代数簇

关于仿射代数簇坐标环的同调维数与krull维数的一个注记

A Note on Krull Dimensions and Homological Dimensions of Coordinate Rings of Affine Algebraic Varieties

因此给出样条曲线曲面的求交算法是CAGD中的重要问题之一，而这一问题的本质可以归结为分片代数簇的计算。

The intersection of spline curves / surfaces becomes an important problem in CAGD . However , this problem boils down to the computation of piecewise algebraic varieties .

（2,1）-代数簇及其自由对象

Varieties of ( 2,1 ) - Algebras and Their Free Objects

因此，研究分片代数簇的计算是十分重要的。

Hence , it is important to study the piecewise algebraic variety .

准素理想的商理想与代数簇

Algebraic varieties of ideal quotients in the pre-prime ideal

奇数维代数簇的小收缩映射

On small contraction maps of odd dimensional projective varieties

第三章我们讨论了分片代数簇的某些问题。

In chapter 3 , we discuss several problems on piecewise algebraic varieties .

拟代数簇包含关系的判定算法

A decidable algorithm for inclusion of quasi-algebraic varieties

关于代数簇的小收缩映射的翻转

On flip of small contraction of projective varieties

关于BCK-代数簇的一个问题

A Problem about the BCK-algebras Variety

奇维数射影代数簇的小收缩态射的极小维例外集的结构

Structure of the Minimal Dimensional Exceptional Locus of Small Contraction over Projective Varieties of Odd Dimension

多元样条、多元弱样条及分片代数簇是本文的主要研究对象。

In this doctorial dissertation , we mainly study multivariate spline , multivariate weak spline and piecewise algebraic variety .

本文主要对多元样条与分片代数簇计算展开若干研究。

In this thesis , we mainly study some applications of multivariate splines and computation of piecewise algebraic varieties .

判定拟代数簇的包含关系问题不能由计算其相应的饱和理想来确定。

The problem of deciding inclusion of quasi-algebraic varieties can not be determined by computing their saturated ideals respectively .

分片代数簇作为多元样条组的公共零点集合，是经典代数簇的推广，丰富和发展。

As the zeros of multivariate splines , the piecewise algebraic variety is a generalization of the classical algebraic variety .

另一方面，我们给出了零维分片代数簇实根简单而有效的分离算法。

On the other hand , we give the effective and fast algorithm of real root isolation for zero-dimensional piecewise algebraic variety .

该算法主要基于凸多面体内代数簇的计算和一元区间多项式实根的计算来实现。

It is primarily based on the computation of algebraic variety on a given convex polyhedron and the real roots of the univariate interval polynomial .

然而，等时中心问题的研究迄今还没有一个成熟的方法，并且，由于其中涉及大量多元多项式的代数簇计算，计算机的计算能力也限制着此问题的发展。

However , there is no general method to investigate the problem of isochronous centers and the computation power of computers restricts the development of this problem because many computations are involved .

内容摘要：高维代数簇的双有理等价分类是代数几何研究的一个重要分支，其主要问题就是通过代数簇的收缩态射构造极小模型。

One of the main research fields in algebraic geometry is the birational equivalent classifications of higher dimensional algebraic varieties , of which the key problem is to construct minimal models through contractions of algebraic varieties .

给出了分片代数曲线（簇）的定义，并对研究的理论与应用背景进行了阐述。

Last , we present the recent researches on piecewise algebraic curves and piecewise algebraic varieties .

分片代数曲线与分片代数簇的若干研究

Some Researches on Piecewise Algebraic Curves and Piecewise Algebraic Varieties

分片代数曲线、分片代数簇与分片半代数集的某些问题研究

Some Researches on Piecewise Algebraic Curves , Piecewise Algebraic Varieties , and Piecewise Semialgebraic Sets

局部化（Localization）方法是交换代数中一个重要工具，通过研究一个代数簇（AlgebraicVariety）在某点或某点附近的局部性质，往往可以把握代数簇的整体特性。

Method of localization is a important tool in Commutative Algebra . The whole properties are always obtained by studying local properties of Algebraic Variety .

因此，我们构造了整体G2-连续的三次代数样条来逼近参数曲线以实现近似隐式化。最后，我们讨论了分片代数簇计算中的某些问题。

In order to solve it , we use a piecewise cubic algebraic curve to give a global G2 continuity approximation to the original parametric curve . Lastly , we discuss several computation problems on piecewise algebraic varieties .