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Computing periods of rational integrals. (English) Zbl 1337.68301

The author considers rational functions in \(n\) complex variables and depending on a parameter. The integrals of such functions over \(n\)-cycles are called periods. Periods satisfy ordinary linear differential equations called Picard-Fuchs equations. The author gives an elementary algorithm extending the Griffiths-Dwork reduction which can be applied to the computation of Picard-Fuchs equations within the framework of solving problems which previously have been out of reach.

MSC:

68W30 Symbolic computation and algebraic computation
14K20 Analytic theory of abelian varieties; abelian integrals and differentials
14F40 de Rham cohomology and algebraic geometry
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
34M03 Linear ordinary differential equations and systems in the complex domain
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