Polynomial complexity of the Newton-Puiseux algorithm
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Complexity of Quantifier Elimination in the Theory of Algebraically Closed Fields
Proceedings of the Mathematical Foundations of Computer Science 1984
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
A polynomial reduction from multivariate to bivariate integral polynomial factorization.
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Formal solutions of differential equations
Journal of Symbolic Computation
Complexity of irreducibility testing for a system of linear ordinary differential equations
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Finding all hypergeometric solutions of linear differential equations
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
A modular algorithm for computing greatest common right divisors of Ore polynomials
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On factorization of nonlinear ordinary differential equations
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Bounds on numers of vectors of multiplicities for polynomials which are easy to compute
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Decomposition of differential polynomials with constant coefficients
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Generalized Loewy-decomposition of d-modules
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Fast computation of common left multiples of linear ordinary differential operators
ACM Communications in Computer Algebra
Journal of Symbolic Computation
| Hi-index | 0.00 |
Let L=@?0@?k@?n(f"k/f)d^kd^kx be a linear differential operator with rational coefficients, where f"k,f@?@?@?[X] and @?@? is the field of algebraic numbers. Let deg@?"x(L)=max@?0@?k@?n{deg@?"x(f"k),deg@?"x(f)} and let N be an upper bound on deg"x(L"j) for all possible factorizations of the form L = L"1 L"2 L"3, where the operators L"j are of the same kind as L and L"2, L"3, are normalized to have leading coefficient 1. An algorithm is described that factors L within time (N @?)^0^(^n^^^4^) where @? is the bit size of L. Moreover, a bound N @? exp((@?2^n)^2^n) is obtained. We also exhibit a polynomial time algorithm for calculating the greatest common (right) divisor of a family of operators.