@article{GRIGOREV19907,
    Abstract = {Let L=∑0≤k≤n(fk/f)dkdkx be a linear differential operator with rational coefficients, where fk,f∈ℚ¯[X] and ℚ¯ is the field of algebraic numbers. Let deg⁡x(L)=max⁡0≤k≤n{deg⁡x(fk),deg⁡x(f)} and let N be an upper bound on degx(Lj) for all possible factorizations of the form L = L1 L2 L3, where the operators Lj are of the same kind as L and L2, L3, are normalized to have leading coefficient 1. An algorithm is described that factors L within time (N ℒ)0(n4) where ℒ is the bit size of L. Moreover, a bound N ≤ exp((ℒ2n)2n) is obtained. We also exhibit a polynomial time algorithm for calculating the greatest common (right) divisor of a family of operators.},
    Author = {Grigor'ev, D.Yu.},
    File = {Complexity of factoring and calculating the GCD of linear ordinary differential operators - 1-s2.0-S074771710880034X-main - a - k.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Number = {1},
    Pages = {7 - 37},
    Title = {Complexity of factoring and calculating the GCD of linear ordinary differential operators},
    URL = {http://www.sciencedirect.com/science/article/pii/S074771710880034X},
    Volume = {10},
    Year = {1990},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S074771710880034X},
    bdsk-url-2 = {https://doi.org/10.1016/S0747-7171(08)80034-X},
    date-added = {2020-10-24 13:15:45 +0200},
    date-modified = {2020-10-24 13:15:45 +0200},
    doi = {10.1016/S0747-7171(08)80034-X}
}

@article{GRIGOREV19907, Abstract = {Let L=∑0≤k≤n(fk/f)dkdkx be a linear differential operator with rational coefficients, where fk,f∈ℚ¯[X] and ℚ¯ is the field of algebraic numbers. Let deg⁡x(L)=max⁡0≤k≤n{deg⁡x(fk),deg⁡x(f)} and let N be an upper bound on degx(Lj) for all possible factorizations of the form L = L1 L2 L3, where the operators Lj are of the same kind as L and L2, L3, are normalized to have leading coefficient 1. An algorithm is described that factors L within time (N ℒ)0(n4) where ℒ is the bit size of L. Moreover, a bound N ≤ exp((ℒ2n)2n) is obtained. We also exhibit a polynomial time algorithm for calculating the greatest common (right) divisor of a family of operators.}, Author = {Grigor'ev, D.Yu.}, File = {Complexity of factoring and calculating the GCD of linear ordinary differential operators - 1-s2.0-S074771710880034X-main - a - k.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Number = {1}, Pages = {7 - 37}, Title = {Complexity of factoring and calculating the GCD of linear ordinary differential operators}, URL = {http://www.sciencedirect.com/science/article/pii/S074771710880034X}, Volume = {10}, Year = {1990}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S074771710880034X}, bdsk-url-2 = {https://doi.org/10.1016/S0747-7171(08)80034-X}, date-added = {2020-10-24 13:15:45 +0200}, date-modified = {2020-10-24 13:15:45 +0200}, doi = {10.1016/S0747-7171(08)80034-X} }