@article{GIANNI1988149,
    Abstract = {We present an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a constructive PID and that we are given an algorithm to factor polynomials over fields which are finitely generated over R or residue fields of R. We show how basic ideal theoretic operations can be performed using Gr{\"o}bner bases and we exploit these constructions to inductively reduce the problem to zero dimensional ideals. Here we again exploit the structure of Gr{\"o}bner bases to directly compute the primary decomposition using polynomial factorization. We also show how the reduction process can be applied to computing radicals and testing ideals for primality.},
    Author = {Gianni, Patrizia and Trager, Barry and Zacharias, Gail},
    File = {Gröbner bases and primary decomposition of polynomial ideals.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Number = {2},
    Pages = {149-167},
    Title = {Gr{\"o}bner bases and primary decomposition of polynomial ideals},
    URL = {https://www.sciencedirect.com/science/article/pii/S0747717188800403},
    Volume = {6},
    Year = {1988},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717188800403},
    bdsk-url-2 = {https://doi.org/10.1016/S0747-7171(88)80040-3},
    date-added = {2022-11-26 17:09:39 +0100},
    date-modified = {2022-11-26 17:09:39 +0100},
    doi = {10.1016/S0747-7171(88)80040-3}
}

@article{GIANNI1988149, Abstract = {We present an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a constructive PID and that we are given an algorithm to factor polynomials over fields which are finitely generated over R or residue fields of R. We show how basic ideal theoretic operations can be performed using Gr{\"o}bner bases and we exploit these constructions to inductively reduce the problem to zero dimensional ideals. Here we again exploit the structure of Gr{\"o}bner bases to directly compute the primary decomposition using polynomial factorization. We also show how the reduction process can be applied to computing radicals and testing ideals for primality.}, Author = {Gianni, Patrizia and Trager, Barry and Zacharias, Gail}, File = {Gröbner bases and primary decomposition of polynomial ideals.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Number = {2}, Pages = {149-167}, Title = {Gr{\"o}bner bases and primary decomposition of polynomial ideals}, URL = {https://www.sciencedirect.com/science/article/pii/S0747717188800403}, Volume = {6}, Year = {1988}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717188800403}, bdsk-url-2 = {https://doi.org/10.1016/S0747-7171(88)80040-3}, date-added = {2022-11-26 17:09:39 +0100}, date-modified = {2022-11-26 17:09:39 +0100}, doi = {10.1016/S0747-7171(88)80040-3} }