منابع مشابه
Computing Periods of Hypersurfaces
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of period integrals to an initial value problem for ordinary differential equations of Picard–Fuchs type. In this way, the periods can be computed to extreme-pre...
متن کاملComputing periods of rational integrals
— 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 reductio...
متن کاملComputing zeta functions of sparse nondegenerate hypersurfaces
Using the cohomology theory of Dwork, as developed by Adolphson and Sperber, we exhibit a deterministic algorithm to compute the zeta function of a nondegenerate hypersurface defined over a finite field. This algorithm is particularly well-suited to work with polynomials in small characteristic that have few monomials (relative to their dimension). Our method covers toric, affine, and projectiv...
متن کاملComputing Abelian Periods in Words
In the last couple of years many works have been devoted to Abelian complexity of words. Recently, Constantinescu and Ilie (Bulletin EATCS 89, 167–170, 2006) introduced the notion of Abelian period. We show that a word w of length n over an alphabet of size σ can have Θ(n2) distinct Abelian periods. However, to the best of our knowledge, no efficient algorithm is known for computing these perio...
متن کاملAlgorithms for Computing Abelian Periods of Words
Constantinescu and Ilie (Bulletin EATCS 89, 167–170, 2006) introduced the notion of an Abelian period of a word. A word of length n over an alphabet of size σ can have Θ(n2) distinct Abelian periods. The Brute-Force algorithm computes all the Abelian periods of a word in time O(n2× σ) using O(n × σ) space. We present an off-line algorithm based on a select function having the same worst-case th...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2019
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3430