查询词典 polynomial

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。

Then, to decide whether a propositional formula can be deduced from a finite set of such formulas,we only need to decide whether the polynomial vanishes on an algebraic variety which is related to this formula set.

从而判定一个命题公式能否以一组命题公式推出，我们只需判定某一多项式是否在一代数簇上消失。

A polynomial system PS over the rational number field is constructed from the formula...,in a given many-valued logic system such that follows from ...,iff the algebraic variety defined by PS is empty, iff the idealenerated by PS is trivial.

由给定的多值逻辑系统中的一组公式，。。。，，出发，构造出了一组有理数域上的多项式PS，使得是，。。。，的逻辑结论，当且仅当PS定义的代数簇为空集，当且仅当PS生成的理想是平凡理想。

Yet, Edith says, there was always money in the bank.

但是Edith说，她的银行户口里面总是有钱。

We have created a series of files that resolve this problem--one for each day of the 40 days of purpose.

我们制作一系列的档案去解决这问题---一个为标竿40天中的每一天。