@article{ABBOTT201720,
    Abstract = {We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for polynomial parametrizations: one algorithm, ``ElimTH'', has as main step the computation of an elimination ideal via a truncated, homogeneous Gr{\"o}bner basis. The other algorithm, ``Direct'', computes the implicitization directly using an approach inspired by the generalized Buchberger--M{\"o}ller algorithm. Either may be used inside the third algorithm, ``RatPar'', to deal with parametrizations by rational functions. Finally we show how these algorithms can be used in a modular approach, algorithm ``ModImplicit'', for avoiding the high costs of arithmetic with rational numbers. We exhibit experimental timings to show the practical efficiency of our new algorithms.},
    Author = {Abbott, John and Bigatti, Anna Maria and Robbiano, Lorenzo},
    File = {Implicitization of hypersurfaces - 1-s2.0-S0747717116301213-main - r.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Keywords = {Hypersurface, Implicitization},
    Pages = {20 - 40},
    Title = {Implicitization of hypersurfaces},
    URL = {http://www.sciencedirect.com/science/article/pii/S0747717116301213},
    Volume = {81},
    Year = {2017},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0747717116301213},
    bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2016.11.002},
    date-added = {2020-11-27 11:11:36 +0100},
    date-modified = {2020-11-27 11:11:36 +0100},
    file-2 = {BigattiACA2016 - r.pdf},
    doi = {10.1016/j.jsc.2016.11.002}
}

@article{ABBOTT201720, Abstract = {We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for polynomial parametrizations: one algorithm, ElimTH'', has as main step the computation of an elimination ideal via a truncated, homogeneous Gr{\"o}bner basis. The other algorithm,Direct'', computes the implicitization directly using an approach inspired by the generalized Buchberger--M{\"o}ller algorithm. Either may be used inside the third algorithm, RatPar'', to deal with parametrizations by rational functions. Finally we show how these algorithms can be used in a modular approach, algorithmModImplicit'', for avoiding the high costs of arithmetic with rational numbers. We exhibit experimental timings to show the practical efficiency of our new algorithms.}, Author = {Abbott, John and Bigatti, Anna Maria and Robbiano, Lorenzo}, File = {Implicitization of hypersurfaces - 1-s2.0-S0747717116301213-main - r.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Keywords = {Hypersurface, Implicitization}, Pages = {20 - 40}, Title = {Implicitization of hypersurfaces}, URL = {http://www.sciencedirect.com/science/article/pii/S0747717116301213}, Volume = {81}, Year = {2017}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0747717116301213}, bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2016.11.002}, date-added = {2020-11-27 11:11:36 +0100}, date-modified = {2020-11-27 11:11:36 +0100}, file-2 = {BigattiACA2016 - r.pdf}, doi = {10.1016/j.jsc.2016.11.002} }