查询词典 degree of a polynomial

Let H. f and g be real polynomials in x, y of degree n+1, at most n and at most n respectively,△ be a set of h such that the real algebraic curve H =h has a compact component δ, and ω=gdx-fdy be a polynomial 1-form.

设H是n+1次实多项式，f，g为至多n次的实多项式，记△为使实代数曲线H=h有一个紧分支δ的所有h之值的集合，ω=gdx-fdy为多项式1-形式。

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。

Since any n x n doubly stochastic circulant matrix has a unique representation as a polynomial of degree n - 1 in the shift operator wn, the classification problem of primes in the doubly stochastic circulant matrices can be reduced to the solution of an equation over a doubly stochastic circulant matrix.

由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式，从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程。

Since any n×n doubly stochastic circulant matrix has a unique representation as a polynomial of degree n-1 in the shift operatorω_n,the classification problem of primes in the doubly stochastic circulant matrices can be reduced to the solution of an equation over a doubly stochastic circulant matrix.

由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式，从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程。

By using the Euclidean algorithm and invertible linear transformation over a polynomial ring, the solutions of polynomial indeterminate equations of first degree was investigated in theory, and its matrix solution based on the elementary matrix transformation was proposed.

利用欧几里德算法和多项式环上的可逆线性变换，从理论上对多项式环上的一次不定方程组的解进行深入的研究，给出了用矩阵的初等变换求解多项式环上的一次不定方程组的矩阵解法，并利用MATLAB数学软件开发了相应的计算机程序。

Ythagorean hodograph curves enjoy a number of remarkable properties, such as, its offset curves have exact rational representations; the arc length function of a Pythagorean hodograph curve is simply a polynomial function of the curve parameter; and the lower degree Pythagorean hodograph curves have intuitive geometrical interpretation.

H曲线具有诸如有精确的有理 Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质。基于复分析方法，避免了实分析讨论中出现的复杂表示及繁琐计算，构造了满足给定 C1 Hermite插值条件且以C1拼接连续的三次 PH曲线偶。该曲线偶可灵活处理拐点，从而克服了一般三次 PH曲线因恒凸而无法处理拐点的缺陷。

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。

For the interpolation problems in which the nodes are on one or more algebraic manifolds, we pointed out the interpolation bases of the lowest degree w.r.t.a graded term order and gave a new algorithm. We also gave a estimation for the degree of the interpolation polynomial.

我们针对插值节点位于一个或几个代数流形上的插值问题，从理论上指出了插值问题在某一分次序下最低次的插值基并给出了新的算法，同时也对插值多项式的次数作了估计。

Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.

首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。

An n×n sign pattern A is a spectrally arbitrary pattern if for any given real monic polynomial f of degree n, there is a real matrix B∈Q and B has characteristic polynomial f.

设A为n阶符号模式矩阵，若对任意给定的一个n次首1实系数多项式f，都存在一个实矩阵B∈Q，使得B的特征多项式为f，则称A为谱任意符号模式。

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％。