The concept of H-bases, introduced long ago by Macauly, has become an important ingredient for the treatment of various problems in computational algebra. The concept of H-bases is for ideals in polynomial rings, which allows an investigation of multivariate polynomial spaces degree by degree. Similarly, we have the analogue of H-bases for subalgebras, termed as SH-bases. In this paper, we present an analogue of H-bases for finitely generated ideals in a given subalgebra of a polynomial ring, and we call them “HSG-bases.” We present their connection to the SAGBI-Gröbner basis concept, characterize HSG-basis, and show how to construct them.

中文翻译：

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一种计算子代数理想 H 基的算法

很久以前由Macauly 引入的H 基的概念已经成为处理计算代数中各种问题的重要组成部分。H 基的概念用于多项式环中的理想，它允许逐次研究多元多项式空间。类似地，我们有子代数的 H 基类似物，称为 SH 基。在本文中，我们提出了多项式环的给定子代数中有限生成理想的 H 基的类似物，我们称它们为“HSG 基”。我们展示了它们与 SAGBI-Gröbner 基概念的联系，表征了 HSG 基，并展示了如何构建它们。