Publications of Xiao-Shan Gao

    Preprints

    Publications by Topics

    Publications by Years

    Books

  1. 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.
  2. X.S. Gao, J. Z. Zhang, and S.C. Chou, Geometry Expert (in Chinese), Nine Chapters Pub., Taiwan, 1998.
  3. S.C. Chou, X.S. Gao, and J.Z. Zhang, Machine Proofs in Geometry, World Scientific, Singapore, 1994.

    Proceedings/Collection of Papers

  4. X.S. Gao and D. Micheluchi (eds), Geometric Constraints, IJCGA, 16, World Scientific, 2006.
  5. A. Cohen, X.S. Gao, N. Takayama (eds), Symbolic Computation in Algebra and Geometry, a special issue of Journal of Symbolic Computation, 38, 2004.
  6. A. Cohen, X.S. Gao, N. Takayama (eds), Mathematical Software, World Scientific Pub., Singapore, 2002.
  7. X.S. Gao and D. Wang (eds), Mathematics Mechanization and Applications, Academic Press, London, 2000.
  8. X.S. Gao and D. Wang (eds), Computer Mathematics-Proc. of ASCM'2000, World Scientific, Singapore, 2000.
  9. X.S. Gao, D. Wang and L. Yang (eds), Automated Deduction in Geometry, Procs. of ADG98 Springer, Berlin, 1999.

    Survey Papers

  10. W.T. Wu and X.S. Gao, Mathematics Mechanization and Applications After Thirty Years, Frontiers in Computer Science, 1(1), 1-8, 2007.
  11. X.S. Gao and K. Jiang, Survey on Geometric Constraint Solving (in Chinese), J. of CAD & CG, 16(4), 385-396, 2004.
  12. 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.
  13. X.S. Gao, Mathematics Mechanization: A Survey (In Chinese), Advances in Mathematics, 30(5), 385-404, 2001.
  14. X.S. Gao, Search Methods Revisited, in Mathematics Mechanization and Application, 253-272, Academic Press, 2000.
  15. X.S. Gao, Conversion between Implicit and Parametric Representations of Algebraic Varieties, in Mathematics Mechanization and Applications, 253-272, Academic Press, 2000.
  16. 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.
  17. 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

    2009

  18. 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.
  19. X.S. Gao, J. Van der Hoeven, C.M. Yuan, G.L. Zhang, Characteristic set method for differential¨Cdifference polynomial systems, Journal of Symbolic Computation, 44(9), 2009, 1137-1163.
  20. 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.
  21. 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.
  22. 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.
  23. M. Zhang and X.S. Gao, Decomposition of ordinary difference polynomials, Journal of Symbolic Computation}, 44, 1394-1409, 2009.
  24. 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.
  25. J.S. Cheng, X.S. Gao, J. Li, Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities, In {\em Computer Algebra in Scientific Computing}, LNCS 5743, 89-93, 2009.
  26. J.S. Cheng, X.S. Gao, J. Li, Topology determination and isolation for implicit plane curves. {\em Proc. ACM Symposium on Applied Computing}, 1140-1141, ACM Pres, 2009.

    2008

  27. 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.
  28. X.S. Gao and M. Zhang, Decomposition of Differential Polynomials, Applicable Algebra in Engineering, Communication and Computing, 19(1), 1-25, 2008.
  29. J. Li, L. Shen, X.S. Gao, Proper Reparametrization of Rational Ruled Surface, Journal of Computer Science and Technology, 23(2), 290-297, 2008.

    2007

  30. 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.
  31. 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.
  32. X. Zhao and X.S. Gao, Binary Affinity Genetic Algorithm£¬ Journal of Heuristics, 13, 133-150, 2007.
  33. 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

  34. 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.
  35. E.W. Chionh, X.S. Gao and L.Y. Shen, Inherently improper surface parametric supports, Computer Aided Geometric Design, 23, 629-639, 2006.
  36. 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.
  37. X.S. Gao and C. Yuan, Resolvent Systems of Difference Polynomial Ideals, Proc. ISSAC 2006, ACM Press, New York, 2006.
  38. 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.
  39. 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.
  40. 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.
  41. 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,.
  42. 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.
  43. 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

