Computing periods of rational integrals

@article{Lairez2016ComputingPO,
  title={Computing periods of rational integrals},
  author={Pierre Lairez},
  journal={Math. Comput.},
  year={2016},
  volume={85},
  pages={1719-1752}
}
  • Pierre Lairez
  • Published 20 April 2014
  • Mathematics, Computer Science
  • Math. Comput.
A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on a parameter: in this case the period under consideration satisfies a linear differential equation, the Picard-Fuchs equation. I give a reduction algorithm that extends the Griffiths-Dwork reduction and apply it to the computation of Picard-Fuchs equations. The resulting algorithm is elementary and… 
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