@article{Rouillier:1999tj,
    Abstract = {This paper is devoted to the resolution of zero-dimensional systems in K{$[$}X1, {\ldots}Xn{$]$}, where K is a field of characteristic zero (or strictly positive under some conditions). We follow the definition used in MMM95 and basically due to Kronecker for solving zero-dimensional systems: A system is solved if each root is represented in such way as to allow the performance of any arithmetical operations over the arithmetical expressions of its coordinates. We propose new definitions for solving zero-dimensional systems in this sense by introducing the Univariate Representation of their roots. We show by this way that the solutions of any zero-dimensional system of polynomials can be expressed through a special kind of univariate representation (Rational Univariate Representation):},
    Author = {Rouillier, Fabrice},
    Date = {1999/05/01},
    File = {Solving Zero-Dimensional Systems Through the Rational Univariate Representation - Rouillier1999\_Article\_SolvingZero-DimensionalSystems.pdf},
    ISBN = {1432-0622},
    Journal = {Applicable Algebra in Engineering, Communication and Computing},
    Number = {5},
    Pages = {433--461},
    Title = {Solving Zero-Dimensional Systems Through the Rational Univariate Representation},
    URL = {https://doi.org/10.1007/s002000050114},
    Volume = {9},
    Year = {1999},
    bdsk-url-1 = {https://doi.org/10.1007/s002000050114},
    date-added = {2021-12-03 21:38:31 +0100},
    date-modified = {2021-12-03 21:38:32 +0100},
    id = {Rouillier1999},
    doi = {10.1007/s002000050114}
}

@article{Rouillier:1999tj, Abstract = {This paper is devoted to the resolution of zero-dimensional systems in K{$[$}X1, {\ldots}Xn{$]$}, where K is a field of characteristic zero (or strictly positive under some conditions). We follow the definition used in MMM95 and basically due to Kronecker for solving zero-dimensional systems: A system is solved if each root is represented in such way as to allow the performance of any arithmetical operations over the arithmetical expressions of its coordinates. We propose new definitions for solving zero-dimensional systems in this sense by introducing the Univariate Representation of their roots. We show by this way that the solutions of any zero-dimensional system of polynomials can be expressed through a special kind of univariate representation (Rational Univariate Representation):}, Author = {Rouillier, Fabrice}, Date = {1999/05/01}, File = {Solving Zero-Dimensional Systems Through the Rational Univariate Representation - Rouillier1999_Article_SolvingZero-DimensionalSystems.pdf}, ISBN = {1432-0622}, Journal = {Applicable Algebra in Engineering, Communication and Computing}, Number = {5}, Pages = {433--461}, Title = {Solving Zero-Dimensional Systems Through the Rational Univariate Representation}, URL = {https://doi.org/10.1007/s002000050114}, Volume = {9}, Year = {1999}, bdsk-url-1 = {https://doi.org/10.1007/s002000050114}, date-added = {2021-12-03 21:38:31 +0100}, date-modified = {2021-12-03 21:38:32 +0100}, id = {Rouillier1999}, doi = {10.1007/s002000050114} }