On expansion of algebraic functions in power and puiseux series, I
Journal of Complexity
On expansion of algebraic functions in power and Puiseux series, II
Journal of Complexity
Integration of elementary functions
Journal of Symbolic Computation
Absolute factorization of polynomials: a geometric approach
SIAM Journal on Computing
An algorithm for computing an integral basis in an algebraic function field
Journal of Symbolic Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Computing GCDs of polynomials over algebraic number fields
Journal of Symbolic Computation
Rational parametrizations of algebraic curves using a canonical divisor
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Fast evaluation of holonomic functions
Theoretical Computer Science - Special issue on real numbers and computers
Modern computer algebra
All Algebraic Functions Can Be Computed Fast
Journal of the ACM (JACM)
Factoring Polynomials Over Algebraic Number Fields
ACM Transactions on Mathematical Software (TOMS)
Complexity of computation of embedded resolution of algebraic curves
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
A computational introduction to number theory and algebra
A computational introduction to number theory and algebra
Computing monodromy groups defined by plane algebraic curves
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Differential equations for algebraic functions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
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
Journal of Symbolic Computation
Complexity bounds for the rational Newton-Puiseux algorithm over finite fields
Applicable Algebra in Engineering, Communication and Computing
Continuations and monodromy on random riemann surfaces
Proceedings of the 2009 conference on Symbolic numeric computation
Computing monodromy via continuation methods on random Riemann surfaces
Theoretical Computer Science
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We have designed a new symbolic-numeric strategy for computing efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field. In essence, computations modulo a well-chosen prime number p are used to obtain the exact information needed to guide floating point computations. In this paper, we detail the symbolic part of our algorithm. First of all, we study modular reduction of Puiseux series and give a good reduction criterion for ensuring that the information required by the numerical part is preserved. To establish our results, we introduce a simple modification of classical Newton polygons, that we call ''generic Newton polygons'', which turns out to be very convenient. Finally, we estimate the size of good primes obtained with deterministic and probabilistic strategies. Some of these results were announced without proof at ISSAC'08.