Exact bivariate polynomial factorization over ℚ by approximation of roots
- 126 Downloads
Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients. The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library. In addition, the numerical computation part often only requires double precision and is easily parallelizable.
KeywordsFactorization of multivariate polynomials interpolation methods minimal polynomial numerical continuation
Unable to display preview. Download preview PDF.
- Chattopadhyay A, Grenet B, Koiran P, Portier N, and Strozecki Y, Factoring bivariate lacunary polynomials without heights, in Proceedings of the 2013 international symposium on Symbolic and Algebraic Computation, Boston, USA, 2013, 141–148.Google Scholar
- Wu W, Chen J, and Feng Y, Sparse bivariate polynomial factorization, Science China Mathematics, 2014, 57, doi: 10.1007/s11425-014-4850-y.Google Scholar
- Huang Y, Wu W, Stetter H J, and Zhi L, Pseudofactors of multivariate polynomials, in Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation, St. Andrews, Scotland, 2000, 161–168.Google Scholar
- Sasaki T, Approximate multivariate polynomial factorization based on zero-sum relations, in Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, London, Canada, 2001, 284–291.Google Scholar
- Corless R M, Giesbrecht MW, van Hoeij M, Kotsireas I, and Watt S M, Towards factoring bivariate approximate polynomials, in Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, London, Canada, 2001, 85–92.Google Scholar
- Gao S, Kaltofen E, May J P, Yang Z, and Zhi L, Approximate factorization of multivariate polynomials via differential equations, in Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, Santander, Spain, 2004, 167–174.Google Scholar
- Chen J, Feng Y, Qin X, and Zhang J, Exact polynomial factorization by approximate high degree algebraic numbers, Proceedings of the 2009 Conference on Symbolic Numeric Computation, Kyoto, Japan, 2009, 21–28.Google Scholar