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- Jin-San Cheng, Sylvain Lazard, Luis Mariano PeÃ±aranda, Marc Pouget, Fabrice Rouillier, Elias P. Tsigaridas
- Mathematics in Computer Science
- 2010

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular andâ€¦ (More)

- Jin-San Cheng, Xiao-Shan Gao, Ming Li
- IMA Conference on the Mathematics of Surfaces
- 2005

An algorithm is proposed to determine the topology of an implicit real algebraic surface in R. The algorithm consists of three steps: surface projection, projection curve topology determination andâ€¦ (More)

We consider the computational problem of isolating all the real zeros of a zero-dimensional triangular polynomial system Fn âŠ† Z[x1, . . . , xn]. We present a complete numerical algorithm for thisâ€¦ (More)

In this talk, an algorithm is proposed to determine the topology of an implicit real algebraic surface in R. The algorithm consists of four steps: surface projection, projection curve topologyâ€¦ (More)

- Jin-San Cheng, Xiao-Shan Gao, Jia Li
- ISSAC
- 2009

A local generic position method is proposed to isolate the real roots of a bivariate polynomial system ∑={<i>f</i>(<i>x,y</i>),<i>g</i>(<i>x,y</i>)}. In this method, the roots of the system areâ€¦ (More)

- Jin-San Cheng, Kai Jin, Xiao-Shan Gao, Daniel Lazard
- J. Symb. Comput.
- 2013

In this paper, an algorithm to determine the topology of an algebraic space curve and to compute a certified G rational parametric approximation of the algebraic space curve is given by extending theâ€¦ (More)

- Jin-San Cheng, Xiao-Shan Gao, Chee-Keng Yap
- ISSAC
- 2007

We present a complete numerical algorithm of isolating all the real zeros of a zero-dimensional triangular polynomial system <i>F</i><sub>n</sub> Z[<i>x</i><sub>1</sub>…,<i>x</i><sub>n</sub>].â€¦ (More)

- Jin-San Cheng, Xiao-Shan Gao, Chee-Keng Yap
- J. Symb. Comput.
- 2009

We present a complete numerical algorithm of isolating all the real zeros of a zero-dimensional triangular polynomial system Fn âŠ† Z[x1, . . . , xn]. Our system Fn is general, with no furtherâ€¦ (More)

- Jin-San Cheng, Xiao-Shan Gao, Leilei Guo
- J. Symb. Comput.
- 2012

In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linearâ€¦ (More)

- Jin-San Cheng, Kai Jin
- J. Symb. Comput.
- 2015

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 zerodimensionalâ€¦ (More)