Section: New Results

Local Generic Position for Root Isolation of Zero-dimensional Triangular Polynomial Systems.

In [30] we present an algorithm based on local generic position (LGP) to isolate the complex or real roots and their multiplicities of a zero-dimensional triangular polynomial system. The Boolean complexity of the algorithm for computing the real roots is single exponential: ${\tilde{O}}_B\left(N^{n^2}\right)$, where $N=max\{d,\tau \}$, $d$ and $\tau$, is the degree and the maximum coefficient bitsize of the polynomials, respectively, and $n$ is the number of variables.