Home Page for Xiao-Shan Gao (高小山)


hello!        Xiao-Shan Gao, Professor
   Key Laboratory of Mathematics Mechanization
   Academy of Mathematics and System Sciences, Vice President
   Chinese Academy of Sciences
   Beijing 100190
   China

   E-Mail: xgaoATmmrc.iss.ac.cn


| Publications| Research| CNC Group| Software| Geometry Expert| Chinese CV|
Publications of Xiao-Shan Gao

    Publications by Topics
        Quantum Algorithms and Quantum AI

        Differential and Difference Sparse Resultant and Chow Form
        Characteristic Set Method for Symbolic Equation Solving
        Constructive Algebraic Geometry
        Constructive Differential Algebraic Geometry
        Algebraic Methods for Cryptanalysis

        Automated Geometry Reasoning
        Geometric Constraint Solving, Intelligent CAD, Computer Vision, Robotics

        Optimal Interpolation and Path-Planing for CNC Machining and Robotics

        Software Packages
    Publications by Years
    Books
    S.C. Chou, X.S. Gao, and J.Z. Zhang, Machine Proofs in Geometry, World Scientific, Singapore, 1994.
    X.S. Gao, D.K. Wang, Z. Qiu, and H. Yang, Equation Solving and Machien Proving - Problem Solving with MMP (in Chinese ), Science Press, Beijing, 2006.
    X.S. Gao, J. Z. Zhang, and S.C. Chou, Geometry Expert (in Chinese), Nine Chapters Pub., Taiwan, 1998.
    Proceedings/Collection of Papers
    X.S. Gao, H. Li, D. Wang (eds.), Special Issue to Celebrate Wu Wen-Tsun’s Centenary Birthday, Journal of Systems Science and Complexity, Vol. 32(1), 2019.
    X.S. Gao and D. Kapur (eds), Advances in Mathematics MechanizationMathematics Mechanization, JSC, 47(6), 2012.
    X.S. Gao, C. Hoffmann, R. Joan-Arinyo (eds), Geometric Constraints and Reasoning, CAGD, 29, 2012.
    X.S. Gao and D. Micheluchi (eds), Geometric Constraints, IJCGA, 16, World Scientific, 2006.
    A. Cohen, X.S. Gao, N. Takayama (eds), Symbolic Computation in Algebra and Geometry, a special issue of Journal of Symbolic Computation, 38, 2004.
    A. Cohen, X.S. Gao, N. Takayama (eds), Mathematical Software, World Scientific Pub., Singapore, 2002.
    X.S. Gao and D. Wang (eds), Mathematics Mechanization and Applications, Academic Press, London, 2000.
    X.S. Gao and D. Wang (eds), Computer Mathematics-Proc. of ASCM'2000, World Scientific, Singapore, 2000.
    X.S. Gao, D. Wang and L. Yang (eds), Automated Deduction in Geometry, Procs. of ADG98 Springer, Berlin, 1999.
    Survey Papers
    X.S. Gao, A Brief Introduction to Computer Mathematics (in Chinese), Bulletin of Chinese Academy of Sciences, 27(2), 189-196, 2012.
    W.T. Wu and X.S. Gao, Mathematics Mechanization and Applications After Thirty Years, Frontiers in Computer Science, 1(1), 1-8, 2007.
    X.S. Gao and K. Jiang, Survey on Geometric Constraint Solving (in Chinese), J. of CAD & CG, 16(4), 385-396, 2004.
    S.C. Chou and X.S. Gao, Automated reasoning in geometry, Handbook of Automated Reasoning, (eds. A. Robinson and A. Voronkov), 709-749, Elsevier, Amsterdam, 2001.
    X.S. Gao, Mathematics Mechanization: A Survey (In Chinese), Advances in Mathematics, 30(5), 385-404, 2001.
    X.S. Gao, Search Methods Revisited, in Mathematics Mechanization and Application, 253-272, Academic Press, 2000.
    X.S. Gao, Conversion between Implicit and Parametric Representations of Algebraic Varieties, in Mathematics Mechanization and Applications, 253-272, Academic Press, 2000.
    S.C. Chou, X.S. Gao, Z. Liu, D. Wang, and D.K. Wang, Geometric Theorem Provers and Algebraic Equation Solvers, in Mathematics Mechanization and Applications, 491-506, Academic Press, 2000.
    S.C. Chou and X.S. Gao, ``A Survey of Geometric Reasoning Using Algebraic Methods'', Learning and Geometry: Computational Approaches, D.W. Kueker and Carl Smith Eds., p. 97--120, Birkhauser, 1996.
    Research Papers
    2020
