Abstract
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.
Highlights
Introduction e concept ofH-bases, introduced long ago by Macaulay [1], is based solely on homogeneous terms of a polynomial
Some applications of H-bases are given in [3]; in addition, many of the problems in applications which can be solved by the Grobner technique can be treated successfully with H-bases. e concept of H-basis for ideals of a polynomial ring over a field K can be adopted in a natural way to K-subalgebras of a polynomial ring
Like H-bases, the concept of SH-basis is tied to homogeneous polynomials
Summary
Introduction e concept ofH-bases, introduced long ago by Macaulay [1], is based solely on homogeneous terms of a polynomial. We will present an analogue to H-bases for ideals in a given subalgebra of a polynomial ring, and we call them “HSG-bases.” Input: a subalgebra A, a finite subset G ⊂ A, and a polynomial f ∈ A. ALGORITHM 2: Algorithm for the construction of HSG basis.
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