Irreducibility of multivariate polynomials
Journal of Computer and System Sciences
Factoring sparse multivariate polynomials
Journal of Computer and System Sciences
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Factoring multivariate polynomials over algebraic number fields
SIAM Journal on Computing
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Integration of rational functions: Rational computation of the logarithmic part
Journal of Symbolic Computation
Absolute factorization of polynomials: a geometric approach
SIAM Journal on Computing
Effective Noether irreducibility forms and applications
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
Algorithms for computer algebra
Algorithms for computer algebra
Factoring rational polynomials over the complex numbers
SIAM Journal on Computing
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
Mathematics of Computation
Complexity and real computation
Complexity and real computation
Subquadratic-time factoring of polynomials over finite fields
Mathematics of Computation
Modern computer algebra
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
Multivariate Polynomial Factorization
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
On Wiedemann's Method of Solving Sparse Linear Systems
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
A new modular interpolation algorithm for factoring multivariate polynominals
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Hensel lifting and bivariate polynomial factorisation over finite fields
Mathematics of Computation
A block Lanczos algorithm for finding dependencies over GF(2)
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Linear differential operators for polynomial equations
Journal of Symbolic Computation
Yet another practical implementation of polynomial factorization over finite fields
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Polynomial factorization: a success story
ISSAC '03 Proceedings of the 2003 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
Computer algebra handbook
Complexity issues in bivariate polynomial factorization
ISSAC '04 Proceedings of the 2004 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
The approximate GCD of inexact polynomials
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Improved dense multivariate polynomial factorization algorithms
Journal of Symbolic Computation
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
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Lower bounds for approximate factorizations via semidefinite programming: (extended abstract)
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Differential forms in computational algebraic geometry
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
Parallel methods for absolute irreducibility testing
The Journal of Supercomputing
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
Approximate factorization of polynomials over Z
Proceedings of the 2009 conference on Symbolic numeric computation
Journal of Symbolic Computation
Deterministic distinct-degree factorization of polynomials over finite fields
Journal of Symbolic Computation
On a generalization of Stickelberger's Theorem
Journal of Symbolic Computation
Modular Las Vegas algorithms for polynomial absolute factorization
Journal of Symbolic Computation
A lifting and recombination algorithm for rational factorization of sparse polynomials
Journal of Complexity
Computing monodromy via continuation methods on random Riemann surfaces
Theoretical Computer Science
A note on Gao's algorithm for polynomial factorization
Theoretical Computer Science
Improved explicit estimates on the number of solutions of equations over a finite field
Finite Fields and Their Applications
Ruppert matrix as subresultant mapping
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
On the bit-complexity of sparse polynomial and series multiplication
Journal of Symbolic Computation
Extracting sparse factors from multivariate integral polynomials
Journal of Symbolic Computation
Factoring bivariate lacunary polynomials without heights
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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A new method is presented for factorization of bivariate polynomials over any field of characteristic zero or of relatively large characteristic. It is based on a simple partial differential equation that gives a system of linear equations. As in Berlekamp's and Niederreiter's algorithms for factoring univariate polynomials, the dimension of the solution space of the linear system is equal to the number of absolutely irreducible factors of the polynomial to be factored, and any basis for the solution space gives a complete factorization by computing gcd's and by factoring univariate polynomials over the ground field. The new method finds absolute and rational factorizations simultaneously and is easy to implement for finite fields, local fields, number fields, and the complex number field. The theory of the new method allows an effective Hilbert irreducibility theorem, thus an efficient reduction of polynomials from multivariate to bivariate.