    C. Zhao and X.S. Gao QDNN: DNN with Quantum Neural Network Layers,, arXiv:1912.12660, Dec. 29, 2019 .
    Q.L. Huang and X.S. Gao, Faster Interpolation Algorithms for Sparse Multivariate Polynomials Given by Straight-Line Programs., Accepted by Journal of Symbolic Computation, arxiv 1709.08979, 2018.
    Q.L. Huang and X.S. Gao, Deterministic Interpolation of Sparse Black-box Multivariate Polynomials using Kronecker Type Substitutions, accepted by Chinese Science: Mathematics (in Chinese), arxiv 1710.01301, 2018.
    Y. Hu and X.S. Gao, Tropical Differential Gr\"obner Bases, accepted by Mathematics in Computer Science, 2019.
    2019
    R.J. Jing, C.M. Yuan, X.S. Gao, A Polynomial-time Algorithm to Compute Generalized Hermite Normal Forms of Matrices over Z[x], Theoretical Computer Science, 755(10), 89-109, 2019.
    Y. Hu and X.S. Gao, Ritt-Wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems, J. Syst. Sci. Complex., 32: 62-77, 2019.
    Q.L. Huang and X.S. Gao, Revisit Sparse Polynomial Interpolation based on Randomized Kronecker Substitution, Proc. CASC2019, LNCS 11661, Springer, 216-235, 2019.
    2018
    Y.A. Chen and X.S. Gao. Quantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems, arxiv 1712.06239.
    Y.A. Chen, X.S. Gao, C.M. Yuan. Quantum Algorithms for Optimization and Polynomial Systems Solving over Finite Fields, arxiv 1802.03856.
    2017
    X.S. Gao, Z. Huang, C.M. Yuan. Binomial difference ideals, Journal of Symbolic Computation, 80(3), 665-706, 2017.
    X.S. Gao, Z. Huang, J. Wang, C.M. Yuan. Toric Difference Variety, J. Syst. Sci. Complex., 30(1), 173-195, 2017.
    W. Zhu and X.S. Gao, A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity, J. Syst. Sci. Complex., 30(2), 464-483, 2017.
    Y.A. Chen and X.S. Gao, Criteria for Finite Difference Groebner Bases of Normal Binomial Difference Ideals, Prof. ISSAC'17, 93-100, ACM Press, 2017.
    K. Erkorkmaz, Q.G. Chen, M.Y. Zhao, X. Beudaert, X.S. Gao. Linear programming and windowing based feedrate optimization for spline toolpaths, CIRP Annals - Manufacturing Technology, 66(1),393-396, 2017.
    Q. Zhang, X.S. Gao, H.B. Li, M.Y. Zhao. Minimum time corner transition algorithm with confined feedrate and axial acceleration for nc machining along linear tool path, Int J Adv Manuf Techno, 89(1), 941-956, 2017
    M.Y. Zhao and X.S. Gao. An Efficient Stochastic Approach for Robust Time-Optimal Trajectory Planning of Robotic Manipulators Under Limited Actuation, Robotica, 35(12), 2400-241, 2017.
    2016
    Q. Zhang, S. Li, J.X. Guo, X.S. Gao. Time-optimal path tracking for robots under dynamics constraints based on convex optimization., Robotica, 34(9), 2116–2139, 2016.
    2015
    W. Li, C.M. Yuan, X.S. Gao, Sparse Differential Resultant for Laurent Differential Polynomials, Foundations of Computational Mathematics, 15(2), 451-517, 2015.
    W. Li, C.M. Yuan, X.S. Gao, Sparse Difference Resultant, Journal of Symbolic Computation, 68, 169-203, 2015.
    Z. Yang, L.Y. Shen, C.M. Yuan, X.~S. Gao. Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines, Computer-Aided Design, 66, 62-72, 2015.
    J.X. Guo, Q. Zhang, X.~S. Gao, H. Li. Time Optimal Feedrate Generation with Confined Tracking Error based on Linear Programming, J Syst Sci Complex, 28, 80-95, 2015.
    C. Min and X.~S. Gao. Iso-scallop Tool-path Generation of 5-axis CNC Machining for Cyclide Patches. Journal of Engineering Manufacture, 229(7), 1144-1156, 2015.
    Q. Zhang, S. Li, J.X. Guo, X.~S. Gao. Tractable Algorithm for Robust Time-Optimal Trajectory Planning of Robotic Manipulators under Confined Torque, International Journal of Computers, Communications & Control, 10(1), 123-135, 2015.
    2014
    J.S. Cheng and X.S. Gao, Multiplicity-preserving triangular set decomposition of two polynomials, J Syst Sci Complex, 27(6), 2014.
