Algorithms for the theory of restrictions of scalar \(n\) -D systems to proper

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• 作者：Debasattam Pal ; Harish K. Pillai
• 关键词：Systems of PDEs ; Restriction ideals ; Computational algorithms
• 刊名：Multidimensional Systems and Signal Processing
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：26
• 期：2
• 页码：439-457
• 全文大小：427 KB
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• 刊物类别：Engineering
• 刊物主题：Circuits and Systems
  Electronic and Computer Engineering
  Signal,Image and Speech Processing
  Artificial Intelligence and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-0824

文摘

In this paper, we study the restrictions of solutions of a scalar system of PDEs to a proper subspace of the domain \(\mathbb {R}^n\) . The object of study is associated with certain intersection ideals. In the paper, we provide explicit algorithms to calculate these intersection ideals. We next deal with when a given subspace is “free-with respect to the solution set of a system of PDEs—this notion of freeness is related to restrictions and intersection ideals. We again provide algorithms and checkable algebraic criterion to answer the question of freeness of a subspace. Finally, we provide an upper bound to the dimension of free subspaces that can be associated with the solution set of a system of PDEs.