An algorithm to compute the H-bases for ideals of subalgebras (Q2046963)

Summary: 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.