Calculating The Quotient
The above properties can be used to calculate the quotient of ideals in a polynomial ring given their generators. For example, if I = (f1, f2, f3) and J = (g1, g2) are ideals in k, then
Then elimination theory can be used to calculate the intersection of I with (g1) and (g2):
Calculate a Gröbner basis for tI + (1-t)(g1) with respect to lexicographic order. Then the basis functions which have no t in them generate .
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