Displaying similar documents to “The first derivative of period function of a plane vector field.”

Liouvillian first integrals of homogeneouspolynomial 3-dimensional vector fields

Jean Moulin Ollagnier (1996)

Colloquium Mathematicae

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Given a 3-dimensional vector field V with coordinates V x , V y and V z that are homogeneous polynomials in the ring k[x,y,z], we give a necessary and sufficient condition for the existence of a Liouvillian first integral of V which is homogeneous of degree 0. This condition is the existence of some 1-forms with coordinates in the ring k[x,y,z] enjoying precise properties; in particular, they have to be integrable in the sense of Pfaff and orthogonal to the vector field V. Thus, our theorem...

Rigid cohomology and p -adic point counting

Alan G.B. Lauder (2005)

Journal de Théorie des Nombres de Bordeaux

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I discuss some algorithms for computing the zeta function of an algebraic variety over a finite field which are based upon rigid cohomology. Two distinct approaches are illustrated with a worked example.

A polynomial reduction algorithm

Henri Cohen, Francisco Diaz Y Diaz (1991)

Journal de théorie des nombres de Bordeaux

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The algorithm described in this paper is a practical approach to the problem of giving, for each number field K a polynomial, as canonical as possible, a root of which is a primitive element of the extension K / ℚ . Our algorithm uses the L L L algorithm to find a basis of minimal vectors for the lattice of ℝ n determined by the integers of K under the canonical map.