Minimal homogeneous bases for polynomial ideals
The minimal homogeneous basis is defined. It is shown that every minimal homogeneous basis of an ideal has the same number of elements. An algorithm for finding a minimal homogeneous basis is developed. The main idea is to modify the classical Buchberger's algorithm for finding a Grobner basis so that a minimal homogeneous basis can be obtained as a subset of a Grobner basis.
polynomial ideals grobner bases syzygies