33 citations · 106 across the 19 of their papers we have counts for
21 papers
Complexity Analysis of Root Clustering for a Complex Polynomial
Ruben Becker, Michael Sagraloff, Vikram Sharma +2
Let be an arbitrary complex polynomial. We introduce the local root clustering problem, to compute a set of natural -clusters of roots of in some box reg…
Bounds for polynomials on algebraic numbers and application to curve topology
Daouda Niang Diatta, Sény Diatta, Fabrice Rouillier +2
Let be a given square-free polynomial of total degree with integer coefficients of bitsize less than , and let $V_{\mathbb{R}} (P) := \{ (x,y) \in…
Counting Solutions of a Polynomial System Locally and Exactly
Ruben Becker, Michael Sagraloff
We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdot…
Efficiently Computing Real Roots of Sparse Polynomials
Gorav Jindal, Michael Sagraloff
We propose an efficient algorithm to compute the real roots of a sparse polynomial having non-zero real-valued coefficients. It is assumed that arbitrarily…
Computing Real Roots of Real Polynomials ... and now For Real!
Alexander Kobel, Fabrice Rouillier, Michael Sagraloff
Very recent work introduces an asymptotically fast subdivision algorithm, denoted ANewDsc, for isolating the real roots of a univariate real polynomial. The method combines Descart…
On the Complexity of Solving Zero-Dimensional Polynomial Systems via Projection
Cornelius Brand, Michael Sagraloff
Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we propose a certified and complete method to compute all complex solutions of the sy…