。这些实现最初是为了促进对算法之间联系的研究。然而，该代码的能力，以保证顺序不变的输出，导致其使用在新的研究CAD这是最小的某些问题。此外，这里描述的实现是CADW的唯一完整实现（因为Qepcad目前没有使用McCallum的描绘多项式），因此可以解决其他CAD实现不允许的问题。
英文摘要：
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets. Originally introduced by Collins in the 1970s for use in quantifier elimination it has since found numerous applications within algebraic geometry and beyond. Following from his original work in 1988, McCallum presented an improved algorithm, CADW, which offered a huge increase in the practical utility of CAD. In 2009 a team based at the University of Western Ontario presented a new and quite separate algorithm for CAD, which was implemented and included in the computer algebra system Maple. As part of a wider project at Bath investigating CAD and its applications, Collins and McCallum's CAD algorithms have been implemented in Maple. This report details these implementations and compares them to Qepcad and the Ontario algorithm. The implementations were originally undertaken to facilitate research into the connections between the algorithms. However, the ability of the code to guarantee order-invariant output has led to its use in new research on CADs which are minimal for certain problems. In addition, the implementation described here is of interest as the only full implementation of CADW, (since Qepcad does not currently make use of McCallum's delineating polynomials), and hence can solve problems not admissible to other CAD implementations.
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。
