Numeric and Symbolic Methods for Polynomial Manipulation

的符号和数值操作算法 基本的符号、数字和几何系统都需要 计算及其在图形学、几何 建模、机器人、视觉和工程。 这项研究采取了三重方法 这些问题使用多多项式结式：（1）发展更好 符号结式计算及非线性多项式求解算法 使用结式和矩阵计算的方程。 算法正在被 在精确算术和浮点运算的背景下开发的 算术 它涉及到更好的公式化的结式在矩阵方面， 行列式以及利用矩阵的符号和数值算法的使用 公式化。 (2)将这些算法专门用于计算机应用 图形学、几何建模和机器人技术， 这些应用中出现的多项式系统。 (3)开发一个例程库， ELIMPACK，用于符号结果计算和求 多项式方程（精确和浮点运算）。 这个包裹是 对符号计算、数值计算、几何计算、 应用程序和工程社区。 这些结果也有助于 理解几何问题的复杂性， 多项式方程

Algorithms for symbolic and numeric manipulation of systems are needed for basic symbolic, numeric and geometric computations and their application to problems in graphics, geometric modeling, robotics, vision and engineering. This research takes a three-fold approach to these problems using multipolynomial resultants: (1) Develop better algorithms for symbolic resultant computation and solving nonlinear polynomial equations using resultants and matrix computations. Algorithms are being developed in the context of exact arithmetic as well as floating point arithmetic. It involves better formulations of resultants in terms of matrices and determinants and use of symbolic and numeric algorithms making use of the matrix formulation. (2) Specialize these algorithms to applications in computer graphics, geometric modeling and robotics by making use of the specific polynomial systems arising in these applications. (3) Develop a library of routines, ELIMPACK, for symbolic resultant computation and finding roots of polynomial equations (in exact and floating point arithmetic). This package is of great utility to symbolic computation, numerical computation, geometric applications and the engineering community. The results also help in understanding the complexity of geometric problems described in terms of polynomial equations.