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New structure theorems for subresultants

Henri Lombardi 1 Marie-Françoise Roy Mohab Safey El Din 2, 3
2 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
3 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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 $\tau$ 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 $2\tau$. The key idea is to precise the relations between the successive Sylvester matrix of $A$ and $B$ in one hand and of $A$ and $XB$ on the other hand, using the notion of G-remainder we introduce. We also compare our new algorithm with another algorithm with the same characteristics given by L. Ducos.
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https://hal.inria.fr/inria-00099274
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Submitted on : Tuesday, September 26, 2006 - 8:52:18 AM
Last modification on : Friday, May 24, 2019 - 5:30:29 PM

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Henri Lombardi, Marie-Françoise Roy, Mohab Safey El Din. New structure theorems for subresultants. Journal of Symbolic Computation, Elsevier, 2000, 29 (4-5), pp.663-690. ⟨10.1006/jsco.1999.0322⟩. ⟨inria-00099274⟩

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