Irreducibility of multivariate polynomials
Journal of Computer and System Sciences
Absolute factorization of polynomials: a geometric approach
SIAM Journal on Computing
Effective Noether irreducibility forms and applications
Selected papers of the 23rd annual ACM symposium on Theory of computing
Massively parallel search for linear factors in polynomials with many variables
Applied Mathematics and Computation
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
SIAM Journal on Numerical Analysis
Irreducible decomposition of curves
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Linear differential operators for polynomial equations
Journal of Symbolic Computation
Polynomial Factorization 1987-1991
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Lifting and recombination techniques for absolute factorization
Journal of Complexity
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
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
Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm
International Journal of Computational Science and Engineering
From an approximate to an exact absolute polynomial factorization
Journal of Symbolic Computation
Probabilistic algorithms for polynomial absolute factorization
ACM Communications in Computer Algebra
Modular Las Vegas algorithms for polynomial absolute factorization
Journal of Symbolic Computation
Ruppert matrix as subresultant mapping
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
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A recent algorithmic procedure for computing the absolute factorization of a polynomial P(X,Y), after a linear change of coordinates, is via a factorization modulo X3. This was proposed by A. Galligo and D. Rupprecht in [7],[16]. Then absolute factorization is reduced to finding the minimal zero sum relations between a set of approximated numbers b;i;, i =1 to n such that ∑n;i =1; b;i; =0, (see also [17]). Here this problem with an a priori exponential complexity, is efficiently solved for large degrees (n›100). We rely on LLL algorithm, used with a strategy of computation inspired by van Hoeij's treatment in [23]. For that purpose we prove a theorem on bounded integer relations between the numbers b;i;,, also called linear traces in [19].