Fast algorithms for polynomial solutions of linear differential equations

@article{Bostan2005FastAF,
  title={Fast algorithms for polynomial solutions of linear differential equations},
  author={A. Bostan and T. Cluzeau and B. Salvy},
  journal={Proceedings of the 2005 international symposium on Symbolic and algebraic computation},
  year={2005}
}
  • A. Bostan, T. Cluzeau, B. Salvy
  • Published 2005
  • Mathematics, Computer Science
  • Proceedings of the 2005 international symposium on Symbolic and algebraic computation
We investigate polynomial solutions of homogeneous linear differential equations with coefficients that are polynomials with integer coefficients. The problems we consider are the existence of nonzero polynomial solutions, the determination of the dimension of the vector space of polynomial solutions, the computation of a basis of this space. Previous algorithms have a bit complexity that is at least quadratic in the largest integer valuation N of formal Laurent series solutions at infinity… Expand
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