Parallel algorithms for algebraic problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Logarithmic depth circuits for algebraic functions
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Factoring sparse multivariate polynomials
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Deterministic irreducibility testing of polynomials over large finite fields
Journal of Symbolic Computation
Parallelism and algorithms for algebraic manipulation: current work
ACM SIGSAM Bulletin
Computing the irreducible real factors and components of an algebraicf curve
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Factoring rational polynomials over the complexes
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
On factoring multi-variate polynomials over algebraically closed fields (abstract)
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Effective Noether irreducibility forms and applications
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Counting curves and their projections
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Specified precision polynomial root isolation is in NC
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
The computational complexity of recognizing permutation functions
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A numerical absolute primality test for bivariate polynomials
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Efficient algorithms for computing the nearest polynomial with a real root and related problems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Semi-numerical determination of irreducible branches of a reduced space curve
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
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
Computer algebra handbook
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Change of order for bivariate triangular sets
Proceedings of the 2006 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
Differential forms in computational algebraic geometry
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
Computational complexity of sentences over fields
Information and Computation
Extracting numerical factors of multivariate polynomials from taylor expansions
Proceedings of the 2009 conference on Symbolic numeric computation
Approximate factorization of polynomials over Z
Proceedings of the 2009 conference on Symbolic numeric computation
Deterministic distinct-degree factorization of polynomials over finite fields
Journal of Symbolic Computation
Probabilistic algorithms for polynomial absolute factorization
ACM Communications in Computer Algebra
Proceedings of the 4th International Workshop on Parallel and 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
| Hi-index | 0.00 |
We present a fast parallel deterministic algorithm for testing multivariate integral polynomials for absolute irreducibility, that is irreducibility over the complex numbers. More precisely, we establish that the set of absolutely irreducible integral polynomials belongs to the complexity class NC of Boolean circuits of polynomial size and logarithmic depth. Therefore it also belongs to the class of sequentially polynomial-time problems. Our algorithm can be extended to compute in parallel one irreducible complex factor of a multivariate integral polynomial. However, the coeffieients of the computed factor are only represented modulo a not necessarily irreducible polynomial specifying a splitting field. A consequence of our algorithm is that multivariate polynomials over finite fields can be tested for absolute irreducibility in deterministic sequential polynomial time in the size of the input. We also obtain a sharp bound for the last prime p for which, when taking an absolute irreducible integral polynomial modulo p, the polynomial's irreducibility in the algebraic closure of the finite field of order p is not preserved.