A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems
Abstrak
We improve the local generic position method for isolating the real roots of a zero-dimensional bivariate polynomial system with two polynomials and extend the method to general zero-dimensional polynomial systems. The method mainly involves resultant computation and real root isolation of univariate polynomial equations. The roots of the system have a linear univariate representation. The complexity of the method is $\tilde{O}_B(N^{10})$ for the bivariate case, where $N=\max(d,τ)$, $d$ resp., $τ$ is an upper bound on the degree, resp., the maximal coefficient bitsize of the input polynomials. The algorithm is certified with probability 1 in the multivariate case. The implementation shows that the method is efficient, especially for bivariate polynomial systems.
Topik & Kata Kunci
Penulis (2)
Jin-San Cheng
Kai Jin
Akses Cepat
- Tahun Terbit
- 2013
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