Polynomial bounds are proved in terms of intrinsic quantities for the height and degree of the coefficients of triangular sets of zero-dimensional varieties defined over the rational field.Expand

The best currently known upper bounds for factoring integers deterministically and for computing the Cartier-Manin operator of hyperelliptic curves are improved.Expand

A new algorithm is introduced that computes an isogeny of degree l (l different from the characteristic) in time quasi-linear with respect to l based on fast algorithms for power series expansion of the Weierstrass ℘-function and related functions.Expand

This work presents a probabilistic algorithm to compute a parametric resolution of parameters of a polynomial system of n equations in n unknowns, and presents several applications, notably to computa- tions in the Jacobian of hyperelliptic curves and to questions of real geometry.Expand

We present lifting techniques for triangular decompositions of zero-dimensional varieties, that extend the range of the previous methods. We discuss complexity aspects, and report on a preliminary… Expand

We present an algorithm based on the birthday paradox, which is a low-memory parallel counterpart to the algorithm of Matsuo, Chao and Tsujii. This algorithm computes the group order of the Jacobian… Expand