 
Summary: Classification of all the minimal bilinear algorithms for computing
the coefficients of the product of two polynomials modulo a polynomial,
Part II: The algebra G[u]= ! u n ?
Amir Averbuch
TelAviv University
Zvi Galil
Columbia University and TelAviv University
Shmuel Winograd
IBM T.J. Watson Research Center
ABSTRACT
In this paper we will classify all the minimal bilinear algorithms for computing the coefficients
of (
P n\Gamma1
i=0 x i u i )(
P n\Gamma1
i=0 y i u i )modQ(u) l where deg Q(u) = j; jl = n and Q(u) is irreducible (over G)
is studied. The case where l = 1 was studied in [1]. For l ? 1 the main results are that we have to
distinguish between two cases: j ? 1 and j = 1. The case where j ? 1 was studied in [5].
For j = 1 it is shown that up to equivalence every minimal ( 2n \Gamma 1 multiplications) bilinear algo
rithm for computing the coefficients of (