  44. 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.
  45. 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.
  46. R. Feng and X.S. Gao Polynomial general solutions of first order autonomous ODEs, in Computer Algebra and Geometric Algebra with Applications, H. Li, P. Olver, G . Sommer (eds.), LNCS 3519, 7-19, Springer Berlin Heidelberg, 2005.
  47. 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.
  48. 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.
  49. Y. Zhu and X.S. Gao, A New Algorithm to Compute the Adomian Polynomials (in Chinese), J. Sys. Sci. & Math. Sci., 25(1), 18-28, 2005.
  50. J.S. Cheng and X.S. Gao, Constructing Bledning Surface for Two Arbitrary Surfaces (in Chinese), Journal of Engineering Graphics, 26(1), 39-44, 2005.
  51. S.C. Chou, X.S. Gao, and Z. Ye, Java Geometry Expert, to appear in, Proc. ATCM 2005, 2005.

    2004

  52. X.S. Gao and M. Li, Rational Quadratic Approximation to Real Algebraic Curves, Computer Aided Geometric Design, 21, 805-828, 2004.
  53. 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.
  54. 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.
  55. J. Wang and X.S. Gao, An Algorithm for Solving Partial Differential Parametric Systems, Discrete Applied Mathematics. 136(1), 105-116, 2004.
  56. R. Feng and X.S. Gao, Rational General Solutions of Algebraic Ordinary Differential Equations, Proc. ISSAC2004, 155-162, ACM Press, New York, 2004.
  57. X.S. Gao and M. Zhang, Decomposition of Differential Polynomials with Constant Coefficients, Proc. ISSAC2004, 175-182, ACM Press, New York, 2004.
  58. X.M. Wang and X.S. Gao, An Improved Bareiss Algorithm of Solving Linear Equations Symbolically (in Chinese), Systems Engineering: Theory and Practice, 24, 98-104, 2004.
  59. F. Xie and X.S. Gao, Exact travelling wave solutions for a class of nonlinear partial differential equations, Chaos, Solitons and Fractals 19 (2004) 1113-1117.
  60. F. Xie and X.S. Gao, A Computational Approach to the New Type Solutions of Whitham Broer Kaup Equation in Shallow Water, Commun. Theor. Phys. 41 (2004)179-182.
  61. F. Xie and X.S. Gao, Applications of Computer Algebra in Solving Nonlinear Evolution Equations, Commun. Theor. Phys. 41 (2004) 353-356.
  62. F. Xie and X.S. Gao, Conservation Laws of K(m, n) and mK(m, n) Equations, Commun. Theor. Phys. 42 (2004) 661-663.

    2003

  63. X.S. Gao, Implicitization for Differential Rational Parametric Equations, J. of Symbolic Computation, 811-824, 36(5), 2003..
  64. 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
  65. Y. Chen and X.S. Gao, Involutive Bases of Algebraic Partial Differential Equation Systems, Science in China (A), 33(2), 97-113, 2003.
  66. 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.
  67. 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.
  68. X.S. Gao, G. Zhang and W. Yang, Geometric Constraint Solving and Simulation of Complex Linkages, (in Chinese), J. of CAD and CG, 517--522, 15(5), 2003.

    2002

  69. X.S. Gao, K. Jiang, and C.-C. Zhu, Geometric Constraint Solving with Conics and Linkages, Computer Aided Design, 34(6), 421-433, 2002.
  70. 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.
  71. T. Chaolu and X.S. Gao, Nearly Differential Characteristic Set for Differential Polynomial System, Acta Mathematica Sinica, 45(6), 1041-1050, 2002.
  72. X.S. Gao and T. Xu, Luroth's Theorem in Differential Fields, J. Sys. Sci. and Complexity, 15(4), 376-383, 2002.
  73. X.S. Gao and M. Li, Solving Piecewise Hermite Interpolation Problem with Blending Methods, Proc. Geometric Modeling and Processing, H. Suzuki and R. Martin (eds), 53-59, IEEE Press, Los Alamitos, 2002.
  74. 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.
  75. K. Jiang and X.S. Gao, 3D Geometric Constraint Solving with Conicoid, Journal of Software, 13(4), 482-489, 2002.
  76. X.S. Gao, W. Yang and G. Zhang, Simulation of Complex Linkages (in Chinese), Geometric Design and Computing, 208-215, Chinese Petrolium University Press, ShanDong, 2002.