    Z.Y. Zhang, C.M. Yuan, X.S. Gao, Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials, Computer Mathematics, 479-503, Springer, 2014.
    2013
    X.S. Gao, W. Li, C.M. Yuan, Intersection Theory in Differential Algebraic Geometry: Generic Intersections and the Differential Chow Form, Trans. Amer. Math. Soc., 365(9), 4575-4632, 2013.
    W. Li, C.M. Yuan, X.S. Gao, Sparse Difference Resultant, Proc. ISSAC 2013, 275-282, ACM Press, New York, 2013. Also arXiv:1111.1084, 2012.
    J.X. Guo, K. Zhang, Q. Zhang, X.S. Gao. Efficient Time Optimal Feedrate Planning under Dynamic Constraints for High-order CNC Servo System. Computer-Aided Design, 45(12), 1538-1546, 2013.
    K. Zhang, C.M. Yuan, X.S. Gao. Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration. Int J Adv Manuf Technol. 66(9), 1685-1697, 2013.
    K. Zhang, J. Guo, X.S. Gao. Cubic Spline Trajectory Generation with Axis Jerk and Tracking Error Constraints. Int J Precis Eng Manuf, 14(7), 1141-1146, 2013.
    W. Fan, X.~S. Gao, C.H. Lee, K. Zhang, Q. Zhang. Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming. Int J Adv Manuf Technol, 69(5), 1373-1388, 2013.
    2012
    J.S. Cheng，X.S. Gao，L. Guo, Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation., Journal of Symbolic Computation, 47 (2012) 843-858.
    X.S. Gao and Z. Huang, Characteristic Set Algorithms for Equation Solving in Finite Fields, Journal of Symbolic Computation, 47 (2012) 655–679.
    W. Li and X.S. Gao, Chow form for projective differential variety, Journal of Algebra, 370(2012) 344-360.
    S.W. Zhao, R. Feng, and X.S. Gao. On Functional Decompisition of Multivariate Polynomials with Differentiation and Homogenization., J Syst Sci Complex, 25(2), 329-347, 2012.
    Zhang K., Gao X.S., Li H.B., Yuan C.M. A greedy algorithm for feed-rate planning of CNC machines along curved tool paths with confined jerk for each axis., Robotics and Computer Integrated Manufacturing, 28 (2012) 472-483.
    Fan W., Gao X.S., Yan W., Yuan C.M. Interpolation of parametric CNC machining path under confined jounce., Int J Adv Manuf Technol. 62, 719-739, 2012.
    2011
    W. Li, X.S. Gao, C.M. Yuan, Sparse Differential Resultant, Proc. ISSAC 2011, 225-232, ACM Press, New York, 2011. (ISSAC Distinguished Paper Award)
    M. Zhang, W. Yan, C.M. Yuan, D. Wang, X.S. Gao, Curve fitting and time-optimal interpolation on CNC machines, Science China, Series E, 54(7): 1407-1418, 2011.
    L.X. Zhang, R.Y. Sun, X.S. Gao, H. Li, High speed interpolation for micro-line trajectory and adaptive real-time lookahead in CNC machining, Science China, Information Sciences, 54(6), 1481-1495, 2011.
    L. Shen, E. Chionh, X.S. Gao, J. Li. Proper Reparametrization for inherently improper unirational varieties., Journal of Systems Science and Complexity, 24(2), 367-380, 2011.
    2010
    Z. Ye, S.C. Chou, X.S. Gao, Visually Dynamic Presentation of Proofs in Plane Geometry, Part 1. Basic Features and the Manual Input Method, Journal of Automated Reasoning, 45, 213-241, 2010.
    Z. Ye, S.C. Chou, X.S. Gao, Visually Dynamic Presentation of Proofs in Plane Geometry, Part 2. Automated Generation of Visually Dynamic Presentations with the Full-Angle Method and the Deductive Database Method, Journal of Automated Reasoning, 45, 213-241, 2010.
    2009
    X.S. Gao, Y. Luo, and C. Yuan, A Characteristic Set Method for Difference Polynomial Systems, Journal of Symbolic Computation, 44(3), 242-260, 2009.
    X.S. Gao, J. Van der Hoeven, C.M. Yuan, G.L. Zhang, Characteristic set method for differential–difference polynomial systems, Journal of Symbolic Computation, 44(9), 2009, 1137-1163.
    X.S. Gao, C. Yuan, and G. Zhang, Ritt-Wu's Characteristic Set Method for Ordinary Difference Polynomial Systems with Arbitrary Ordering, Acta Mathematica Scientia, 29(3,4), 1063-1080, 2009.
