Buchberger's algorithm: Difference between revisions

Revision as of 14:52, 17 June 2006

Revision as of 22:51, 21 June 2006

Line 18:

The algorithm succeeds because it is consistently increasing the size of the monomial ideal generated by the leading terms of our set ''F'', and [[Dickson's lemma]] (or the [[Hilbert basis theorem]]) guarantees that any such ascending chain must eventually become constant. Therefore this algorithm does indeed stop. Unfortunately, it may take a very long time to terminate, corresponding to the fact that Gröbner bases can be ''extremely'' large.

==External links==

* {{MathWorld | urlname=BuchbergersAlgorithm | title=Buchberger's Algorithm}}

[[Category:Algebra]]