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 ${\tilde{O}}_B(d^6+d^5\tau )$, where $\tilde{O}$ refers to the complexity where polylogarithmic factors are omitted and $O_B$ refers to the bit complexity. We also present probabilistic Las-Vegas variants of our two first algorithms, which have expected bit complecity ${\tilde{O}}_B(d^5+d^4\tau )$. A key ingredient of our proofs of complexity is an amortized analysis of the triangular decomposition algorithm via subresultants, which is of independent interest.