Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Irreducible decomposition of curves
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On approximate irreducibility of polynomials in several variables
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Absolute polynomial factorization in two variables and the knapsack problem
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Numerical factorization of multivariate complex polynomials
Theoretical Computer Science - Algebraic and numerical algorithm
Lifting and recombination techniques for absolute factorization
Journal of Complexity
Approximate bivariate factorization: a geometric viewpoint
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Algebraic cycles from a computational point of view
Theoretical Computer Science
A characteristic set method for equation solving over finite fields
ACM Communications in Computer Algebra
Absolute factoring of bidegree bivariate polynomials
ACM Communications in Computer Algebra
Towards toric absolute factorization
Journal of Symbolic Computation
Exact polynomial factorization by approximate high degree algebraic numbers
Proceedings of the 2009 conference on Symbolic numeric computation
Continuations and monodromy on random riemann surfaces
Proceedings of the 2009 conference on Symbolic numeric computation
Finding exact minimal polynomial by approximations
Proceedings of the 2009 conference on Symbolic numeric computation
Computing monodromy via continuation methods on random Riemann surfaces
Theoretical Computer Science
Rational Hausdorff divisors: A new approach to the approximate parametrization of curves
Journal of Computational and Applied Mathematics
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We propose an algorithm for computing an exact absolute factorization of a bivariate polynomial from an approximate one. This algorithm is based on some properties of the algebraic integers over Z and is certified. It relies on a study of the perturbations in a Vandermonde system. We provide a sufficient condition on the precision of the approximate factors, depending only on the height and the degree of the polynomial.