代数多项式

The appliance of polynomial symbolic algebraic in formal verification ,people have given two polynamial denotative module WGLs and TEDs,and gives the corresponding equivalence checking algorithms .

关于多项式符号代数理论在形式化验证方面的研究，人们给出了WGLs和TEDs两个多项式表示模型，并给出了相应的等价性验证算法。

In this paper, we have made a systemic theoretic research on modelling and reshaping several types of spline curves/surfaces in CAGD. And some creative productions are given as follows. At first, the uniform C-B-spline basis is proved to be a normalized totally positive basis, and can be extended to a normalized B-basis. C-B-spline and C-Bézier basis, similar to B-spline basis and Bézier basis in algebraic space, are two bases in algebraic trigonometric space.

本文围绕着CAGD中常用的几种曲线曲面造型和形状调整进行了深入的研究，主要获得了以下一些成果：首先，证明了代数三角空间中的n次均匀C-B-spline基是一组标准全正基，并进一步扩充为一组标准B基。C-B-spline基与C-Bézier基是多项式与三角混合空间中的两组基，是适应工程实践中设计特殊曲线曲面的需要而产生的，类似于多项式空间中的B-spline基与Bézier基，是CAGD中重要的造型工具。

The parametric speed of the curve is firstly approximated by the Bernstein polynomial, which takes the lengths of control point vectors of the direction curve of normal as Bézier coordinates.

其次 ，基于参数速度的 L egendre多项式逼近和插值区间端点的 Jacobi多项式逼近，导出了保持法矢平移方向的两种代数方式的等距有理逼近算法。

In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment of the closed-loop systems is transferr.

以代数几何方法为工具，将此闭环系统的特征多项式配置问题转化为判别有理映射是否为到上的，推导出多输入的 2 D广义系统Roe sser模型由状态反馈几乎任意配置特征多项式系数的充分条件。

The polynomial greatest common divisor is one of the most important polynomial contents, as which is not only the basic summary in the whole Higher Mathematics and Number Theory .

多项式最大公因式是多项式众多内容中十分重要的一项，它在整个高等代数、抽象代数、数论等科目当中，既是基础性的内容，也是很多其它项目研究中要求具有的储备知识。

Polynomial function ; Finite commutative ring ; Finite commutative local ring; Teichmller representatives; Witt polynomial

基础科学，数学，代数、数论、组合理论多项式函数；有限交换环；有限交换局部环； Teichmller提升； Witt多项式

In the section, the definitions and main properties of the operator have been discussed systematically, the operational rules of one dimensional PGOPO have been strictly established based on the theory of convergence in the mean square, error and convergence analysis of approximation by PGOPO has been discussed.

系统地论述了分段广义正交多项式算子的定义、性质，并为一维PGOPO算子严格地建立一套在均方收敛意义下的代数运算规则，给出了分段广义正交多项式算子作用下的误差及收敛性分析结果。

By using the techniques of an explicit criterion to determine the number of real roots of a univariate polynomial in ( [13] , [73] ); B-net form of bivariate splines function; discriminant sequence of polynomial (cf. [13] , [73] ) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, this paper determines the number of real intersection points two piecewise algebraic curves whose common points are finite.

3：利用杨路，张景中，侯晓荣在文献（[13]，[73]）中关于一元多项式实根的显式判准，以及二元样条函数的B-网形式，多项式的判别序列和Sturm序列的最高次数项系数序列的变号数，本文给出了两个分片代数曲线的实交点数的计算公式。

Secondly, linear algebra, can create a polynomial coefficient and multiple lines between the matrix-style counterparts, so as to transform line for the primary use of the domain P polynomial the greatest common factor.

其次，在线性代数中，可以建立多项式的系数与多行矩阵表示式之间的对应关系，从而利用初等行变换求数域P上的多项式的最大公因式。

The theory of rings is an important content of Modern Algebra, while the polynomial rings is an important part of the rings. Polynomial ring is similar with power series ring, and it is a subset of the power series.

摘要环论是近世代数中的重要内容，而多项式环的性质又是环论理论中的重要组成部分，多项式环是幂级数环的子环且与幂级数环形式相近。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。