Revision as of 01:07, 20 July 2022 edit Cedar101 (talk \| contribs) Extended confirmed users 18,555 edits m →Algorithm: {{math}} {{var}} {{sfrac}} ← Previous edit		Revision as of 10:45, 15 August 2022 edit undo Salix alba (talk \| contribs) Edit filter managers, Administrators 26,197 edits →Algorithm: fix capitalisation of indices in formula Next edit →
Line 13: :# ''G'' := ''F'' :# For every ''f<sub>i</sub>'', ''f<sub>j</sub>'' in ''G'', denote by ''g<sub>i</sub>'' the leading term of ''f<sub>i</sub>'' with respect to the given ordering, and by ''a<sub>ij</sub>'' the [[least common multiple]] of ''g<sub>i</sub>'' and ''g<sub>j</sub>''. :# Choose two polynomials in ''G'' and let {{math\|1=''S''<sub>''ij''</sub> = {{sfrac\|''a''<sub>''ij''</sub> \| ''g''<sub>{{var\|Ii}}</sub>}} ''f''<sub>{{var\|Ii}}</sub> − {{sfrac\|''a''<sub>''ij''</sub> \| ''g''<sub>''j''</sub>}} ''f''<sub>''j''</sub>}} ''(Note that the leading terms here will cancel by construction)''. :# Reduce ''S''<sub>''ij''</sub>, with the [[multivariate division algorithm]] relative to the set ''G'' until the result is not further reducible. If the result is non-zero, add it to ''G''. :# Repeat steps 2-4 until all possible pairs are considered, including those involving the new polynomials added in step 4.

Buchberger's algorithm: Difference between revisions