Lgp

Root isolation for bivariate polynomial systems with local generic position method. A local generic position method is proposed to isolate the real roots of a bivariate polynomial system ∑={f(x,y),g(x,y)}. In this method, the roots of the system are represented as linear combinations of the roots of two univariate polynomial equations t(x)=0 and T(X)=0: {x = α, y = β -- α/s | α ε V(t(x)), β ε V(T(X)), ||β -- α| < S}, where s, S are constants satisfying certain conditions. The multiplicities of the roots of Σ=0 are the same as that of the corresponding roots of T(X)=0. This representation leads to an efficient and stable algorithm to isolate the real roots of Σ.


References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice: Separating linear forms and rational univariate representations of bivariate systems (2015)
  2. Cheng, Jin-San; Jin, Kai: A generic position based method for real root isolation of zero-dimensional polynomial systems (2015)
  3. Kobel, Alexander; Sagraloff, Michael: On the complexity of computing with planar algebraic curves (2015)
  4. Mehlhorn, Kurt; Sagraloff, Michael; Wang, Pengming: From approximate factorization to root isolation with application to cylindrical algebraic decomposition (2015)
  5. Berberich, Eric; Emeliyanenko, Pavel; Kobel, Alexander; Sagraloff, Michael: Exact symbolic-numeric computation of planar algebraic curves (2013)
  6. Cheng, Jin-San; Jin, Kai; Lazard, Daniel: Certified rational parametric approximation of real algebraic space curves with local generic position method (2013)
  7. Qin, Xiaolin; Feng, Yong; Chen, Jingwei; Zhang, Jingzhong: Parallel computation of real solving bivariate polynomial systems by zero-matching method (2013)
  8. Cheng, Jin-San; Gao, Xiao-Shan; Guo, Leilei: Root isolation of zero-dimensional polynomial systems with linear univariate representation (2012)
  9. Gao, Ben; Chen, Yufu: Finding the topology of implicitly defined two algebraic plane curves (2012)
  10. Li, Jia; Cheng, Jin-San; Tsigaridas, Elias P.: Local generic position for root isolation of zero-dimensional triangular polynomial systems (2012)
  11. Berberich, Eric; Emeliyanenko, Pavel; Sagraloff, Michael: An elimination method for solving bivariate polynomial systems: eliminating the usual drawbacks (2011)
  12. Cheng, Jin-San; Gao, Xiao-Shan; Li, Jia: Root isolation for bivariate polynomial systems with local generic position method (2009)
  13. Cheng, Jin-San; Gao, Xiao-Shan; Li, Jia: Ambient isotopic meshing for implicit algebraic surfaces with singularities (plenary talk) (2009)