Effective Noether irreducibility forms and applications
Selected papers of the 23rd annual ACM symposium on Theory of computing
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Towards certified irreducibility testing of bivariate approximate 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
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Towards more accurate separation bounds of empirical polynomials
ACM SIGSAM Bulletin
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
Extracting numerical factors of multivariate polynomials from taylor expansions
Proceedings of the 2009 conference on Symbolic numeric computation
Ruppert matrix as subresultant mapping
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
| Hi-index | 0.00 |
We study the problem of bounding a polynomial which is absolutely irreducible, away from polynomials which are not absolutely irreducible. These separation bounds are useful for testing whether an empirical polynomial is absolutely irreducible or not, for the given tolerance or error bound of its coefficients. In the former paper, we studied some improvements on Kaltofen and May's method which finds applicable separation bounds using an absolute irreducibility criterion due to Ruppert. In this paper, we study the similar improvements on the method using the criterion due to Gao and Rodrigues for sparse polynomials satisfying Newton polytope conditions, by which we are able to find more accurate separation bounds, for such bivariate polynomials. We also discuss a concept of separation bound continuations for both dense and sparse polynomials.