Improved Kolchin–Ritt Algorithm

@article{Ferro2003ImprovedKA,
  title={Improved Kolchin–Ritt Algorithm},
  author={Giuseppa Carr{\`a} Ferro and Vladimir P. Gerdt},
  journal={Programming and Computer Software},
  year={2003},
  volume={29},
  pages={83-87}
}
An algorithm for computation of an extended characteristic sets for finitely generated differential ideals is suggested. This algorithm improves the well-known Kolchin–Ritt algorithm. The improvement is achieved through computing algebraic Gröbner bases on intermediate stages of the computation process. The rank of the extended characteristic set obtained is less than or equal to that of the set obtained by the Kolchin–Ritt algorithm. Examples demonstrating the rank reduction are presented.