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corrected definition of S-polynomial; added name; reference to commutative algebra |
fixed definition that I had broken; brought it into line with conventional defs to avoid confusion |
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A crude version of this algorithm proceeds as follows:
1. Start with ''F'' = {''f''<sub>1</sub>, ''f''<sub>2</sub>, ..., ''f''<sub>''k''</sub>}, a set of generators for your ideal. Let ''g<sub>i</sub>'' be the leading term of ''f<sub>i</sub>'' with respect to the given ordering, and denote the [[
2. Let ''S''<sub>''ij''</sub> = (''a''<sub>''ij''</sub> / ''g''<sub>''
3. Using the [[multivariate division algorithm]], reduce all the ''S<sub>ij</sub>'' relative to the set ''F''.
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