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TitleA generic position based method for real root isolation of zero-dimensional polynomial systems
Author(s) Jin-San Cheng, Kai Jin
TypeArticle in Journal
AbstractAbstract 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 ( 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.
KeywordsPolynomial systems, Real root isolation, Linear univariate representation, Generic position
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717114000856
LanguageEnglish
JournalJournal of Symbolic Computation
Volume68, Part 1
Number0
Pages204 - 224
Year2015
Edition0
Translation No
Refereed No
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