    J.S. Cheng, X.S. Gao, and C.K. Yap, Complete Numerical Isolation of Real Roots in Zero-dimensional Triangular Systems, Journal of Symbolic Computation， 44(7)， 768-785, 2009.
    S.W. Zhao and X.S. Gao, Minimal Achievable Approximation Ratio for MAX-MQ in Finite Fields, Theoretical Computer Science, 410(21-23), 2285-2290, 2009.
    M. Zhang and X.S. Gao, Decomposition of ordinary difference polynomials, Journal of Symbolic Computation, 44, 1394-1409, 2009.
    J.S. Cheng, X.S. Gao, J. Li, Root Isolation for Bivariate Polynomial Systems with Local Generic Position , Proc. ISSAC 2009, 103-109, ACM Press, New York, 2009.
    J.S. Cheng, X.S. Gao, J. Li, Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities, In Computer Algebra in Scientific Computing, LNCS 5743, 89-93, 2009.
    J.S. Cheng, X.S. Gao, J. Li, Topology determination and isolation for implicit plane curves. Proc. ACM Symposium on Applied Computing, 1140-1141, ACM Pres, 2009.
    2008
    F. Chai, X.S. Gao, and C. Yuan, A Characteristic Set Method for Solving Boolean Equations and Applications in Cryptanalysis of Stream Ciphers, Journal of Systems Science and Complexity, 21(2), 191-208, 2008.
    X.S. Gao and M. Zhang, Decomposition of Differential Polynomials, Applicable Algebra in Engineering, Communication and Computing, 19(1), 1-25, 2008.
    J. Li, L. Shen, X.S. Gao, Proper Reparametrization of Rational Ruled Surface, Journal of Computer Science and Technology, 23(2), 290-297, 2008.
    G.L. Zhang and X.S. Gao, Properties of Ascending Chians fr Partial Difference Polynomial Systems, ASCM2007, LNAI 5081, 307-321, Springer-Verlag, Berlin Heidelberg, 2008.
    2007
    X.S. Gao, J. van der Hoeven, C. Yuan, and G. Zhang, Characteristic Set Method for Differential-Difference Polynomial Systems, Mega 2007, Electronic Proceedings, Austria.
    J.S. Cheng, X.S. Gao, and C.K. Yap, Complete Numerical Isolation of Real Zeros in General Triangular Systems, ISSAC 2007, 92-99, ACM Press, New York, 2007.
    X. Zhao and X.S. Gao, Binary Affinity Genetic Algorithm， Journal of Heuristics, 13, 133-150, 2007.
    X. Zhao, X.S. Gao, and Z. Hu, Evolutionary Programming Based on Non-uniform Mutation，Applied Mathematics and Computation, 192(1), 1-11, 2007.
    2006
    R.Y. Feng and X.S. Gao, A Polynomial Time Algorithm To Find Rational General Solutions Of First Order Autonomous ODEs, Journal of Symbolic Computation, 41(7), 739-762, 2006.
    E.W. Chionh, X.S. Gao and L.Y. Shen, Inherently improper surface parametric supports, Computer Aided Geometric Design, 23, 629-639, 2006.
    X.S. Gao, Q. Lin, and G. Zhang, A C-tree Decomposition Algorithm for 2D and 3D Geometric Constraint Solving, Computer-Aided Design, 38(1), 1-13, 2006.
    X.S. Gao and C. Yuan, Resolvent Systems of Difference Polynomial Ideals, Proc. ISSAC 2006, ACM Press, New York, 2006.
    X.S. Gao and J. Tang, On the Probability of the Number of Solutions for the P4P Problem, Journal of Mathematical Imaging and Vision, 25, 79-86, 2006.
    M. Li, X.S. Gao, and S.C. Chou, Quadratic Approximation to Plane Parametric Curves and Applications in Approximate Implicitization, Visual Computers, 22, 906-917, 2006.
    G.F. Zhang and X.S. Gao, Well-constrained Completion and Decomposition for Under-constrained Geometric Constraint Problems, 16, International Journal of Computational Geometry & Applications, 461-478, 2006.
    G.F. Zhang and X.S. Gao, Planar Generalized Stewart-Gough Platforms and their Direct Kinematics, ADG 2004, LNAI 3763, 198-211, Springer-Verlag, Berlin, 2006,.
    G.F. Zhang and X.S. Gao, Spatial Geometric Constraint Solving Based on k-connected Graph Decomposition, 973-977, Proc. of The 21st Annual ACM Symposium on Applied Computing, Dijon, France, ACM Press, 2006.
    J. Li and X.S. Gao, The Proper Parametrization of a Special Class of Rational Parametric Equations, J. of Sys. Sci. and Complexity, 19, 331-339, 2006.
    2005
