New structure theorems for subresultants

pdf file.
with Roy M.-F. and Safey El Din M.
Journal of Symbolic Computation 29 (4-5), (2000), 663--690.

Abstract : We give a new structure theorem for subresultants precising their gap structure and derive from it a new algorithm for computing them.
If d is a bound on the degrees and t a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has O(d^2) arithmetic operations and size of intermediate computations 2t.
The key idea is to precise the relations between the successive Sylvester submatrices of A and B in one hand and of A and B on the other hand, using the notion of G-remainder we introduce.