Symbolic Computation/Computer Algebra, Computational Geometry, Computer Aided Geometric Design.
Currently, I focus on the following two topics.
Certified and efficient method for topology determination and
approximation of algebraic curves and surfaces.
Algebraic polynomial system solving
Providing some new geometric technique, with symbolic and numeric
computation, determining the topology of, and efficiently
approximating of algebraic curves and surfaces.
With algebraic or geometric techniques to get the zeros or components (may include their multiplicities) of algebraic
polynomial system, isolating the zeros
of the system (zero-dimensional case) or giving an
algebraic representation of the zeros. For zero-dimensional case, one can get the zeros of the system only by
root-isolating of univariate polynomial equations from the algebraic
2003.9–2006.7, Ph.D., Applied Mathematics, Academy of Mathematics and Systems Science, CAS
Supervisor: GAO Xiao-Shan
Dissertation: Topology determination and approximation of real algebraic curves and surfaces
2000.9–2003.7, M.Sci., Computational Mathematics, Institute of Mathematics, Jilin University
Supervisor: FENG Guochen
Dissertation: Blending pipe quadric surfaces via base curve method.
1996.9–2000.7, B.Sci., Computational Mathematics, Department of Mathematics, Jilin University
(Full list of publications available here)
- Cheng, J.-S., Jin, K., Lazard, D. Certified Rational Parametric Approximation of Real Algebraic Space Curves with Local Generic Position Method. Accepted by Journal of Symbolic Computation, 2013.
- Cheng, J.-S., Gao, X.-S.: Multiplicity Preserving Triangular Set Decomposition of Two Polynomials. Accepted by Journal of Systems Science and Complexity, 2013.
- Shen, L., Cheng, J.-S., Jia, X.: Homeomorphic approximation of the intersection curve of two rational surfaces. Computer Aided Geometric Design 29(8): 613-625 (2012).
- Li, J., Cheng, J.-S., Tsigaridas, E.P.: Local Generic Position for Root Isolation of Zero-Dimensional Triangular Polynomial Systems. CASC 2012: 186-197.
- Cheng, J.-S., Gao, X.-S., Guo, L. Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation. Journal of Symbolic Computation, 47(7): 843-858 (2012).
- Cheng, J.-S., Lazard, S., Penaranda, L., Pouget, M., Rouillier, F., and Tsigaridas, E. On the topology of planar algebraic curves, Mathematics in Computer Science, 2010(4):113-137 (The full version of the conference paper of SoCG 2009 ).
- Cheng, J.-S., Gao, X.-S., Li, J. Root isolation for bivariate polynomial systems with local generic position method. ISSAC 2009: 103-110.
- Cheng, J.-S., Gao, X.-S., Li, J. Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities. CASC 2009: 89-93.
- Cheng, J.-S., Gao, X.-S., and Yap, C.K. Complete Numerical Isolation of Real Zeros in Zero-dimensional
Triangular Systems, J. Symb. Comput. 44(7): 768-785 (2009) (This is a complete version with new contents from the conference paper of ISSAC 2007).
- Cheng, J.-S., Gao, X.-S., and Li, M. Determining the Topology
of Real Algebraic Surfaces, Mathematics of Surfaces XI, R.
Martin, H. Bez, M. Sabin (editors), LNCS 3604, Springer-Verlag,
2005, pp. 121-146.
Visual C++ software:
- Quadric surfaces blending (part of the Mathematics Mechanization Platform MMP).
- Associate Professor (Apr. 2012 ~ present): Key Lab of Mathematics Mechanization, Institute of Systems Science, CAS.
- Assistant Professor (Apr. 2009 ~ present): Key Lab of Mathematics Mechanization, Institute of Systems Science, AMSS, CAS.
- Post-doctor (Oct. 2007 ~ Mar. 2009): LORIA, INRIA Nancy - Grand Est, Nancy, France.
- Post-doctor (Jun. 2006 ~ Sep. 2007): Key Lab of Systems and Control, Institue of Systems Science, CAS.
- Short-term visit (Jun. 2006): Korea Institute for Advanced Study, Seoul, South Korea.
- Short-term visit (Aug. 2005 ~ Sep. 2005): Department of Computer Science, Cardiff university,
- PhD candidate: Kai Jin (2011 ~ 2014)
- Master candidate: Xiaojie Dou (2013 ~ 2016)
- Master candidate: Junyi Wen (2015 ~ 2018)