实分片代数曲线的某些研究

Some Researches on Real Piecewise Algebraic Curves

中文关键词:  二元样条  分片代数曲线  分片代数簇  代数几何.

英文关键词:bivariate splines  piecewise algebraic curves  piecewise algebraic varieties  algebraic geometry.

中文摘要:

      分片代数曲线作为二元样条函数的零点集合是经典代数曲线的推广. 利用代数的基本知识, 本文对实分片代数曲线的基本性质进行了初步讨论, 并且将实分片代数曲线与相应的二元样条分类进行讨论. 最后, 对实分片代数曲线上的孤立点进行了研究.

英文摘要:

      The piecewise algebraic curve, defined by a bivariate spline, is a generalization of the classical algebraic curve. In this paper, we present some researches on real piecewise algebraic curves using elementary algebra. A real piecewise algebraic curve is studied according to the fact that a real spline for the curve is indefinite, definite or semidefinite (nondefinite). Moreover, the isolated points of a real piecewise algebraic curve is also discussed.