    X.S. Gao, D. Lei, Q. Liao, and G. Zhang, Generalized Stewart Platforms and their Direct Kinematics, IEEE Trans. Robotics, vol 21, 141-151, 2005.
    J.M. Aroca, J.Cano R. Feng and X.S. Gao, Algebraic general solutions of algebraic ODEs, Proc. ISSAC2005, 29-36，ACM Press, New York, 2005.
    J.S. Cheng, X.S. Gao, and M. Li, Determine the Topology of Real Algebraic Surfaces, Mathematics of Surfaces, 121-146, LNCS, Springer-Verlag, 2005.
    M. Li, X.S. Gao, and J.S. Cheng, Generating Symbolic Interpolants for Scattered Satat with Normal Vectors, Journal of Computer Science and Technology, 20, 861-874 2005.
    2004
    X.S. Gao, C.M. Hoffmann and W. Yang, Solving spatial basic geometric constraint configurations with locus intersection, Computer Aided Design, 111-122, 36(2), 2004.
    X.S. Gao and M. Li, Rational Quadratic Approximation to Real Algebraic Curves, Computer Aided Geometric Design, 21, 805-828, 2004.
    X.S. Gao and Q. Lin, MMP/Geometer - A Software Package for Automated Geometry Reasoning, Automated Deduction in Geometry, (ed. F. Winkler), 44-66, Springer, Berlin, 2004.
    J. Wang and X.S. Gao, An Algorithm for Solving Partial Differential Parametric Systems, Discrete Applied Mathematics. 136(1), 105-116, 2004.
    R. Feng and X.S. Gao, Rational General Solutions of Algebraic Ordinary Differential Equations, Proc. ISSAC2004, 155-162, ACM Press, New York, 2004.
    X.S. Gao and M. Zhang, Decomposition of Differential Polynomials with Constant Coefficients, Proc. ISSAC2004, 175-182, ACM Press, New York, 2004.
    F. Xie and X.S. Gao, Applications of Computer Algebra in Solving Nonlinear Evolution Equations, Commun. Theor. Phys. 41 (2004) 353-356.
    2003
    X.S. Gao, Implicitization for Differential Rational Parametric Equations, J. of Symbolic Computation, 811-824, 36(5), 2003..
    X.S. Gao, X. Hou, J. Tang and H. Chen, Complete Solution Classification for the Perspective-Three-Point Problem, IEEE Tran. on PAMI, 930-943, 25(8), 2003..
    Here is the appendix to this paper
    Y. Chen and X.S. Gao, Involutive Bases of Algebraic Partial Differential Equation Systems, Science in China (A), 33(2), 97-113, 2003.
    X.S. Gao and D.K. Wang, Zero Decomposition Theorems for Counting the Number of Solutions for Parametric Equation Systems, in Computer Mathematics, Proc. of ASCM2003, (eds. Z. Li and W. Sit), 130-145, World Scientific, Singapore, 2003.
    X.S. Gao and G. Zhang, Geometric Constraint Solving via C-tree Decomposition, (Appendix) ACM Solid Modelling 2003, 45-55, Seattle, USA, ACM Press, New York, 2003.
    2002
    X.S. Gao, K. Jiang, and C.-C. Zhu, Geometric Constraint Solving with Conics and Linkages, Computer Aided Design, 34(6), 421-433, 2002.
    X.S. Gao, C. Zhu, S.-C. Chou, and J.-X. Ge, Automated Generation of Kempe Linkages for Algebraic Curves and Surfaces, Mechanism and Machine Theory, 36(9), 1019-1033, 2002.
    T. Chaolu and X.S. Gao, Nearly Differential Characteristic Set for Differential Polynomial System, Acta Mathematica Sinica, 45(6), 1041-1050, 2002.
    X.S. Gao and T. Xu, Luroth's Theorem in Differential Fields, J. Sys. Sci. and Complexity, 15(4), 376-383, 2002.
    X.S. Gao, C.M. Hoffmann and W. Yang, Solving Basic Gometric Constraint Configurations with Locus Intersection, Proc. ACM Solid Modelling 2002, 95-104, ACM Press, New York, 2002.
    2001
    Y.F. Chen and X.S. Gao, Involutive Directions and New Involutive Divisions, Computers and Mathematics with Applications, 41(7-8), 2001, 945-956.
    X.S. Gao, L. Huang, and K, Jiang, Geometric Constraint Solving with Geometric Transformation, Science in China (Series F), 44(1), 50-59, 2001.
    X.S. Gao, L. Huang, and K, Jiang, A Hybrid Method for Solving Geometric Constraint Problems in Automated Deduction in Geometry, J. Richter-Gebert and D. Wang (eds), 16-25, LNAI No. 2061, Springer-Verlag, Berlin, 2001.
