New Structure Theorem 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 a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has O(d2) arithmetic operations and size of intermediate computations 2. 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 already appeared in [4].

• Type: Journal
• Year: 2000
• Where: JSC
• Authors: Henri Lombardi, Marie-Françoise Roy, Mohab Safey El Din
• Keywords: Algorithm, Gap Structure, JSC 2000, Sylvester Matrix