Abstract:
The main aim of this paper is to propose effective methods to construct minimal homogeneous bases for polynomial ideals. These specific generating sets for ideals are the homogeneous counterpart of Gröbner bases, the so-called minimal H-bases. A modification of Buchberger's algorithm to compute such bases was proposed in [18]. Here we show how to rectify this algorithm by applying Buchberger's criteria to speed up the computation of minimal H-bases in a significant way. Finally, a general framework for computing minimal H-bases is presented, and it is shown that not any approach to compute Gröbner bases can be employed to produce minimal H-bases.
Key Words: Polynomial ideals, Gröbner bases, Buchberger's algorithm, Buchberger's criteria, minimal homogeneous bases, minimal H-bases, syzygy module.
2010 Mathematics Subject Classification: Primary 13P10; Secondary 68W30.
