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EN FR
DISCO - 2015
Overall Objectives
New Results
Bilateral Contracts and Grants with Industry
Bibliography
Overall Objectives
New Results
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

Improved algorithm for computing separating linear forms for bivariate systems

Participants : Yacine Bouzidi [Disco] , Sylvain Lazard [Vegas] , Guillaume Moroz [Vegas] , Marc Pouget [Vegas] , Fabrice Rouillier [Ouragan] .

We present new algorithms for computing linear separating forms, RUR decompositions and isolating boxes of the solutions. We show that these three algorithms have worst-case bit complexity O˜B(d6+d5τ), where O˜ refers to the complexity where polylogarithmic factors are omitted and OB refers to the bit complexity. We also present probabilistic Las-Vegas variants of our two first algorithms, which have expected bit complecity O˜B(d5+d4τ). A key ingredient of our proofs of complexity is an amortized analysis of the triangular decomposition algorithm via subresultants, which is of independent interest.