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.