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Classification of all the minimal bilinear algorithms for computing the coefficients of the product of two polynomials modulo a polynomial,
 

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 (

  

Source: Averbuch, Amir - School of Computer Science, Tel Aviv University

 

Collections: Computer Technologies and Information Sciences