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| 1 | Computing polynomial univariate representations of zero-dimensional ideals by Grbner basis显示文摘Rational Univariate Representation(RUR) of zero-dimensional ideals is used to describe the zeros of zero-dimensional ideals and RUR has been studied extensively.In 1999,Roullier proposed an efficient algorithm to compute RUR of zero-dimensional ideals.In this paper,we will present a new algorithm to compute Polynomial Univariate Representation(PUR) of zero-dimensional ideals.The new algorithm is based on some interesting properties of Grbner basis.The new algorithm also provides a method for testing separating elements. | MA XiaoDong SUN Yao WANG DingKang | 2012 | Science China Mathematics2012，55，6： | 3 |
| 2 | Global Optimization of Polynomials over Real Algebraic Sets显示文摘Let f, g_1, ···, g_s be polynomials in R[X_1, ···, X_n]. Based on topological properties of generalized critical values, the authors propose a method to compute the global in?mum f~? of f over an arbitrary given real algebraic set V = {x ∈ R^n| g_1(x) = 0, ···, g_s(x) = 0}, where V is not required to be compact or smooth. The authors also generalize this method to solve the problem of optimizing f over a basic closed semi-algebraic set S = {x ∈ R^n| g_1(x) ≥ 0, ···, g_s(x) ≥ 0}. | WANG Chu YANG Zhi-Hong ZHI Lihong | 2019 | Journal of Systems Science & Complexity2019，32，1： | 1 |
| 3 | 捕获等式约束下多项式在闭长方体上的最小值显示文摘对于给定的一个实多项式函数f∈R[x1,…,xn],R[x1,…,xn]中一个非空的有限子集H以及Rn中一个闭长方体n∏=i1[ai,bi],给出了一个有效算法,可产生有限个单元多项式,使得这些单元多项式的一个实根正是多项式函数f在集合n∏i=1[ai,bi]∩ZeroR(H)上的最小值,这里ZeroR(H)为H的实零点集。有关算法通过Maple软件被编制成一个通用程序,可处理相关实例。 | 曾广兴 万玮 | 2015 | 南昌大学学报(理科版)2015，39，1： | 1 |
| 4 | Equality-constrained minimization of polynomial functions显示文摘This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients. | XIAO ShuiJing ZENG GuangXing | 2015 | Science China Mathematics2015，58，10： | 0 |
| 5 | SEMI-ALGEBRAICALLY CONNECTED COMPONENTS OF MINIMUM POINTS OF A POLYNOMIAL FUNCTION显示文摘In a recent article,the authors provided an effective algorithm for both computing the global infimum of / and deciding whether or not the infimum of / is attained,where / is a multivariate polynomial over the field R of real numbers.As a complement,the authors investigate the semialgebraically connected components of minimum points of a polynomial function in this paper.For a given multivariate polynomial / over R,it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of / whenever /has its global minimum. | XIAO Shuijing ZENG Guangxing | 2013 | Journal of Systems Science & Complexity2013，26，6： | 0 |
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