On inverse systems and squarefree decomposition of zero-dimensional polynomial ideals

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• 作者：Werner Heiß ; Ulrich Oberst and Franz Pauer
• 关键词：Dual basis ; Inverse system ; Squarefree decomposition ; Systems of generators of minimal length
• 刊名：Journal of Symbolic Computation
• 出版年：2006
• 出版时间：March-April 2006
• 年：2006
• 卷：41
• 期：3-4
• 页码：261-284
• 全文大小：314 K

文摘

Let I be a zero-dimensional ideal in a polynomial ring F[s]:=F[s₁,…,s_n] over an arbitrary field F. We show how to compute an F-basis of the inverse system I of I. We describe the F[s]-module I by generators and relations and characterise the minimal length of a system of F[s]-generators of I. If the primary decomposition of I is known, such a system can be computed. Finally we generalise the well-known notion of squarefree decomposition of a univariate polynomial to the case of zero-dimensional ideals in F[s] and present an algorithm to compute this decomposition.