    2000
    J. Ge, S.C. Chou and X.S. Gao, Geometric Constraint Satisfaction Using Optimization Methods, Computer Aided Design, 31(14), 867-879, 2000.
    S.C. Chou, X.S. Gao, and J.Z. Zhang, A Deductive Database Approach To Automated Geometry Theorem Proving and Discovering, J. Automated Reasoning, 25(3), 219-246, 2000.
    X.S. Gao and K. Jiang, Order in Solving Polynomial Equations, Computer Mathematics, Proc. of ASCM'2000, pp. 308-318, World Scientific, 2000.
    X.S. Gao, W.Q. Yang, and L. Huang, Intelligent Dynamic Geometry, Proc. ATCM'2000, ATCM Inc, Thailand, pp.162-171.
    1999
    X.S. Gao and S. C. Chou, On the Theory of Resolvents and Its Applications, Sys. Sci. and Math. Sci., 12, Suppl., 17--30, 1999,
    X.S. Gao, Automated Geometry Diagram Construction and Engineering Geometry, in Automated Deduction in Geometry, Proc. of ADG98, pp. 226-252, Springer, 1999.
    X.S. Gao, Building Dynamic Mathematical Models with Geometry Expert, III. A Geometry Deductive Database Proc. Of ATCM'99, 153-162, 1999, ATCM Inc., USA.
    1998
    X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, I. A Global Propagation Approach, Computer Aided Design, Vol. 30, No. 1, 47-54, 1998.
    X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, II. A Symbolic Computational Approach, Computer Aided Design, Vol. 30, No.2, 115-122, 1998.
    L. Yang, X.S. Gao, S. C. Chou, and Z. J. Zhang, Automated Proving and Discovering of Theorems in Non-Euclidean Geometries, in: Automated Deduction in Geometry, LNAI 1360, Springer-Verlag, Berlin Heidelberg, 1998, pp. 171--188.
    X.S. Gao, C. C. Zhu, and Y. Huang, Building Dynamic Mathematical Models with Geometry Expert, I. Geometric Transformations, Functions and Plane Curves, Proceedings of the Third Asian Technology Conference in Mathematics, eds W.C. Yang, pp. 216-224, Springer, 1998.
    X.S. Gao, C. C. Zhu, and Y. Huang, Building Dynamic Mathematical Models with Geometry Expert, II. Linkages, Proc. of the Third Asian Symposium on Computer Mathematics, eds Z. B. Li, pp. 15-22, LanZhou University Press, 1998.
    1996
    S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of of Readable Proofs with Geometric Invariants, I. Multiple and Shortest Proof Generation, J. of Automated Reasoning, 17, 325-347, 1996.
    S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of of Readable Proofs with Geometric Invariants, II. Proving Theorems with Full-Angles, J. of Automated Reasoning, 17, 349-370, 1996.
    S.C. Chou, X.S. Gao, and J.Z. Zhang, An Introduction to Geometry Expert, Proc. CADE-13, p. 235-239, 1996, L.N.A.I. No. 1104, (eds. M. A. McRobbie and J. K. Slaney), Springer-Verlag.
    1995
    S.C. Chou, X.S. Gao, J.Z. Zhang, Automated Production of Traditional Proofs in Solid Geometry, Journal of Automated Reasoning, 14, p.257-291, 1995.
    S.C. Chou, X.S. Gao, and J. Z. Zhang) ``Automated Production of Traditional Proofs for Theorems in Euclidean Geometry, Part I. The Hilbert Intersection Point Theorems'', Annals of Mathematics and Artificial Intelligence, 13, (1995), p.109-137.
    X.S. Gao and S.C. Chou, The Computer Searches for Pascal Conics, Journal of Computers and Mathematical Applications, Vol. 29, No. 2, pp. 63-71, 1995.
    X.S. Gao and D.K. Wang, On the Automatic Derivation of a Set of Geometric Formulae, Journal of Geometry, vol. 53, p.79-88, 1995.
    1994
    S.C. Chou, X.S. Gao, N.M. Mcphee, and S. C. Chou, ``Mechanically Proving Geometry Theorems Using a Combination of Wu's Method and Collins' Method'', in Proceedings of CADE-12, Nancy, France, June 1994, 222--236.
    1993
    X.S. Gao and S. C. Chou, A Zero Structure Theorem for Differential Parametric Systems, Journal of Symbolic Computation, Vol. 16, 585-595, 1993.
    X.S. Gao and S. C. Chou, The Dimension of Ascending Chains, Chinese Science Bulletin, Vol. 38, No.5, 1993, 396--399.
