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 , where refers to the complexity where polylogarithmic factors are omitted and refers to the bit complexity. We also present probabilistic Las-Vegas variants of our two first algorithms, which have expected bit complecity . A key ingredient of our proofs of complexity is an amortized analysis of the triangular decomposition algorithm via subresultants, which is of independent interest.