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Journal Articles Journal of Symbolic Computation Year : 2000

New structure theorems for subresultants


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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Dates and versions

inria-00099274 , version 1 (26-09-2006)



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