    2001

  77. Y.F. Chen and X.S. Gao, Involutive Directions and New Involutive Divisions, Computers and Mathematics with Applications, 41(7-8), 2001, 945-956.
  78. X.S. Gao, L. Huang, and K, Jiang, Geometric Constraint Solving with Geometric Transformation, Science in China (Series F), 44(1), 50-59, 2001.
  79. X.S. Gao and H. Chen, New Algorithms for the Perspective-Three-Point Problem, J. of Computer Science and Technology, 16(3), 194--207, 2001.
  80. X.S. Gao and K. Jiang, Geometric Constraint Solving with Conics (in Chinese), Chinese J. of Image and Graphics, 563-567, 2001.
  81. 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.
  82. Y. Ma and X.S. Gao, Polynomial Solutions of Algebraic Differential Equations, in Computer Mathematics, Proc. of ASCM 2001, (eds. K. Shirayanagi and K. Yokoyama), 92-101, World Scientific, Singapore, 2001.
  83. K. Jiang and X.S. Gao, 3D Geometric Constraint Solving with Conicoid, Proc. Inter. Conf. On CAD/CG'01, 25-32, Kunming, 2001.
  84. X.S. Gao, D, Lin, and H. Shi, Mathematics Mechenizatio and Mechenized Mathematics, in Modern Mathematics Handbook- Computer Mathemtaics, ed. L. Xu, 727-778, Univ. of HuaZhong Sci. and Tech., WuHan, China, 2001.

    2000

  85. J. Ge, S.C. Chou and X.S. Gao, Geometric Constraint Satisfaction Using Optimization Methods, Computer Aided Design, 31(14), 867-879, 2000.
  86. 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.
  87. X.S. Gao and C. Zhu, Geometric Constraint Solving with Linkages, Journal of Software, 11(9), 1151-1158, 2000.
  88. X.S. Gao and K. Jiang, Order in Solving Polynomial Equations, Computer Mathematics, Proc. of ASCM'2000, pp. 308-318, World Scientific, 2000.
  89. X.S. Gao, W.Q. Yang, and L. Huang, Intelligent Dynamic Geometry, Proc. ATCM'2000, ATCM Inc, Thailand, pp.162-171.

    1999

  90. 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,
  91. X.S. Gao and C. Zhu, Automated Generation of Kempe Linkage and Its Complexity, J. of Computer Science and Technology, 14, 460-467, 1999.
  92. X.S. Gao, Automated Geometry Diagram Construction and Engineering Geometry, in Automated Deduction in Geometry, Procs. of ADG98, pp. 226-252, Springer, 1999.
  93. 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.
  94. X.S. Gao and K, Jiang, Geometric Constraint Solving with Conics, Proc. Of Six Inter. Conf. On CAD/CG'99, pp.101-106, 1999, ShangHai WenHui Pub.

    1998

  95. X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, I. A Global Propagation Approach, Computer Aideded Design, Vol. 30, No. 1, 47-54, Elsevier Sci Ltd., 1998.
  96. 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, Elsevier Sci Ltd., 1998.
  97. 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\/ (D.\ Wang, ed.), LNAI 1360, Springer-Verlag, Berlin Heidelberg, 1998, pp. 171--188.
  98. 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.
  99. 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.
  100. X.S. Gao and H. F. Cheng, On the Solution Classification of the ``P3P'' Problem, Proceedings of the Third Asian Symposium on Computer Mathematics, eds Z. B. Li, pp. 185-200, LanZhou University Press, 1998.
  101. X. Gao and D. Lin, Wu's method and its applications, in Mathematical Modeling for University Students, (Ed. Ye Qixiao), (in Chinese), 39-85 (1998).

