Summary: Theoretical Computer Science 58 (1988) 17-56
CLASSIFICATION OF ALL THE MINIMAL BILINEAR
ALGORITHMS FOR COMPUTING THE COEFFICIENTS OF
THE PRODUCT OF TWO POLYNOMIALS MODULO A
POLYNOMIAL, PART I: THE ALGEBRA G[u]/< Q(u)`>, 1> 1
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A., and Tel-Aviv University,
Ramat Aviv, 69978 Tel-Aviv, Israel
Columbia University, Morningside Heights, NY 10027, U.S.A., and Tel-Aviv University, Ramat
Aviv, 69978 Tel-Aviv, Israel
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
Abstract. In this paper we will classify all the minimal bilinear algorithms for computing the
coefficients of (Cyld x,u')(~:`~~ y,u') mod Q(U)' where deg Q(u) = j, jl = n and Q(U) is irreducible.
The case where I = 1 was studied in [ 11. For I > 1 the main results are that we have to distinguish
between two cases: j > 1 and j = 1. The first case is discussed here while the second is classified
in . For j > 1 it is shown that up to equivalence every minimal (2n - 1 multiplications) bilinear
algorithm for computing the coefficients of (x:1; x,u')(C:`I,; y,u') mod Q(u)' is done by first