Research Interest
Computer algebra, symbolic-numeric computation and their applications
Computing the real or complex solutions of nonlinear polynomial systems
Solving parametric polynomial systems
Triangular decomposition, regular chain, cylindrical algebraic decomposition, quantifier elimination
High performance and parallel computing
PhD Thesis
Solving polynomial systems via triangular decomposition
Abstract
Finding the solutions of a polynomial system is
a fundamental problem with numerous applications
in both the academic and industrial world.
In this thesis, we target on computing symbolically both
the real and the complex solutions of nonlinear polynomial
systems with or without parameters.
To
this end, we improve existing algorithms
for computing triangular decompositions.
Based on that,
we develop various new tools
for solving polynomial systems and illustrate
their effectiveness by
applications.
Published Papers
Changbo Chen, Changliang Ren, Xiang-Jun Ye, and Jing-Ling Chen. Mapping criteria between nonlocality and steerability in qudit-qubit systems and between steerability and entanglement in qubit-qudit systems. PHYSICAL REVIEW A 98, 052114 (2018).
Download LinkChangbo Chen, Wenyuan Wu: Revealing Bistability in Neurological Disorder Models By Solving Parametric Polynomial Systems Geometrically. AISC 2018: 170-180.
Download LinkChangbo Chen, Wenyuan Wu: A Continuation Method for Visualizing Planar Real Algebraic Curves with Singularities. CASC 2018: 99-115.
Download LinkChangbo Chen, Wenyuan Wu, Yong Feng: Full Rank Representation of Real Algebraic Sets and Applications. CASC 2017: 51-65. Download
Wenyuan Wu, Changbo Chen, Greg Reid: Penalty Function Based Critical Point Approach to Compute Real Witness Solution Points of Polynomial Systems. CASC 2017: 377-391 Download
Jing-Ling Chen, Changliang Ren, Changbo Chen, Xiang-Jun Ye and Arun Kumar Pati. Bell's Nonlocality Can be Detected by the Violation of Einstein-Podolsky-Rosen Steering Inequality. Sci. Rep. 6, 39063; doi: 10.1038/srep39063 (2016). Download Supplementary Material
Changbo Chen and Wenyuan Wu. A Numerical Method for Analyzing the Stability of Bi-parametric Biological Systems. SYNASC 2016, 72-80, 2016. Download
Changbo Chen and Wenyuan Wu. A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications. CASC 2016: pp 156-171, 2016. Download
Changbo Chen, Marc Moreno Maza. Quantifier elimination by cylindrical algebraic decomposition based on regular chains. J. Symb. Comput. 75: 74-93 (2016).
Changbo Chen, Svyatoslav Covanov, Farnam Mansouri, Marc Moreno Maza, Ning Xie, Yuzhen Xie. Parallel Integer Polynomial Multiplication. SYNASC 2016, 72-80, 2016.
Changbo Chen and Marc Moreno Maza. An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions. Computer Mathematics, R. Feng et al., Springer-Verlag, pp 199-221, 2014.
Francois Boulier, Changbo Chen, Francois Lemaire, and Marc Moreno Maza. Real Root Isolation of Regular Chains. Computer Mathematics, R. Feng et al., Springer-Verlag, pp 33-48, 2014.
Changbo Chen, Marc Moreno Maza. Real Quantifier Elimination in the RegularChains Library. Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 283-290.
Changbo Chen, Marc Moreno Maza. Cylindrical Algebraic Decomposition in the RegularChains Library. Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 425-433.
Parisa Alvandi, Changbo Chen, Steffen Marcus, Marc Moreno Maza, Ă‰ric Schost, Paul Vrbik. Doing Algebraic Geometry with the RegularChains Library. Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 472-479.
Changbo Chen, Marc Moreno Maza. Solving Parametric Polynomial Systems by RealComprehensiveTriangularize. Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 504-511.
Changbo Chen, Svyatoslav Covanov, Farnam Mansouri, Marc Moreno Maza, Ning Xie, Yuzhen Xie. The Basic Polynomial Algebra Subprograms. Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 669-676.
Changbo Chen, Marc Moreno Maza. Quantifier Elimination by Cylindrical Algebraic Decomposition Based on Regular Chains. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC '14, Kobe, Japan, ACM, pages 91-98.
Russell J. Bradford, Changbo Chen, James H. Davenport, Matthew England, Marc Moreno Maza, David J. Wilson. Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains. Proceedings of Computer Algebra in Scientific Computing, CASCâ€?014 - Lecture Notes in Computer Science, volume 8660, Springer, pages 44-59.
Matthew England, Russell J. Bradford, Changbo Chen, James H. Davenport, Marc Moreno Maza, David J. Wilson. Problem Formulation for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition. Proceedings of Intelligent Computer Mathematics - International Conference, CICM 2014, Coimbra, Portugal, July 7, Lecture Notes in Computer Science, volume 8543, Springer, pages 45-60.
Changbo Chen, Svyatoslav Covanov, Farnam Mansouri, Marc Moreno Maza, Ning Xie, Yuzhen Xie. Basic Polynomial Algebra Subprograms. ACM Communications in Computer Algebra, Vol. 48, No. 4, Issue 190, December 2014, pages 197-201.
Changbo Chen, Robert M. Corless, Marc Moreno Maza, Pei Yu, Yiming Zhang. An application of regular chain theory to the study of limit cycles. International Journal of Bifurcation and Chaos, volume 23, number 9.
Parisa Alvandi, Changbo Chen, Marc Moreno Maza. Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One. Proceedings of Computer Algebra in Scientific Computing - 15th International Workshop, CASC 2013, Berlin, Germany, Lecture Notes in Computer Science, volume 8136, Springer-Verlag, pages 30-45.
