@inproceedings{10.1145/1277548.1277553,
    Abstract = {It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function. We also show that there exists a linear differential equation of order linear in the degree whose coefficients are only of quadratic degree. Furthermore, we prove the existence of recurrences of order and degree close to optimal. We study the complexity of computing these differential equations and recurrences. We deduce a fast algorithm for the expansion of algebraic series.},
    Address = {New York, NY, USA},
    Author = {Bostan, Alin and Chyzak, Fr\'{e}d\'{e}ric and Salvy, Bruno and Lecerf, Gr\'{e}goire and Schost, \'{E}ric},
    BookTitle = {Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation},
    File = {Differential Equations for Algebraic Functions - 0703121 - a - m.pdf},
    ISBN = {9781595937438},
    Keywords = {computer algebra, creative telescoping, differential resolvents, algebraic series, complexity},
    Location = {Waterloo, Ontario, Canada},
    Pages = {25--32},
    Publisher = {Association for Computing Machinery},
    Series = {ISSAC '07},
    Title = {Differential Equations for Algebraic Functions},
    URL = {https://doi.org/10.1145/1277548.1277553},
    Year = {2007},
    bdsk-url-1 = {https://doi.org/10.1145/1277548.1277553},
    date-added = {2020-10-18 10:34:02 +0200},
    date-modified = {2020-10-18 10:34:02 +0200},
    file-2 = {Differential Equations for Algebraic Functions - BoChLeSaSc07-hal - a - m.pdf},
    file-3 = {Differential Equations for Algebraic Functions - salvy-slides - a - m.pdf},
    numpages = {8},
    doi = {10.1145/1277548.1277553}
}

@inproceedings{10.1145/1277548.1277553, Abstract = {It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function. We also show that there exists a linear differential equation of order linear in the degree whose coefficients are only of quadratic degree. Furthermore, we prove the existence of recurrences of order and degree close to optimal. We study the complexity of computing these differential equations and recurrences. We deduce a fast algorithm for the expansion of algebraic series.}, Address = {New York, NY, USA}, Author = {Bostan, Alin and Chyzak, Fr\'{e}d\'{e}ric and Salvy, Bruno and Lecerf, Gr\'{e}goire and Schost, \'{E}ric}, BookTitle = {Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation}, File = {Differential Equations for Algebraic Functions - 0703121 - a - m.pdf}, ISBN = {9781595937438}, Keywords = {computer algebra, creative telescoping, differential resolvents, algebraic series, complexity}, Location = {Waterloo, Ontario, Canada}, Pages = {25--32}, Publisher = {Association for Computing Machinery}, Series = {ISSAC '07}, Title = {Differential Equations for Algebraic Functions}, URL = {https://doi.org/10.1145/1277548.1277553}, Year = {2007}, bdsk-url-1 = {https://doi.org/10.1145/1277548.1277553}, date-added = {2020-10-18 10:34:02 +0200}, date-modified = {2020-10-18 10:34:02 +0200}, file-2 = {Differential Equations for Algebraic Functions - BoChLeSaSc07-hal - a - m.pdf}, file-3 = {Differential Equations for Algebraic Functions - salvy-slides - a - m.pdf}, numpages = {8}, doi = {10.1145/1277548.1277553} }