کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
401760 | 676079 | 2015 | 21 صفحه PDF | دانلود رایگان |
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 O˜B(N10) for the bivariate case, where N=max(d,τ)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.
Journal: Journal of Symbolic Computation - Volume 68, Part 1, May–June 2015, Pages 204–224