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This paper by Eisenstein and Criterion On a few of the conclusions presented several integer coefficients irreducible polynomials way of judging, but the discussion of not more than four times the whole of the polynomial coefficients can be about issues, by some three to four times the entire polynomial coefficient about the summary judgment method.

本文由艾森斯坦因判别法及数论中的有关结论给出了几个整系数多项式不可约的判定方法，同时讨论了不高于四次的整系数多项式的可约性问题，得到了某些三次，四次整系数多项式可约性的简易判定方法。

Zeros of linear polynomials with real efficients are the real solutions of the original polynomial equation.

5四元数二次方程的显式解：利用改进的新方法完全可以得到二次方程解的显式表示以及关于解的具体情况的一些充分必要条件。

We first introduce the positive real spectrum function and bounded spectrum function then establish the parametrization of the power spectrum by the Levinson polynomials associated with the autocorrelation matrix of the output and bounded spectrum function.

首先引入正实谱函数的和有界谱函数的概念，利用正实函数和有界实函数理论，通过和过程自相关矩阵相关联的Levinson多项式和有界谱函数，建立了功率谱参数化的表达式。

In Z2 to judge whether a polynomial primitive polynomial, and the right to the inverse polynomials.

在Z2中判断一个多项式是否本原多项式，并能对给定的多项式求逆。

The basic steps of this method are as follows.The firststep is to derive a necessary condition such that the families of quasipolynomials withone parameter,corresponding to the edges of the polytope,have pure imaginary rootsby using the Dixon's resultant for polynomials.Then to check that the casescorresponding to the parameters obtained in the first step are in fact impossible byusing the generalized Sturm criterion and some stability criteria.

其基本思路是先利用多项式方程组的Dixon结式理论导出使各棱边对应的单参数特征拟多项式有纯虚根时，参数值应满足的一个等式条件，即所谓的Dixon结式等于零，然后由广义Sturm判别法验证对所有参数值，Dixon结式不等于零，或使结式等于零的解不产生特征拟多项式的纯虚根。

Questions in this content area are based on an understanding of the quadratic formula, rational and radical expressions, absolute value equations and inequalities, sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers.

中等代数（ 15 ％）。这方面的考试内容包括理解二次公式，有理式及根式，绝对值方程和不等式，序列，方程组，二次不等式，函数，建模，矩阵，多项式的根以及复数。

The paper provided a new digital signature scheme according to the characteristics of factoring polynomials over a large infinite field and quadratic residue.

依据有限域中因式分解和二次剩余的特性，得到一种在GF上有效求解二次模p方程的算法，并根据该算法提出一种数字签名方案。

In this paper, a simple interpolation method using quartic polynomials to fill in the missing projections is presented. The clipping on the pixel values of the reconstructed image is also proposed.

为了消除这种金属伪影，提出了一种用四次多项式来对缺失的投影值进行插值，并对重构的图象进行值裁剪的方法。

Here, we chose simple polynomials as shape functions, and derive the element matrice on the regular element (a isosceles triangle with a right angle).

这里选取逐渐升幂的简单多项式作为基底函数，并且据此推导了升到六阶的正规单元矩阵。

The local minimum relative distances and the corresponding times, as well as the time when one space object enters and exits in the ellipsoidal region of another one are determined by solving the roots of the polynomials.

由A-N算法提出的准则不能直接计算插值时间步长并可能导致丢根，对此根据多项式插值误差理论提出了一种自适应的插值时间步长选取方法。

My father is over 60 years old, and he lifts weights every day.

我爸爸六十多岁了，他每天都练习举重。

Then in a serious tone she declared:"It doesn't pay, dear boy, to look like a ninny with one's wife the first night."

两眼湿润了，她把身子蜷得很小，这样似乎可以更好地闻闻自己。