Publications of XiaoShan Gao
Publications by Topics
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 and D. Kapur (eds),
Advances in Mathematics MechanizationMathematics Mechanization,
JSC, 47(6), 2012.
 X.S. Gao, C. Hoffmann, R. JoanArinyo (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 MathematicsProc. 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), 189196, 2012.

W.T. Wu and X.S. Gao,
Mathematics Mechanization and Applications After Thirty Years,
Frontiers in Computer Science, 1(1), 18, 2007.

X.S. Gao and K. Jiang,
Survey on Geometric Constraint Solving
(in Chinese), J. of CAD & CG, 16(4), 385396, 2004.

S.C. Chou and X.S. Gao,
Automated reasoning in geometry,
Handbook of Automated Reasoning,
(eds. A. Robinson and A. Voronkov), 709749, Elsevier, Amsterdam, 2001.

X.S. Gao,
Mathematics Mechanization: A Survey (In Chinese),
Advances in Mathematics, 30(5), 385404, 2001.

X.S. Gao,
Search Methods Revisited,
in Mathematics Mechanization and Application,
253272, Academic Press, 2000.

X.S. Gao,
Conversion between Implicit and Parametric Representations
of Algebraic Varieties,
in Mathematics Mechanization and Applications,
253272, 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,
491506, 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. 97120, Birkhauser, 1996.
Research Papers
2017
 X.S. Gao, Z. Huang, C.M. Yuan.
Binomial difference ideals.
Journal of Symbolic Computation,
80(3), 665706, 2017.

X.S. Gao, Z. Huang, J. Wang, C.M. Yuan.
Toric Difference Variety,
J. Syst. Sci. Complex., 30(1), 173195, 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), 464483, 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,
http://dx.doi.org/10.1016/j.cirp.2017.04.058.
 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), 941956, 2017
 M.Y. Zhao and X.S. Gao.
An Efficient Stochastic Approach for Robust TimeOptimal Trajectory
Planning of Robotic Manipulators Under Limited Actuation,
accepted by Robotica, 2017.
2016
 Q. Zhang, S. Li, J.X. Guo, X.S. Gao.
Timeoptimal path tracking for robots under dynamics constraints based on convex optimization.,
Robotica, 34(9), 2116¨C2139, 2016.
2015
 W. Li, C.M. Yuan, X.S. Gao,
Sparse Differential Resultant for Laurent Differential Polynomials,
Foundations of Computational Mathematics,
15(2), 451517, 2015.
 W. Li, C.M. Yuan, X.S. Gao,
Sparse Difference Resultant,
Journal of Symbolic Computation,
68, 169203, 2015.
2014
 J.S. Cheng and X.S. Gao,
Multiplicitypreserving 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, 479503, 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), 45754632, 2013.
 W. Li, C.M. Yuan, X.S. Gao,
Sparse Difference Resultant, Proc. ISSAC 2013, 275282, 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 Highorder CNC Servo System.
ComputerAided Design, 45(12), 15381546, 2013.
 K. Zhang, C.M. Yuan, X.S. Gao.
Efficient algorithm for timeoptimal feedrate planning and smoothing with confined chord error and acceleration.
Int J Adv Manuf Technol. 66(9), 16851697, 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), 11411146, 2013.
2012
 J.S. Cheng£¬X.S. Gao£¬L. Guo,
Root Isolation of Zerodimensional Polynomial Systems
with Linear Univariate Representation.,
Journal of Symbolic Computation, 47 (2012) 843858.
 X.S. Gao and Z. Huang,
Characteristic Set Algorithms for Equation
Solving in Finite Fields,
Journal of Symbolic Computation, 47 (2012) 655¨C679.
 W. Li and X.S. Gao,
Chow form for projective differential variety,
Journal of Algebra, 370(2012) 344360.
 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), 329347, 2012.
 Zhang K., Gao X.S., Li H.B., Yuan C.M.
A greedy algorithm for feedrate planning of CNC machines
along curved tool paths with confined jerk for each axis.,
Robotics and Computer Integrated Manufacturing}, 28 (2012) 472483.
 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, 719739, 2012.
2011
 W. Li, X.S. Gao, C.M. Yuan,
Sparse Differential Resultant,
Proc. ISSAC 2011, 225232, ACM Press, New York, 2011. (ISSAC Distinguished Paper Award)
 M. Zhang, W. Yan, C.M. Yuan, D. Wang, X.S. Gao,
Curve fitting and timeoptimal interpolation on CNC machines,
Science China, Series E}, 54(7): 14071418, 2011.
 L.X. Zhang, R.Y. Sun, X.S. Gao, H. Li,
High speed interpolation for microline trajectory and adaptive realtime lookahead in CNC machining, Science China, Information Sciences, 54(6), 14811495, 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), 367380, 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, 213241, 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 FullAngle Method and the Deductive Database
Method, Journal of Automated Reasoning, 45, 213241, 2010.
2009
 X.S. Gao, Y. Luo, and C. Yuan,
A Characteristic Set Method for
Difference Polynomial Systems, Journal of Symbolic Computation,
44(3), 242260, 2009.
 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, 11371163.
 X.S. Gao, C. Yuan, and G. Zhang,
RittWu's Characteristic Set Method
for Ordinary Difference Polynomial Systems with Arbitrary Ordering,
Acta Mathematica Scientia, 29(3,4), 10631080, 2009.
 J.S. Cheng, X.S. Gao, and C.K. Yap,
Complete Numerical Isolation of Real Roots in Zerodimensional
Triangular Systems,
Journal of Symbolic Computation£¬ 44(7)£¬ 768785, 2009.
 S.W. Zhao and X.S. Gao,
Minimal Achievable Approximation Ratio for MAXMQ in Finite Fields,
Theoretical Computer Science, 410(2123), 22852290, 2009.
 M. Zhang and X.S. Gao,
Decomposition of ordinary difference polynomials,
Journal of Symbolic Computation}, 44, 13941409, 2009.
 J.S. Cheng, X.S. Gao, J. Li,
Root Isolation for Bivariate Polynomial Systems with Local Generic Position ,
Proc. ISSAC 2009, 103109, ACM Press, New York, 2009.
 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, 8993, 2009.
 J.S. Cheng, X.S. Gao, J. Li,
Topology determination and isolation for implicit plane curves.
Proc. ACM Symposium on Applied Computing, 11401141, 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), 191208, 2008.

