@article{GAO20091137,
    Abstract = {In this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreducible ascending chains and study their properties. We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial sets into the union of the zero sets of regular and consistent ascending chains. As a consequence, we solve the perfect ideal membership problem for differential and difference polynomials.},
    Author = {Gao, X.S. and der Hoeven, J. Van and Yuan, C.M. and Zhang, G. L.},
    File = {Characteristic set method for differential–difference polynomial systems - jsc\_dd - 1-s2.0-S0747717109000145-main - a - t.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Keywords = {Characteristic set, Differential and difference polynomial, Regular ascending chain, Irreducible ascending chain, Zero decomposition algorithm, Perfect ideal membership problem},
    Note = {Effective Methods in Algebraic Geometry},
    Number = {9},
    Pages = {1137 - 1163},
    Title = {Characteristic set method for differential--difference polynomial systems},
    URL = {http://www.sciencedirect.com/science/article/pii/S0747717109000145},
    Volume = {44},
    Year = {2009},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0747717109000145},
    bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2008.02.010},
    date-added = {2020-04-13 11:09:42 +0200},
    date-modified = {2020-04-13 11:09:42 +0200},
    doi = {10.1016/j.jsc.2008.02.010}
}

@article{GAO20091137, Abstract = {In this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreducible ascending chains and study their properties. We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial sets into the union of the zero sets of regular and consistent ascending chains. As a consequence, we solve the perfect ideal membership problem for differential and difference polynomials.}, Author = {Gao, X.S. and der Hoeven, J. Van and Yuan, C.M. and Zhang, G. L.}, File = {Characteristic set method for differential–difference polynomial systems - jsc_dd - 1-s2.0-S0747717109000145-main - a - t.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Keywords = {Characteristic set, Differential and difference polynomial, Regular ascending chain, Irreducible ascending chain, Zero decomposition algorithm, Perfect ideal membership problem}, Note = {Effective Methods in Algebraic Geometry}, Number = {9}, Pages = {1137 - 1163}, Title = {Characteristic set method for differential--difference polynomial systems}, URL = {http://www.sciencedirect.com/science/article/pii/S0747717109000145}, Volume = {44}, Year = {2009}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0747717109000145}, bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2008.02.010}, date-added = {2020-04-13 11:09:42 +0200}, date-modified = {2020-04-13 11:09:42 +0200}, doi = {10.1016/j.jsc.2008.02.010} }