Symbolic Computation/Computer Algebra, Computational Geometry, Computional Algebraic Geometry.
Currently, I focus on the following two topics.
Certified and efficient method for topology determination and
approximation of algebraic curves and surfaces.
Nonlinear system solving
Providing some new geometric technique, with symbolic and numeric
computation, determining the topology of, and efficiently
approximating of algebraic curves and surfaces. Approximating the intersection of two rational parametric surfaces with correct topology, controlled error efficiently.
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
Isolating the real roots of a zero-dimensional nonlinear system inside a box with numerical method
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., Zhang, B., Xiao, Y., Li, M.: Topology-driven approximation to rational surface-surface intersection via interval algebraic topology analysis, accepted by SIGGRAPH2023 (to appear on ACM Transaction on Graphics).
- Cheng, J.-S., Wen, J., Zhang, B.: Certified numerical real root isolation for bivariate nonlinear systems. Journal of Symbolic Computation, 114: 149-171, 2023
Jia, X., Li, K., Cheng, J.-S.*: Computing the Intersection of Two Rational Surfaces Using Matrix Representations. Computer Aided Design, 150: 103303, 2022 .
- Cheng, J.-S., Dou, X., Wen, J.: A new deflation method for verifying the isolated singular zeros of polynomial systems. Journal of Computational and Applied Mathematics. 376: 112825, 2020.
- Cheng, J.-S., Jin, K. A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems, Journal of Symbolic Computation, 68:204-224, 2015.
- Cheng, J.-S., Jin, K., Lazard, D. Certified Rational Parametric Approximation of Real Algebraic Space Curves with Local Generic Position Method. Journal of Symbolic Computation, 58: 18--40, 2013.
- 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., 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).
- Pai (A certified numerical real root isolation software for multivariate nonlinear square systems, Linux only) and a simple user guider and the paper.
- Associate Professor (Apr. 2014 ~ present): Key Lab of Mathematics Mechanization, Institute of Systems Science, CAS.
- Assistant Professor (Apr. 2009 ~ Mar. 2014): 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.
- PhD students: Kai Jin (2011 ~ 2014) , Xiaojie Dou (2013-2018), Junyi Wen (2015-2020)
- Master students: Wenjian Zhang (2017 ~ 2020), Xianhui Wu (2019-2022)
- PhD candidate: Bingwei Zhang (2018-2023)
- Master candidates: Xiwen Shi (2020 ~ 2023), Yisong Huang (2021~ 2024), Xi Wu (2022-2025)
- Program Committee member, The 6th International Congress on Mathematical Software (ICMS'2018) will be held from July 24-27 in University of Notre Dame, USA. We organize a session: Algorithms and applications for curves and surfaces .
- Program Committee member, International Workshop on Computer Algebra in Scitific Computing (CASC'2015) will be held from September 14 to 18 in Aachen, Germany.
- Program Committee member, International Workshop on Symbolic-Numeric Computation (SNC'2014) will be held from July 28 to 31 in Shanghai, China.
- Program Committee member, The 4th International Congress on Mathematical Software (ICMS'2014) will be held from August 5 to 9 in Hanyang University, Seoul, Korea.
- Program Committee member, International Workshop on Computer Algebra in Scitific Computing (CASC'2014) will be held from September 8 to 12 in Warsaw, Poland.