| RESEARCH ANNOUNCEMENTS——The Construction of Eigenvalue Problem Equivalent to Multivariate Polynomial System and the Groebner Basis |
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| 引用本文： | 冯果忱,吴文达,黄铠.RESEARCH ANNOUNCEMENTS——The Construction of Eigenvalue Problem Equivalent to Multivariate Polynomial System and the Groebner Basis[J].数学进展,1993(3). |
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| 作者姓名： | 冯果忱 吴文达 黄铠 |
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| 作者单位： | Jilin University，Changchun，130023，Jilin，P.R.C.，Jilin University，Changchun，130023，Jilin，P.R.C.，Beijing Municipal Computer Center，Beijing，100005，P.R.C |
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| 基金项目： | State Major Key Project for Basic Researches in China. |
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| 摘 要： | In this paper we will show that one cau build up a joint eigenvalue problem eq-uivalent to the. given system. By this way, finding the solutions of the given systemis equivalent to finding all eigenvalues and eigenvectors of one matrix or matrix pen-cil. For the special case that the system has finite isolated solutions, we can obtainall solutions through computing the eigenvalues and eigenvectors of a matrix whichcan Le obtained by Gauss-Jordan elimination. Furthermore, we also find that one canget Groebner Basis for the ideal geuerated by the given system iu this way. For any polynomial f(x)∈Kx_1,x_2,…,x_n],f(x) can be written as
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