**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* = (*f*_{1}, *f*_{2}, *f*_{3}) and *J* = (*g*_{1}, *g*_{2}) are ideals in *k*, then

Then elimination theory can be used to calculate the intersection of *I* with (*g*_{1}) and (*g*_{2}):

Calculate a GrÃ¶bner basis for *tI* + (1-*t*)(*g*_{1}) with respect to lexicographic order. Then the basis functions which have no *t* in them generate .

Read more about this topic: Ideal Quotient

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