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New Structure Theorem for Subresultants

✍ Scribed by Henri Lombardi; Marie-Françoise Roy; Mohab Safey El Din

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
323 KB
Volume
29
Category
Article
ISSN
0747-7171

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✦ Synopsis

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 τ a bound on the bit size of the minors extracted from Sylvester matrix, our algorithm has O(d 2 ) arithmetic operations and size of intermediate computations 2τ . The key idea is to precise the relations between the successive Sylvester matrix of A and B on one hand and of A and XB on the other hand, using the notion of G-remainder that we introduce. We also compare our new algorithm with another algorithm with the same characteristics which appeared in .

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