Note on (De)homogenized Gröbner Bases

Details Note on (De)homogenized Gröbner Bases Note on (De)homogenized Gröbner Bases

2009-07-15

arxiv.org/abs/0907.2483v1

Mathematics

Rings and Algebras

13 pages

Scientific paper

By employing the (de)homogenization technique in a relatively extensive setting, this note studies in detail the relation between non-homogeneous Gr\"obner bases and homogeneous Gr\"obner bases. As a consequence, a general principle of computing Gr\"obner bases (for an ideal and its homogenization ideal) by passing to homogenized generators is clarified systematically. The obtained results improve and strengthen the work of [LWZ], [Li1], [Li2], [Li3], and very recent [SL] concerning the same topic.

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