primary decomposition of zero-dimensional ideals over finite fields
文献类型：期刊论文
| 作者 | Gao Shuhong ; Wan Daqing ; Wang Mingsheng |
| 刊名 | MATHEMATICS OF COMPUTATION
 |
| 出版日期 | 2009 |
| 卷号 | 78期号:265页码:509-521 |
| 关键词 | Primary decomposition primary ideals quasi-primary ideals Groebner bases Frobenius map |
| ISSN号 | 0025-5718 |
| 学科主题 | Mathematics ; Applied |
| 收录类别 | SCI |
| 公开日期 | 2011-03-18 |
| 附注 | A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamps algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a complete decomposition. Unlike previous approaches for decomposing multivariate polynomial systems, the new method does not need primality testing nor any generic projection, instead it reduces the general decomposition problem directly to root finding of univariate polynomials over the ground field. Also, it is shown how Grobner basis structure can be used to get partial primary decomposition without any root finding. |
| 源URL | [http://124.16.136.157/handle/311060/8138]  |
| 专题 | 软件研究所_信息安全国家重点实验室_期刊论文 |
| 推荐引用方式 GB/T 7714 | Gao Shuhong,Wan Daqing,Wang Mingsheng. primary decomposition of zero-dimensional ideals over finite fields[J]. MATHEMATICS OF COMPUTATION,2009,78(265):509-521. |
| APA | Gao Shuhong,Wan Daqing,&Wang Mingsheng.(2009).primary decomposition of zero-dimensional ideals over finite fields.MATHEMATICS OF COMPUTATION,78(265),509-521. |
| MLA | Gao Shuhong,et al."primary decomposition of zero-dimensional ideals over finite fields".MATHEMATICS OF COMPUTATION 78.265(2009):509-521. |
入库方式： OAI收割
来源：软件研究所
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