    S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part I. An Improved Version of Ritt--Wu's Decomposition Algorithm , Journal of Automated Reasoning, 10: 161--172, 1993.
    S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part II. Mechanical Theorem Proving, Journal of Automated Reasoning, 10: 173--189, 1993.
    S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part IV, Bertrand Curves , Journal of Sys. and Math., vol. 6, p.186-192, 1993.
    S.C. Chou, X.S. Gao, J.Z. Zhang, ``Automated Geometry Theorem Proving by Vector Calculation'', Proceedings of ISSAC-93, 284-291.
    S.C. Chou, X.S. Gao, J.Z. Zhang, Automated Production of Traditional Proofs for Theorems in Euclidean Geometry, Proc. of 8th IEEE Symposium on Logic in Computer Science (LICS), extended abstract, 1993, 48--56.
    1992
    S.C. Chou and X.S. Gao, Implicitization of Rational Parametric Equations, Journal of Symbolic Computation, 1992, 14, 459--470.
    S.C. Chou and X.S. Gao, On the Parameterization of Algebraic Curves, Journal of Applicable Algebra in Engineering, Communication and Computing, 3, 27--38 (1992).
    S.C. Chou and X.S. Gao, Proving Geometry Statements of Constructive Type, in Proceedings of CADE-11, Lecture Notes in Computer Science, Vol. 607, 20--34, Springer--Verlag, 1992.
    S.C. Chou, X.S. Gao, and D.S. Arnon, ``On the Mechanical Proof of Geometry Theorems Involving Inequalities'' Advances in Computing Research, 1992, Vol. 6, 139--181. An international journal.
    Transformation Theorems among Caley-Klein Geometries, J. of Sys. Sci. and Math. Sci., 1992, 3: 260--273.
    SC Chou and XS Gao, Automated Reasoning in Differential Geometry and Mechanics Using the Characteristic Set Method; Part III Mechanical Formula Derivation, in Proceedings of the IFIP International Workshop on Automated Reasoning, Elsevier Science Publishers (North--Holland), Beijing, p1--12, 1992.
    SC Chou and XS Gao, Solving Parametric Algebraic Systems, in the Proceedings of ISSAC'92 , Berkeley, 335--341, ACM Press, 1992.
    SC Chou and XS Gao, ``An Algebraic System Based on the Characteristic Set Method'', in Proceedings of International Workshop on Mathematics Mechanization, Beijing, International Academic Publishers, p.1--17, 1992.
    1991
    X.S. Gao and S.C. Chou, Computations with Parameter Equations, in Prof. ISSAC'91, Germany, ACM Press, 122--127, 1991.
    X.S. Gao and S.C. Chou, On the Normal Parameterization of Curves and Surfaces, The International Journal of Computational Geometry & Applications, Vol. 1, No. 2 (1991), 125--136. An international journal.
    X.S. Gao, The Discriminant Systems of Univariate Polynomials and Their Computations, Chinese Quarterly Journal of Mathematics, No2., p1-p11, 1991.
    X.S. Gao, Transcendental Functions and Mechanical Theorem Proving in Elementary Geometries, Journal of Automated Reasoning, 6:403-417, 1990, Kluwer Academic Publishers.
    Before 1990
    S.C. Chou and X.S. Gao, Methods for Mechanical Geometry Formula Deriving in Proceedings of ISSAC'90 , Japan, ACM Press, August 1990, 265--270.
    S.C. Chou and X.S. Gao, Ritt-Wu's Decomposition Algorithm and Geometry Theorem Proving in Proceedings of CADE--10, Lecture Notes in Artificial Intelligence 449, Springer--Verlag, 1990, 207--220.
    X.S. Gao, The Minimal Characteristic Basis of a Differential Polynomial Ideal, Chinese Science Bulletin, vol. 35, No. 6, 1990, 455-458.
    X.S. Gao, The Minimal Characteristic Basis of a Polynomial Ideal, J. Sys Sci \& Math Sci, No.2, 1989, 236-242.
    X.S. Gao, Trigonometric Identities and Mechanical Theorem Proving in Elementary Geometries, J. Sys. Sci. \& Math. Sci. No.3 1987.
    Collection of Geometric Problems
    S.C. Chou, X.S. Gao, and J.Z. Zhang, A Collection of 130 Geometric Constraint Problems and Their Solutions, WSUCS-96-2, CS Dept, Wichita State University, 1996.