Changbo Chen, James H. Davenport, John P. May, Marc Moreno Maza, Bican Xia, Rong Xiao. Triangular decomposition of semi-algebraic systems. Journal of Symbolic Computation. 49: 3-26, 2013.
Changbo Chen, James H. Davenport, Marc Moreno Maza, Bican Xia, Rong Xiao. Computing with semi-algebraic sets: Relaxation techniques and effective boundaries. Journal of Symbolic Computation. 52: 72-96, 2013.
Changbo Chen and M. Moreno Maza. Algorithms for computing triangular decompositions of polynomial systems. Journal of Symbolic Computation, 47(6): 610-642 (2012).
Changbo Chen, Marc Moreno Maza and Yuzhen Xie. Cache Complexity and Multicore Implementation for Univariate Real Root Isolation. High Performance Computing Symposium (HPCS2010). J. of Physics: Conference Series, vol. 341, 012026, 2012.
Changbo Chen, James H. Davenport, M. Moreno Maza, Bican Xia, Rong Xiao. Computing with semi-algebraic sets represented by triangular decomposition. Proceedings of 2011 International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), ACM Press, pp. 75--82, 2011.
Changbo Chen and M. Moreno Maza. Algorithms for computing triangular decompositions of polynomial systems. Proceedings of 2011 International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), ACM Press, pp. 83--90, 2011.
Changbo Chen and Marc Moreno Maza. Semi-algebraic description of the equilibria of dynamical systems. Proceedings of 2011 Computer Algebra in Scientific Computing (CASC 2011), Springer Verlag, LNCS 6885, pages 101--125, 2011.
Changbo Chen, Marc Moreno Maza and Yuzhen Xie. Parallel univariate real root isolation on multicore processors. AIP Conference Proceedings, volume 1368, pages 317-320, 2011.
Changbo Chen, James H. Davenport, FranĂ§ois Lemaire, Marc Moreno Maza, Bican Xia, Rong Xiao, and Yuzhen Xie. Computing the real solutions of polynomial systems with the RegularChains library in Maple. ACM Commun. Comput. Algebra, volume 45, number 3, pages 166-168.
Changbo Chen, James H. Davenport, John P. May, M. Moreno Maza, Bican Xia, Rong Xiao. Triangular decomposition of semi-algebraic systems. Proceedings of 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010), ACM Press, pp. 187--194, 2010.
Changbo Chen, Marc Moreno Maza, Bican Xia and Lu Yang. Cmputing Cylindrical Algebraic Decomposition via Triangular Decomposition. Proceedings of ISSAC 2009, pages 95-102, ACM Press, New York, 2009.
Changbo Chen, Liyun Li, Marc Moreno Maza, Wei Pan, and Yuzhen Xie. On the representation of constructible sets. ACM Commun. Comput. Algebra , volume 42, number 3, pages 162-163, 2008.
Changbo Chen, Marc Moreno Maza, Wei Pan and Yuzhen Xie. On the Verification of Polynomial System Solvers. Frontiers of Computer Science in China, Vol 2, Numb 1, pages 55-66, 2008.
Changbo Chen, FrancoisÂ Lemaire, Liyun Li, Marc Moreno Maza, Wei Pan and Yuzhen Xie. The ConstructibleSetTools and ParametricSystemsTools Modules of the RegularChains Library in Maple. Proceedings of the International Conference on Computational Science and Applications, IEEE Computer Society, pages 342-352, 2008
Changbo Chen, FrancoisÂ Lemaire, Liyun Li, Marc Moreno Maza, Wei Pan and Yuzhen Xie. The ConstructibleSetTools and ParametricSystemsTools Modules of the RegularChains Library in Maple. ACM Commun. Comput. Algebra , volume 42, number 3, pages 182-184, 2008.
Changbo Chen, Francois Lemaire, Oleg Golubitsky, MarcÂ Moreno Maza and Wei Pan. Comprehensive Triangular Decomposition. Proceedings of CASC 2007: Computer Algebra in Scientific Computing, pages 73-101, Lecture Notes in Computer Science, vol. 4770, Springer-Verlag, 2007.
Changbo Chen, Francois Lemaire, Marc Moreno Maza, Wei Pan and Yuzhen Xie. Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library. Proceedings of Computer Algebra Systems and Their Applications'07, Y. Shi et al. (Eds.): ICCS 2007, Part II, LNCS 4488, pp. 268271, Springer-Verlag Berlin Heidelberg 2007.
Some of the talks I Presented
Recent Advances on the Theory of Regular Chains.
ORCCA JLM, London, Canada, March 8, 2013.
An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions
.
ASCM 2012, Beijing, China, October 27, 2012.
Quantifier Elimination via Triangular Decomposition.
CAIMS 2012, Toronto, Canada, June 27, 2012.
Advances on Quantifier Elimination and Applications.
SIAM-DM 2012, Halifax, Nova Scotia, Canada, June 20, 2012.
Solving Polynomial Systems via Triangular Decomposition.
Ph.D. Public Lecture, London, Canada, August 30, 2011.
Cache Complexity and Multicore Implementation for Univariate Real Root Isolation.
HPCS 2011, Montreal, Canada, June 17, 2011.
Triangular Decomposition of Semi-algebraic Systems
.
ISSAC' 10, Munich, Germany, July 27, 2010.
Solving Parametric Polynomial Systems with the RegularChains Library in Maple.
Computing Cylindrical Algebraic Decomposition via Triangular Decomposition
.
ISSAC' 09, Seoul, Korea, July 29, 2009.
Solving Parametric Polynomial Systems with the RegularChains Library in Maple.
ACA'09, MontrĂ©al, June 25, 2009.
Triangular Decompositions for Solving Parametric Polynomial Systems.
MOCAA M^3 workshop 2008, London, Canada, May 9th, 2008.