查询词典 polynomial

By complete discrimination system of polynomial algebraic equation and resultant theory, a symmetry class of quartic systems with stellar node is studied.

利用多项式代数方程的判别系统理论和结式理论，讨论了具有星形结点的一类对称四次系统的代数分类，并对系统进行全局分析。

This paper reviews the historical development of the algebraic solutions of polynomial equations, introduces the life and scientific achievements of Cardano together with the historical background of Ars Magna. Based on this, the paper makes an elaborate study on Ars Magna.

本文首先回顾了多项式方程代数解法的发展过程，介绍了卡尔达诺的生平、科学与数学成就以及《大术》的历史背景，然后在此基础上详细研究了《大术》各章的内容。

Cardano's Ars Magna is a landmark in the history of mathematics. It started the theoretical research on algebraic equations, solved the polynomial equations of third-degree and forth-degree in a general and systematical way, and studied the imaginary number as well as its operations for the first time.

卡尔达诺的《大术》在数学史上具有重要的地位，它开创了代数方程的理论研究，首次系统地给出了三、四次多项式方程的一般解法，并且最早讨论了虚数及其运算。

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。

Formal Verification; Polynomial Symbolic Algebraic; WGLs; TEDs

形式化验证；多项式符号代数； WGLs； TEDs

Secondly, by applying inverse Fourier integral transform to the displacement, and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions, and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these, the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform.

首先，利用积分变换方法，推导出粘弹性层的控制方程组；其次，引入位错密度函数，并结合边界条件和界面连接条件，导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组，然后，应用Chebyshev正交多项式化奇异积分方程组为代数方程组，并采用Schmidt方法对其数值求解，最后，经过Laplace逆变换，求得动态应力强度因子和能量释放率的时间响应。

We researched the problem of Lagrange interpolation of polynomial space on the algebraic manifold.

研究高维空间中代数流形上多项式空间的Lagrange插值问题。

We posed the concept of sufficient intersection about s(1≤s≤n) algebraic hypersurfaces in n-dimensional space and proved the dimension of polynomial space Pm(which denotes the space of all multivariate polynomials of total degree≤m) on the algebraic manifold S=s(f1,…, fs) where f1(X=0,…, f s=0denote s algebraic hypersurfaces of sufficient intersection, then gave a convenient expression for dimension calculation by using the backw ard difference operator.

给出了n维空间中s(1≤s≤n)个代数超曲面充分相交的概念，证明了n元m次多项式空间Pm在充分相交的代数流形S=s(f1，…， fs)（f1=0，…， fs=0表示s个代数超曲面）上的维数，并利用倒差分算子给出一个方便计算的表达式；构造了沿代数流形上插值适定结点组的叠加插值法；证明了在充分相交的代数流形上任意次插值适定结点组的存在性；给出代数流形上插值适定结点组的性质和判定条件。

G^k continuous piecewise algebraic blending surface patches are obtained by solving the system via the generator basis algorithm of module over polynomial ring.

借助围绕一个顶点处的代数曲面光滑拼接条件，利用多项式环上的素模中的生成基方法，给出了凸组合和非凸组合情形下三个坐标平面间的的任意阶几何连续的光滑拼接方法。

In this paper, we present a method to solve system of algebraic equations or system of parametric algebraic equations by computing the normal zero decomposition of polynomial systems.

本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。