X.S. Gao and M. Zhang,
Decomposition of Differential Polynomials,
Applicable Algebra in Engineering, Communication and Computing, 19(1), 125,
2008.

J. Li, L. Shen, X.S. Gao,
Proper Reparametrization of Rational Ruled
Surface, Journal of Computer Science and Technology, 23(2), 290297, 2008.

G.L. Zhang and X.S. Gao,
Properties of Ascending Chians fr Partial Difference Polynomial
Systems, ASCM2007, LNAI 5081, 307321, SpringerVerlag, Berlin
Heidelberg, 2008.
2007

X.S. Gao, J. van der Hoeven, C. Yuan, and G. Zhang,
Characteristic Set Method for DifferentialDifference 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, 9299, ACM Press, New York, 2007.

X. Zhao and X.S. Gao,
Binary Affinity Genetic Algorithm£¬
Journal of Heuristics, 13, 133150, 2007.

X. Zhao, X.S. Gao, and Z. Hu,
Evolutionary Programming Based on
Nonuniform Mutation£¬Applied Mathematics and Computation,
192(1), 111, 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), 739762, 2006.

E.W. Chionh, X.S. Gao and L.Y. Shen,
Inherently improper surface parametric supports,
Computer Aided Geometric Design, 23, 629639, 2006.
 X.S. Gao, Q. Lin, and G. Zhang,
A Ctree Decomposition Algorithm
for 2D and 3D Geometric Constraint Solving,
ComputerAided Design, 38(1), 113, 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, 7986, 2006.

M. Li, X.S. Gao, and S.C. Chou,
Quadratic Approximation to Plane
Parametric Curves and Applications in Approximate Implicitization,
Visual Computers, 22, 906917, 2006.

G.F. Zhang and X.S. Gao,
Wellconstrained Completion and
Decomposition for Underconstrained Geometric Constraint Problems,
16, International Journal of Computational Geometry & Applications, 461478, 2006.
 G.F. Zhang and X.S. Gao,
Planar Generalized StewartGough Platforms
and their Direct Kinematics, ADG 2004, LNAI 3763, 198211,
SpringerVerlag, Berlin, 2006,.

G.F. Zhang and X.S. Gao,
Spatial Geometric Constraint Solving Based
on kconnected Graph Decomposition, 973977, 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, 331339, 2006.
2005
 X.S. Gao, D. Lei, Q. Liao, and G. Zhang,
Generalized Stewart Platforms and their Direct Kinematics,
IEEE Trans. Robotics, vol 21, 141151, 2005.
 J.M. Aroca, J.Cano R. Feng and X.S. Gao,
Algebraic general
solutions of algebraic ODEs, Proc. ISSAC2005, 2936£¬ACM Press, New York,
2005.
 J.S. Cheng, X.S. Gao, and M. Li,
Determine the Topology of Real Algebraic Surfaces,
Mathematics of Surfaces, 121146, LNCS, SpringerVerlag, 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, 861874 2005.
2004

X.S. Gao, C.M. Hoffmann and W. Yang,
Solving spatial basic geometric constraint configurations with locus intersection,
Computer Aided Design, 111122, 36(2), 2004.

