[retour]

##
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 2*t*.

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.