@article{TAKAYAMA1992265,
    Abstract = {The class of ``holonomic function'' is considered. We present a quasi-algorithm that recognizes whether a holonomic function is zero or not. The algorithm consists of procedures which obtain differential operators that annihilate sums, products, and definite integrals with, respect to parameters of holonomic functions. A Weyl algebra-analog of Buchberger's algorithm is used. A ``holonomic'' approach to the zero recognition algorithm was initiated by D. Zeilberger (1990) who realized it by Sylvester's dyalitic elimination. Our algorithm uses Buchberger's algorithm to improve Zeilberger's algorithm.},
    Author = {Takayama, Nobuki},
    File = {An approach to the zero recognition problem by Buchberger algorithm - 1-s2.0-0747717192900397-main - a.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Note = {Symbolic Computation in Combinatorics},
    Number = {2},
    Pages = {265-282},
    Title = {An approach to the zero recognition problem by Buchberger algorithm},
    URL = {https://www.sciencedirect.com/science/article/pii/0747717192900397},
    Volume = {14},
    Year = {1992},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0747717192900397},
    bdsk-url-2 = {https://doi.org/10.1016/0747-7171(92)90039-7},
    date-added = {2022-12-27 09:30:38 +0100},
    date-modified = {2022-12-27 09:30:38 +0100},
    doi = {10.1016/0747-7171(92)90039-7}
}

@article{TAKAYAMA1992265, Abstract = {The class of holonomic function'' is considered. We present a quasi-algorithm that recognizes whether a holonomic function is zero or not. The algorithm consists of procedures which obtain differential operators that annihilate sums, products, and definite integrals with, respect to parameters of holonomic functions. A Weyl algebra-analog of Buchberger's algorithm is used. Aholonomic'' approach to the zero recognition algorithm was initiated by D. Zeilberger (1990) who realized it by Sylvester's dyalitic elimination. Our algorithm uses Buchberger's algorithm to improve Zeilberger's algorithm.}, Author = {Takayama, Nobuki}, File = {An approach to the zero recognition problem by Buchberger algorithm - 1-s2.0-0747717192900397-main - a.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Note = {Symbolic Computation in Combinatorics}, Number = {2}, Pages = {265-282}, Title = {An approach to the zero recognition problem by Buchberger algorithm}, URL = {https://www.sciencedirect.com/science/article/pii/0747717192900397}, Volume = {14}, Year = {1992}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0747717192900397}, bdsk-url-2 = {https://doi.org/10.1016/0747-7171(92)90039-7}, date-added = {2022-12-27 09:30:38 +0100}, date-modified = {2022-12-27 09:30:38 +0100}, doi = {10.1016/0747-7171(92)90039-7} }