25th Annual Symposium onFoundations of Computer Science, 1984. (1984)
Singer Island, FL
Oct. 24, 1984 to Oct. 26, 1984
M. Kaminski , University of Waterloo
Let R be a ring, and let f(/spl alpha/), g(/spl alph/) /spl epsi/ R[/spl alpha/] be univariate polynomials over R of degree n. We Present an algorithm for computing the coefficients of the product f(/spl alpha/)G (/spl alpha/) by O (nlgn) multiplications. This algorithm is based on an algorithm for multiplying polynomials over the ring of integers, and does not depend on R. Also we prove that multiplying the third degree polynomials over the ripg of integers requires at least nine multiplications. This bound is tight.
M. Kaminski, "Multiplication Of Polynomials Over The Ring Of Integers," 25th Annual Symposium onFoundations of Computer Science, 1984.(FOCS), Singer Island, FL, 1984, pp. 251-254.