Integration of Rational Functions: Rational Computation of the Logarithmic Part

@article{Lazard1990IntegrationOR,
  title={Integration of Rational Functions: Rational Computation of the Logarithmic Part},
  author={Daniel Lazard and Renaud Rioboo},
  journal={J. Symb. Comput.},
  year={1990},
  volume={9},
  pages={113-115}
}
This formula is not satisfactory under a computing point of view because it introduces more algebraic quantities than necessary. The number P(a)/Q'(a) is called the residue of the root a of Q. We introduce the notion of multiplicity of a residue b that is the number of roots a having b as a residue. Trager (1976) introduced a new formula involving less algebraic numbers: let S(y) be the resultant S(y) = Resx[P(x) yQ'(x ), Q(x)-l; we have 
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Calcul Formel, Syst~mes et Algorithmes de Manipulation Algbbriques

J. Davenport, Y. Siret, E. Tournier
1987

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