In this paper, an algebraic method which is based on the groebner bases theory is proposed to solve the polynomial functions conditional extreme. Firstly, we describe how to solve conditional extreme value problems by...In this paper, an algebraic method which is based on the groebner bases theory is proposed to solve the polynomial functions conditional extreme. Firstly, we describe how to solve conditional extreme value problems by establishing Lagrange functions and calculating the differential equations derived from the Lagrange functions. Then, by solving the single variable polynomials in the groebner basis, the solution of polynomial equations could be derived successively. We overcome the high number of variables and constraints in the extreme value problem. Finally, this paper illustrates the calculation process of this method through the general procedures and examples in solving questions of conditional extremum of polynomial function.展开更多
Abstract. In this paper we contribute with one main result to the interesting probleminitiated by Hong(1998) on the behaviour of Groebner bases under composition of polyno-mials. Polynomial composition is the operatio...Abstract. In this paper we contribute with one main result to the interesting probleminitiated by Hong(1998) on the behaviour of Groebner bases under composition of polyno-mials. Polynomial composition is the operation of replacing the variables of a polynomialwith other polynomials. The main question of this paper is: Does there exist a decisionprocedure that will determine whether a given composition is comPatible with a given termordering? If so, find one. We will give a better answer.展开更多
This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those...This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.展开更多
The problem of synthesizing a planar four-bar linkage with two given fixed pivots such that the coupler curve passes through five given points is considered with the Groebner-Sylvester hybrid approach.First,closed-for...The problem of synthesizing a planar four-bar linkage with two given fixed pivots such that the coupler curve passes through five given points is considered with the Groebner-Sylvester hybrid approach.First,closed-form equations of a single point are constructed.The reduced Groebner basis in degree lexicographic ordering for the closed-form equations is then obtained using com-puter algebra.A 23623 Sylvester’s matrix can be con-structed by selecting 23 out of 89 Groebner bases.A 36th degree univariate equation is obtained directly from the determinate of the matrix.The same result can be obtained with a continuation method.A numerical example is given and verifies that the problem has at most 36 solutions in the complex field.展开更多
文摘In this paper, an algebraic method which is based on the groebner bases theory is proposed to solve the polynomial functions conditional extreme. Firstly, we describe how to solve conditional extreme value problems by establishing Lagrange functions and calculating the differential equations derived from the Lagrange functions. Then, by solving the single variable polynomials in the groebner basis, the solution of polynomial equations could be derived successively. We overcome the high number of variables and constraints in the extreme value problem. Finally, this paper illustrates the calculation process of this method through the general procedures and examples in solving questions of conditional extremum of polynomial function.
基金the Foundation of Nature Science of Hunan Province(98JJY2052)
文摘Abstract. In this paper we contribute with one main result to the interesting probleminitiated by Hong(1998) on the behaviour of Groebner bases under composition of polyno-mials. Polynomial composition is the operation of replacing the variables of a polynomialwith other polynomials. The main question of this paper is: Does there exist a decisionprocedure that will determine whether a given composition is comPatible with a given termordering? If so, find one. We will give a better answer.
文摘This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.
基金supported by the National Basic Research Program of China(No.2004CB31800)the National Natural Science Foundation of China(Grant No.50475161)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(No.2005-0013006)the National Hi-Tech Research and Development Program of China(No.2007AA04Z211).
文摘The problem of synthesizing a planar four-bar linkage with two given fixed pivots such that the coupler curve passes through five given points is considered with the Groebner-Sylvester hybrid approach.First,closed-form equations of a single point are constructed.The reduced Groebner basis in degree lexicographic ordering for the closed-form equations is then obtained using com-puter algebra.A 23623 Sylvester’s matrix can be con-structed by selecting 23 out of 89 Groebner bases.A 36th degree univariate equation is obtained directly from the determinate of the matrix.The same result can be obtained with a continuation method.A numerical example is given and verifies that the problem has at most 36 solutions in the complex field.