Conference Abbreviation
ACM SM: ACM Symposium on Solid Modeling
ADG: Automated Dedecution in Geometry
ASCM: Asian Symposium on Computer Mathematics
ATCM: Asian Technology Conference on Mathematics
CADE: An International Conference on Automated Deduction
GMP: Geometric Modeling and Processing
ISSAC: International Symposium on Symbolic and Algebraic Computation
LICS: IEEE Symposium on Logic in Computer Science
SMI: International Conference on Shape Modelling


Research Interests and Activities
Research Interests

    Mathematics Mechanization
    Symbolic Computation
    Automated Reasoning
    Computational Algebraic Geometry
    Computational Differential Algebra
    Computed Numerically Controlled System
    Intelligent CAD and CAI

Research Projects

    National Key Basic Research Project (973 Project), "Methods of Mathematics Mechanization and Applications in Information Technology", 2004-2009, Leading Scientist.
    National Key Basic Research Project (973 Project), "Mathematics Mechanization and Platform of Automated Reasoning", 1999-2003, Leading Scientist.
    "Automated Geometry Reasoning and Methods of Diagram Generation", NSF, CCR-0201253, 2000-2003, CO-PI.
    Outstanding Young Scientist Award, The HongKang QiuShi Foundation, 1999-2002.
    Outstanding Young Investigator Award, National Natural Science Foundation of China, 1998-2001.

Journals Involved

    Journal of System Science and Complexity, managing editor.
    Journal of System Science and Mathematical Science, associate chief editor.
    Journal of Symbolic Computation, member of the editorial board.
    Journal of CAD and CG, member of the editorial board.
    Journal of Image and Graphics, member of the editorial board.
    Applied Mathematics, A Journal of Chinese Universities, member of the editorial board.

Book Series Involved

    Mathematics Mechanization, Science Press, associate chief editor.
    Geometry and Computation, Springer, editorial advisory board.
    Modern Applied Mathematics, Science Press, member of editorial board.

Conferences Involved

    Asian Symposium on Computer Mathematics (ASCM)
    PC Co-chair, ASCM 2000,
    PC Member, ASCM 1998, 2001, 2003, 2005, 2007, 2009
    International Workshop on Mathematics Mechanization (IWMM)
    The Chinese Conference on Computer Mathematics
    PC Chair, 2007; Conference Chair, 2008.
    International Symposium on Symbolic and Algebraic Computation (ISSAC),
    PC Member, ISSAC2003, ISSAC2008
    Conference Co-Chair, ISSAC2005
    Member of the ISSAC Steering Committee, 2006-2009; Chair 2008-2009
    ACM Symposium on Applied Computing (SAC)
    Geometric Computing and Reasoning (GCR), Technical Track of SAC2006
    Co-chair, GCR06; Co-chair, GCR07; Co-chair, GCR08; Co-chair, GCR09.
    Automated Deduction in Geometry (ADG)
    PC Co-chair, ADG'1998,
    PC Member, 2000, 2002, 2004, 2006, 2008, 2010
    Algebraic Geometry and Geometric Modeling
    Organizer, 2009
    Geometric Modeling and Processing (GMP)
    PC Member, GMP2002, GMP2004, GMP2006, GMP2010
    International Conference on Computer Aided Design and Computer Graphics
    PC Member, CADCG2005, CADCG2007, CADCG2009
    Geometric Design and Computing (GDC)
    PC Member, GDC2005, GDC2007, GDC2009
    International Conference on Computers, Communications and Control (ICCCC)
    PC Member, 2008
    International Conference on Computational Intelligence and Security (CIS)
    PC Member, 2007
    International Congress of Mathematical Software (ICMS)
    PC Co-chair, ICMS'2002,
    PC Member, ICMS'06, ICMS'10
    IASTED International Conference on Computer Graphics and Imaging (CGIM),
    PC Member: CGIM'04, CGIM'05, CGIM'07.
    Korea-China Joint Conference on Geometric and Visual Computing
    PC Member, KCJC 2005, KCJC 2006
    The Mathematics of Surfaces
    PC Member, 2007
    Korea-China Joint Conference on Geometric and Visual Computing
    PC Member, KCJC 2005, KCJC 2006
    Pacific Conference on Computer Graphics and Applications (PG)
    PC Member, PG02, PG03
    International Conference on Automated Deduction 2002 (CADE)
    PC Member, CADE'02

Bibliography
Automated Reasoning in Geometry

    Artificial Intelligence Approach
    Algebraic Method -- Coordinate Approach
    Algebraic Method -- Non-Coordinate Approach
    ATP in Differential Geometry and Mechanics

Geometric Constraint Solving and Parametric CAD

    General
    Graph Analisys Methods
    Rule-Based Methods
    Numerical Methods
    Symbolic Computation Methods

Differential Algebra and Differential Algebraic Geometry
More Links

    ACM SIGSAM
    ATCM
    ISSAC
    Sigsam
    Siggraph
    Euograph
    Solid Modeling
    Symbolic Net
    National Center for CAD
    J. of Automated Reasoning
    CAD
    CAGD
    Graphical Models
    ACM Transaction on Graphics IEEE Computer Graphics and Applications
    Computer & Graphics