On expansion of algebraic functions in power and puiseux series, I
Journal of Complexity
Integration of elementary functions
Journal of Symbolic Computation
Mathematics for computer algebra
Mathematics for computer algebra
Fast evaluation of holonomic functions
Theoretical Computer Science - Special issue on real numbers and computers
The KP equation with quasiperiodic initial data
Physica D - Special issue on nonlinear waves and solitons in physical systems
Modern computer algebra
Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems
Journal of the ACM (JACM)
Fast evaluation of holonomic functions near and in regular singularities
Journal of Symbolic Computation
Linear differential operators for polynomial equations
Journal of Symbolic Computation
Numerical factorization of multivariate complex polynomials
Theoretical Computer Science - Algebraic and numerical algorithm
Good reduction of puiseux series and complexity of the Newton-Puiseux algorithm over finite fields
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Continuations and monodromy on random riemann surfaces
Proceedings of the 2009 conference on Symbolic numeric computation
Convergence and many-valuedness of hensel seriesnear the expansion point
Proceedings of the 2009 conference on Symbolic numeric computation
Polynomial homotopies on multicore workstations
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Computing monodromy via continuation methods on random Riemann surfaces
Theoretical Computer Science
Sampling algebraic sets in local intrinsic coordinates
Computers & Mathematics with Applications
Good reduction of Puiseux series and applications
Journal of Symbolic Computation
A study of Hensel series in general case
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Hi-index | 0.01 |
We present a symbolic-numeric method to compute the monodromy group of a plane algebraic curve viewed as a ramified covering space of the complex plane. Following the definition, our algorithm is based on analytic continuation of algebraic functions above paths in the complex plane. Our contribution is three-fold : first of all, we show how to use a minimum spanning tree to minimize the length of paths ; then, we propose a strategy that gives a good compromise between the number of steps and the truncation orders of Puiseux expansions, obtaining for the first time a complexity result about the number of steps; finally, we present an efficient numerical-modular algorithm to compute Puiseux expansions above critical points,which is a non trivial task.