代数几何 meaning in English
algebraic geometry
Examples
- The paper applies algebraic geometry , computational geometry , approximation theory to study the following problems : the nother type theory and the riemann - roch type theory of the piecewise algebraic curve ; the number of real intersection points of piecewise algebraic curves ; the real piecewise algebraic variety and the b - net resultant of polynomials
本文应用代数几何，计算几何，函数逼近论等学科的基本理论，分别就分片代数曲线的n ( ? ) ther型与riemann - roch型定理；分片代数曲线的实交点数；实分片代数簇以及多项式的b -网结式进行研究。 - Second , combining with the construction principle of geometry - goppa codes , we present a kind of new algebraic - geometry code by using the properties of algebraic curves on finite fields . we determine the value of the code - length n and d imension k , and the lower bound of the minimal distances of the new algebraic - geometry code . the new algebraic - geometry code have the following characteristics : ( l ) the new code is the generalization of geometry - goppa codes and the algebraic - geometry code constructed by chaoping xing and san ling in 2000 ( 2 ) compared with brouwer ' table of the best known codes , we find more new codes , there are at least 60 new codes under two - dimension cases
其次，结合几何goppa码的构造原理，利用有限域上代数曲线的特点来构造代数几何码，确定了新的代数几何码的码长n和维数k的取值，给出了最小距离d的下限，这类码的特点是： ( 1 )新的代数几何码是几何goppa码和新加坡国立大学chaopingxing和sanling在2000年所构造的代数几何码的推广； ( 2 )这类码中有许多种码的参数优于brouwer码表，仅二维情形时，就有60多种码优于brouwer码表。 - The traditional separation of algebra and geometry has been unfit for the request of time , it must be reformed . to combine " algebra " and " space analysis geometry " is a good reform project . it correctly reflects the inner law , not only show the impact of advanced algebra as a tool of analysis geometry , but also specifically provide to linear algebra with many kinds of geometric background and geometric expression
传统的代数几何分讲已不符合时代发展的要求，必须进行改革，而把高等代数与空间解析几何合并设课是一个较好的选择方案，这样设课不仅体现线性代数作为解析几何的主要工具的作用，而且更具体地给线性代数提供各种几何背景和几何解释。 - Since 1980s , many mathematicians have been engaged in studying the applications of the grobner basis such as solving the system of algebraic equations , factoring polynomials , testing primary ideals , factoring algebraic manifolds , decoding circular codes in corrected codes and algebraically geometrical codes , analyzing and synthesizing high dimensional linear recurring arrays in cryptology , dealing with multidimensional systematic theory , signaling , solving integer programming and so on
) bner基的应用研究包括代数方程组求解，多项式的因子分解，素理想的检验，代数流形的分解，纠错码中循环码和代数几何码的译码，密码学中高维线性递归阵列的分析与综合，多维系统理论，信号处理和求解整数规划等诸多领域。 - The piecewise algebraic curve and the piecewise algebraic variety , as the set of zeros of a bivariate spline function and the set of all common zeros of multivariate splines respectively , are new and important concepts in algebraic geometry and computational geometry . it is obvious that the piecewise algebraic curve ( variety ) is a kind of generalization of the classical algebraic curve ( variety respectively )
分片代数曲线作为二元样条函数的零点集合，分片代数簇作为一些多元样条函数的公共零点集合，它们是代数几何与计算几何中一种新的重要概念，显然也是经典代数曲线与代数簇的推广。