二次曲线分类新准则

New Criterion for Classification of Quadratic Curves

摘要: 利用韦达定理(根与系数关系)引入一般二次曲线的α-割函数，α-定义域，以及α-判别式，并且利用它们给出了一般二次曲线分类新准则。与传统方法不同，此方法不依赖于旋转变换，矩阵，不变量和半不变量等概念，只依赖于α-割函数的简单性质。

Abstract: By virtue of Vieta theorem (or relationship between root and coefficient), we introduce the α-cut function, α-domain and α-discriminant of the quadratic curve, and then use them to give a new criterion to make the classification of general quadratic curves. Different from the classical method, this method does not depend on the concepts of rotation transformation, matrix, invariant, and the semi invariant. It only relies on the primary properties of α-cut function.