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## 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: ${\stackrel{˜}{O}}_{B}\left({N}^{{n}^{2}}\right)$, where $N=max\left\{d,\tau \right\}$, $d$ and $\tau$, is the degree and the maximum coefficient bitsize of the polynomials, respectively, and $n$ is the number of variables.