    1996

  102. 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. (Mathematics Review 97j:03025a)
  103. 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. (Mathematics Review 97j:03025b)
  104. J. Z. Zhang, X.S. Gao and S. C. Chou, A Geometry Information Search System by Forwad Reasoning, Chinese J. of Computers, 19(10), 722-727, 1996.
  105. 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.
  106. S.C. Chou, X.S. Gao, and J.Z. Zhang, Recent Advances of Automated Geometry Theorem Proving with High Level Geometry Invariants, Proc. of Asian Symposium on Computer Mathematcis, Kobe, Janpan, 1996, p.173--186.
  107. S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Solution of Two-Dimensional Geometric Constraint Problems, Proc. of Asian Symposium on Computer Mathematcis, Kobe, Janpan, 1996, p.153-164.

    1995

  108. 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.
  109. 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.
  110. 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.
  111. 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.
  112. J.Z. Zhang, L. Yang, S.C. Chou, X.S. Gao, Automated Production of Readable Proofs for Geometry Theorems, Chinese J. of Computers , 18(5), 380-393, 1995.
  113. S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Geometry Theorem Proving and Geometry Education, Proc. of First Asia Technology Conference in Math., p.319-328, Singapore, 1995.
  114. S. C. Chou, X.S. Gao, and J. Z. Zhang, A Geometry Information Search System by Forward Reasoning, in Logic and Software Engineering, Eds. A. Pnueli and H. Lin, World Scientific, Singapore, 1995.

    1994

  115. 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.
  116. X.S. Gao, Mechanical Theorem Proving in Riemann Geometry, Computer Mathematics, p.136-157, World Scientific Pub., River Edg. NJ, 1994.
  117. S.C. Chou, X.S. Gao, Z Li, Computations with Rational Parametric Equations, Computer Mathematics, p.86-111, World Scientific Pub., River Edg. NJ, 1994.

    1993

  118. X.S. Gao and S. C. Chou, A Zero Structure Theorem for Differential Parametric Systems, Journal of Symbolic Computation, Vol. 16, 585-595, 1993.
  119. X.S. Gao and S. C. Chou, The Dimension of Ascending Chains, Chinese Science Bulletin, Vol. 38, No.5, 1993, 396--399.
  120. 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.
  121. 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.
  122. 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.
  123. S.C. Chou, X.S. Gao, J.Z. Zhang, ``Automated Geometry Theorem Proving by Vector Calculation'', Proceedings of ISSAC-93, 284-291.
  124. An Introduction to Wu's Method of Mechanical Geometry Theorem Proving, IFIP Transaction on , Automated Reasoning, p.13--21, North-Holland,1993.
  125. 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

  126. S.C. Chou and X.S. Gao, Implicitization of Rational Parametric Equations, Journal of Symbolic Computation, 1992, 14, 459--470.
  127. 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).
  128. 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.
  129. 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.
  130. Transformation Theorems among Caley-Klein Geometries, J. of Sys. Sci. and Math. Sci., 1992, 3: 260--273.
  131. 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.
  132. SC Chou and XS Gao, Solving Parametric Algebraic Systems, in the Proceedings of ISSAC'92 , Berkeley, 335--341, ACM Press, 1992.
  133. 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.
  134. X.S. gao, Y. Li, D.D. Lin, & X.S. Liu, A Prover Based on Wu's Method, Proc. of International Workshop on Mathematics Mechanization, Beijing, International Academic Publishers, p.201--205, 1992.

    1991

  135. X.S. Gao and S.C. Chou, Computations with Parameter Equations, in Prof. ISSAC'91, Germany, ACM Press, 122--127, 1991.
  136. 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.
  137. X.S. Gao, The Discriminant Systems of Univariate Polynomials and Their Computations, Chinese Quarterly Journal of Mathematics, No2., p1-p11, 1991.
  138. 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

  139. 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.
  140. 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.
  141. X.S. Gao, The Minimal Characteristic Basis of a Differential Polynomial Ideal, Chinese Science Bulletin, vol. 35, No. 6, 1990, 455-458.
  142. X.S. Gao, The Minimal Characteristic Basis of a Polynomial Ideal, J. Sys Sci \& Math Sci, No.2, 1989, 236-242.
  143. Trigonometric Identities and Mechanical Theorem Proving in Elementary Geometries, J. Sys. Sci. \& Math. Sci. No.3 1987.

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

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