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 .
Read more about this topic: Ideal Quotient
Famous quotes containing the words calculating the and/or calculating:
“[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.”
—Henry Brooks Adams (1838–1918)
“Sin in this country has been always said to be rather calculating than impulsive.”
—Frank Moore Colby (1865–1925)