@article{OAKU2001199,
    Abstract = {In this article, we give two new algorithms to find the polynomial and rational function solutions of a given holonomic system associated to a set of linear differential operators in the Weyl algebra D=k〈x1,{\ldots},xn,∂1,{\ldots},∂n〉, where k is a computable subfield of the complex numbers. Both algorithms are based on the theory of D-modules -- the first algorithm obtains degree bounds on the solutions through Gr{\"o}bner deformations and b-functions while the second algorithm evaluates the dimension of the solutions through duality and restriction.},
    Author = {Oaku, Toshinori and Takayama, Nobuki and Tsai, Harrison},
    File = {Polynomial and rational solutions of holonomic systems - 1-s2.0-S0022404900001535-main.pdf},
    ISSN = {0022-4049},
    Journal = {Journal of Pure and Applied Algebra},
    Note = {Effective Methods in Algebraic Geometry},
    Number = {1},
    Pages = {199-220},
    Title = {Polynomial and rational solutions of holonomic systems},
    URL = {https://www.sciencedirect.com/science/article/pii/S0022404900001535},
    Volume = {164},
    Year = {2001},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022404900001535},
    bdsk-url-2 = {https://doi.org/10.1016/S0022-4049(00)00153-5},
    date-added = {2022-12-05 14:49:58 +0100},
    date-modified = {2022-12-05 14:49:58 +0100},
    doi = {10.1016/S0022-4049(00)00153-5}
}

@article{OAKU2001199, Abstract = {In this article, we give two new algorithms to find the polynomial and rational function solutions of a given holonomic system associated to a set of linear differential operators in the Weyl algebra D=k〈x1,{\ldots},xn,∂1,{\ldots},∂n〉, where k is a computable subfield of the complex numbers. Both algorithms are based on the theory of D-modules -- the first algorithm obtains degree bounds on the solutions through Gr{\"o}bner deformations and b-functions while the second algorithm evaluates the dimension of the solutions through duality and restriction.}, Author = {Oaku, Toshinori and Takayama, Nobuki and Tsai, Harrison}, File = {Polynomial and rational solutions of holonomic systems - 1-s2.0-S0022404900001535-main.pdf}, ISSN = {0022-4049}, Journal = {Journal of Pure and Applied Algebra}, Note = {Effective Methods in Algebraic Geometry}, Number = {1}, Pages = {199-220}, Title = {Polynomial and rational solutions of holonomic systems}, URL = {https://www.sciencedirect.com/science/article/pii/S0022404900001535}, Volume = {164}, Year = {2001}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022404900001535}, bdsk-url-2 = {https://doi.org/10.1016/S0022-4049(00)00153-5}, date-added = {2022-12-05 14:49:58 +0100}, date-modified = {2022-12-05 14:49:58 +0100}, doi = {10.1016/S0022-4049(00)00153-5} }