@article{GALLIGO1995174,
    Abstract = {Let W ⊂ Rn be a semialgebraic set defined by a quantifier-free formula with k atomic polynomials of the kind f ∈ Z[X1, . . . , Xn] such that degX1, . . . , Xn(f) < d and the absolute values of coefficients of f are less than 2M for some positive integers d, M. An algorithm is proposed for producing the complexification, Zariski closure, and also for finding all irreducible components of W. The running time of the algorithm is bounded from above by MO(1)(kd)nO(1). The procedure is applied to computing a Whitney system for a semialgebraic set and the real radical of a polynomial ideal.},
    Author = {Galligo, A. and Vorobjov, N.},
    File = {Complexity of Finding Irreducible Components of a Semialgebraic Set - 1-s2.0-S0885064X85710072-main - a.pdf},
    ISSN = {0885-064X},
    Journal = {Journal of Complexity},
    Number = {1},
    Pages = {174-193},
    Title = {Complexity of Finding Irreducible Components of a Semialgebraic Set},
    URL = {https://www.sciencedirect.com/science/article/pii/S0885064X85710072},
    Volume = {11},
    Year = {1995},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0885064X85710072},
    bdsk-url-2 = {https://doi.org/10.1006/jcom.1995.1007},
    date-added = {2023-02-05 07:38:16 +0100},
    date-modified = {2023-02-05 07:38:16 +0100},
    doi = {10.1006/jcom.1995.1007}
}

@article{GALLIGO1995174, Abstract = {Let W ⊂ Rn be a semialgebraic set defined by a quantifier-free formula with k atomic polynomials of the kind f ∈ Z[X1, . . . , Xn] such that degX1, . . . , Xn(f) < d and the absolute values of coefficients of f are less than 2M for some positive integers d, M. An algorithm is proposed for producing the complexification, Zariski closure, and also for finding all irreducible components of W. The running time of the algorithm is bounded from above by MO(1)(kd)nO(1). The procedure is applied to computing a Whitney system for a semialgebraic set and the real radical of a polynomial ideal.}, Author = {Galligo, A. and Vorobjov, N.}, File = {Complexity of Finding Irreducible Components of a Semialgebraic Set - 1-s2.0-S0885064X85710072-main - a.pdf}, ISSN = {0885-064X}, Journal = {Journal of Complexity}, Number = {1}, Pages = {174-193}, Title = {Complexity of Finding Irreducible Components of a Semialgebraic Set}, URL = {https://www.sciencedirect.com/science/article/pii/S0885064X85710072}, Volume = {11}, Year = {1995}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0885064X85710072}, bdsk-url-2 = {https://doi.org/10.1006/jcom.1995.1007}, date-added = {2023-02-05 07:38:16 +0100}, date-modified = {2023-02-05 07:38:16 +0100}, doi = {10.1006/jcom.1995.1007} }