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 2016
  • 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… CONTINUE READING
    44 Citations

    Figures, Tables, and Topics from this paper.

    Explore Further: Topics Discussed in This Paper

    Computing Periods of Hypersurfaces
    • 4
    • PDF
    Computing Periods of Hypersurfaces
    • E. Sertöz
    • Computer Science, Mathematics
    • Math. Comput.
    • 2019
    • 1
    A numerical transcendental method in algebraic geometry
    • 3
    • PDF
    A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants
    • 4
    • PDF
    Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions
    • 13
    • PDF
    Computing the Volume of Compact Semi-Algebraic Sets
    • 6
    • PDF
    D-Modules and Holonomic Functions
    • 4
    • PDF

    References

    SHOWING 1-10 OF 68 REFERENCES
    On the zeta function of a hypersurface
    • 235
    • PDF
    Creative telescoping for rational functions using the griffiths: dwork method
    • 50
    • PDF
    How to compute the constant term of a power of a Laurent polynomial efficiently
    • 3
    • PDF
    On the Periods of Certain Rational Integrals: II
    • 519
    A generalization of Griffiths's theorem on rational integrals
    • 30
    • PDF
    Factorization of Differential Operators with Rational Functions Coefficients
    • M. V. Hoeij
    • Computer Science, Mathematics
    • J. Symb. Comput.
    • 1997
    • 125
    • PDF
    Singularities and Topology of Hypersurfaces
    • 545
    • PDF
    Picard-Fuchs equations and mirror maps for hypersurfaces
    • 114
    • PDF