Revision as of 19:34, 16 October 2011 edit 81.10.172.210 (talk) No edit summary ← Previous edit		Revision as of 12:17, 6 January 2012 edit undo 137.226.152.117 (talk) Corrected small notation error 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