Revision as of 02:04, 17 May 2006 edit Chewie (usurped) (talk \| contribs) 12 edits m GCD capitalization ← Previous edit		Revision as of 14:52, 17 June 2006 edit undo Mets501 (talk \| contribs) 24,644 edits m clean up using AWB Next edit →
Line 7: :# Let ''g<sub>i</sub>'' be the leading term of ''f<sub>i</sub>'' with respect to the given ordering, and denote the [[least common multiple]] of ''g<sub>i</sub>'' and ''g<sub>j</sub>'' by ''a<sub>ij</sub>''. :# Let ''S''<sub>''ij''</sub> ~~←~~← (''a''<sub>''ij''</sub> / ''g''<sub>''i''</sub>) ''f''<sub>''i''</sub> − (''a''<sub>''ij''</sub> / ''g''<sub>''j''</sub>) ''f''<sub>''j''</sub> <br>''(Note that the leading terms here will cancel by construction)''. :# Using the [[multivariate division algorithm]], reduce all the ''S<sub>ij</sub>'' relative to the set ''F''. :# Add all the nonzero polynomials resulting from step 3 to ''F'', and repeat steps 1-4 until nothing new is added.

Buchberger's algorithm: Difference between revisions