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m the informal use of "resultant" was potentially confusing |
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3. Using the [[multivariate division algorithm]], reduce all the ''S<sub>ij</sub>'' relative to the set ''F''.
4. Add all the nonzero
There are numerous ways to improve this algorithm beyond what has been stated above. For example, one could reduce all the new elements of ''F'' relative to each other before adding them. It also should be noted that if the leading terms of ''f<sub>i</sub>'' and ''f<sub>j</sub>'' share no variables in common, then ''S<sub>ij</sub>'' will ''always'' reduce to 0 (if we use only f<sub>i</sub> and f<sub>j</sub> for reduction), so we needn't calculate it at all.
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