化简二次曲面方程的探究

Research on Simplification of the General Quadratic Surface Equation

通过结合解析几何与代数理论的知识,利用配方法、合同变换法、正交变换法给出了二次曲面方程化简的几种途径,配方法解决了利用坐标系的平移、旋转、不变量对二次曲面分类、化简时运算复杂或无法确定图形具体位置的问题;合同变换法是在不着重研究曲面几何性质时常用的一种方法,它的标准型不唯一;正交变换法正好相反。本文着重讨论它们在实际例题中的应用。

By formulating and contragradient transforming and orthogonal transforming the several approaches to simplify the general quadratic surface equation was given based on analytic geometry and algebraic theory. The formulation solves the complicated operation and the problem of determining the definite location of the graph when classifying and simplifying the general quadratic surface by using parallel uanslation and votation of coordinate system and invariants. However the contragradient transformation is an approach that does not emphasize the geometric propeties of curves, and whose canonical form is not unique. In this paper, their applications to practical instances were discussed.