计算多项式

The paper applies algebraic geometry, computational geometry, approximation theory to study the following problems: the Nother type theory and the Riemann-Roch type theory of the piecewise algebraic curve; the number of real intersection points of piecewise algebraic curves; the real piecewise algebraic variety and the B-net resultant of polynomials.

本文应用代数几何，计算几何，函数逼近论等学科的基本理论，分别就分片代数曲线的Nother型与Riemann-Roch型定理；分片代数曲线的实交点数；实分片代数簇以及多项式的B-网结式进行研究。

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。

In order to solvepiecewise algebraic varieties, we propose a new method to compute an algebraic varietyon a convex polyhedron by adding hyperplanes with the method of Groebner bases. Thus,the algebraic variety on the convex polyhedron is transformed to the positive solutionsof a system of polynomials. Besides, the minimal decomposition is also obtained.

通过添加超平面技巧将Groebner基方法应用到凸多面体内任意维代数簇的计算上，从而把凸多面体内的代数簇转化为另外一组多项式方程组的正解，并且得到了该代数簇在凸多面体内的极小分解。

We present the forward and inverse transform formulas and discuss how to choose the best parameters to avoid aliasing.

讨论了多项式正反Radon变换的公式、实现方法和有关计算参数的选择。

The polynomial approximation method is also employed to obtain simple formulas for frequency and amplitude correction.

本文利用多项式逼近方法获得了频率和幅值修正的计算公式。

We divide this interval into several subintervals, based on deviation points, find the best uniform approximation polynomial of each subinterval, and then denormalize the computation result to the final result.

论文摘要：根据切比雪夫定理，提出了一种适于FPGA实现的函数逼近新方法：通过区间映射关系，将函数定义域映射到较小的逼近区间内，并按照交错点对逼近区间进行分段，分别求出每段的最佳一致逼近多项式，对函数进行分段逼近，最后将逼近结果反映射，得到最终的函数计算结果。

It is shown that the algorithm is polynomial bounded.

其计算复杂性是多项式有界的。

We not only give explicitexpressions of monomial elements in the canonical basis but also representregions of them in "nice" forms which help us compute polynomial elementsin the canonical basis.

我们不仅给出了这种具体表达式，而且把它们对应的区域写成很好的形式，便于我们计算典范基中的多项式元素。

This paper gives a simple algorithm for the computation of the characteristic polynomial of a square matrix.

在线性定常控制系统的分析和综合中，计算矩阵特征多项式的问题，是经常会出现的，因而也是十分基本的。

According to the air trajectory of every rocket-assisted torpedo part, we establish an equation group of air vertical motion, improve the in-air trajectory model, and simulatively calculate the polynomials of firing distance and flight time,and firing distance and shut down time. Making use of the polynomials, we calculate the cooperative time of formation salvo of torpedoes, and determine command ways for different situations. The result may facilitate the research of operational application of rocket-assisted torpedo.

根据火箭助飞鱼雷空中运动各部分的特点，建立了其空中纵向运动方程组，完善了空中弹道模型，仿真计算了射程-飞行时间和射程-关机时间关系多项式，利用关系式计算了编队齐射火箭助飞鱼雷的协同时间，确定了不同态势下的指挥方式，为深入研究火箭助飞鱼雷编队作战使用问题提供了重要的参考数据和理论依据。

I use an example quoted by Hu Jiaqi:"It is reported that America separates the DNA of a kind of virus by making use of genetic technology and combines it with another kind of DNA. Finally, they get a kind of virulent biological agent called a "pyrotoxin". Someone discloses in private that 20 grams of such a kind of biological agent could result in the global death of 6 billion people due to infection."

我在这里例举胡家奇所引用过的例子："据报道，美国利用转基因技术，将一种病毒的DNA分离出来，与另外一种DNA进行结合，拼结成一种剧毒的"热毒素"生物战剂，且私下有人透露，这种生物战剂只需20克，就可以导致全球60亿人全部感染死亡。"

Waiting, for the queers and the coons and the Reds and the Jews.

等待着疯子和黑人还有红色共产主义者还有犹太人