Investigation of the Dixon Resultants

狄克逊的制定同时消除多变量的多元多项式方程组的几个变量将进行调查。求解多项式方程和确定方程有公共解的参数条件是符号计算中的基本问题，几乎无处不在。多项式被用来模拟许多现象-特别是在机器人，运动学，计算机视觉，实体建模，图形学，化学平衡和其他工程，CAD-CAM设计等狄克逊的公式直接推广Bezout-Cayley的公式，以消除单一变量。狄克逊结式没有得到广泛的研究显然是因为他们大概得到蒙上阴影麦考利的制定结式同时消除几个变量。 狄克逊结式、麦考利结式和稀疏结式的实现表明，狄克逊结式在实践中计算效率更高。 狄克逊结果将进行分析，特别强调研究的狄克逊矩阵的大小和结构的输入多项式系统的关系。 ***

Dixon's formulation for simultaneously eliminating several variables from a system of multivariate polynomial equations will be investigated. Solving polynomials equations and identifying conditions on parameters under which the equations have common solutions are fundamental problems in symbolic computations which arise almost everywhere. Polynomials are used to model many phenomena - particularly in robotics, kinematics, computer vision, solid modeling, graphics, chemical equilibrium and other engineering, CAD-CAM design, etc. Dixon's formulation directly generalizes Bezout-Cayley's formulation of a resultant for eliminating a single variable. Dixon resultants have not been extensively investigated apparently because they presumably got overshadowed by Macaulay's formulation of resultants for simultaneously eliminating several variables. Implementations of Dixon resultants, Macaulay resultants and sparse resultants have revealed that Dixon resultants are more efficient to compute in practice. Dixon resultants will be analyzed with a particular emphasis on studying the relationship of the size and structure of the Dixon matrix to the input polynomial system. ***