On rational De Rham cohomology associated with the generalized airy function
Hironobu Kimura (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “The first derivative of period function of a plane vector field.”
On rational De Rham cohomology associated with the generalized airy function
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Liouvillian first integrals of homogeneouspolynomial 3-dimensional vector fields
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Given a 3-dimensional vector field V with coordinates , and 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...
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A polynomial reduction algorithm
Henri Cohen, Francisco Diaz Y Diaz (1991)
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The algorithm described in this paper is a practical approach to the problem of giving, for each number field a polynomial, as canonical as possible, a root of which is a primitive element of the extension . Our algorithm uses the algorithm to find a basis of minimal vectors for the lattice of determined by the integers of under the canonical map.