X.S. Gao and M. Li,
Rational Quadratic Approximation to Real Algebraic Curves,
Computer Aided Geometric Design, 21, 805828, 2004.

X.S. Gao and Q. Lin,
MMP/Geometer  A Software Package for Automated Geometry Reasoning,
Automated Deduction in Geometry, (ed. F. Winkler), 4466, Springer, Berlin, 2004.

J. Wang and X.S. Gao,
An Algorithm for Solving Partial Differential Parametric Systems,
Discrete Applied Mathematics. 136(1), 105116, 2004.

R. Feng and X.S. Gao,
Rational General Solutions of Algebraic
Ordinary Differential Equations, Proc. ISSAC2004, 155162,
ACM Press, New York, 2004.

X.S. Gao and M. Zhang,
Decomposition of Differential Polynomials with Constant Coefficients,
Proc. ISSAC2004, 175182, 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) 353356.
2003

X.S. Gao,
Implicitization for Differential Rational Parametric Equations,
J. of Symbolic Computation, 811824, 36(5), 2003..

X.S. Gao, X. Hou, J. Tang and H. Chen,
Complete Solution Classification for the PerspectiveThreePoint Problem,
IEEE Tran. on PAMI, 930943, 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), 97113, 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), 130145,
World Scientific, Singapore, 2003.

X.S. Gao and G. Zhang,
Geometric Constraint Solving via Ctree Decomposition,
(Appendix)
ACM Solid Modelling 2003, 4555, 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), 421433, 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), 10191033, 2002.

T. Chaolu and X.S. Gao,
Nearly Differential Characteristic Set for Differential Polynomial System,
Acta Mathematica Sinica, 45(6), 10411050, 2002.

X.S. Gao and T. Xu,
Luroth's Theorem in Differential Fields,
J. Sys. Sci. and Complexity, 15(4), 376383, 2002.

X.S. Gao, C.M. Hoffmann and W. Yang,
Solving Basic Gometric Constraint Configurations with Locus Intersection,
Proc. ACM Solid Modelling 2002, 95104, 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(78), 2001, 945956.

X.S. Gao, L. Huang, and K, Jiang,
Geometric Constraint Solving with Geometric Transformation,
Science in China (Series F), 44(1), 5059, 2001.

X.S. Gao, L. Huang, and K, Jiang,
A Hybrid Method for Solving Geometric Constraint Problems
in Automated Deduction in Geometry,
J. RichterGebert and D. Wang (eds), 1625,
LNAI No. 2061, SpringerVerlag, Berlin, 2001.
2000

J. Ge, S.C. Chou and X.S. Gao,
Geometric Constraint Satisfaction Using Optimization Methods,
Computer Aided Design, 31(14), 867879, 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), 219246, 2000.

X.S. Gao and K. Jiang,
Order in Solving Polynomial Equations,
Computer Mathematics, Proc. of ASCM'2000,
pp. 308318, World Scientific, 2000.

X.S. Gao, W.Q. Yang, and L. Huang,
Intelligent Dynamic Geometry,
Proc. ATCM'2000, ATCM Inc, Thailand, pp.162171.
1999

X.S. Gao and S. C. Chou,
On the Theory of Resolvents and Its Applications,
Sys. Sci. and Math. Sci., 12, Suppl., 1730, 1999,

X.S. Gao,
Automated Geometry Diagram Construction and Engineering Geometry,
in Automated Deduction in Geometry, Proc. of ADG98,
pp. 226252, Springer, 1999.

X.S. Gao,
Building Dynamic Mathematical Models with Geometry Expert,
III. A Geometry Deductive Database
Proc. Of ATCM'99, 153162, 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, 4754, 1998.

X.S. Gao and S. C. Chou,
Solving Geometric Constraint Systems,
II. A Symbolic Computational Approach,
Computer Aided Design,
Vol. 30, No.2, 115122, 1998.

L. Yang, X.S. Gao, S. C. Chou, and Z. J. Zhang,
Automated Proving and Discovering of Theorems in NonEuclidean
Geometries, in: Automated Deduction in Geometry,
LNAI 1360, SpringerVerlag, Berlin Heidelberg, 1998,
pp. 171188.

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. 216224, 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. 1522, 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, 325347, 1996.

S.C. Chou, X.S. Gao, and J.Z. Zhang,
Automated Generation of of Readable Proofs with Geometric Invariants,
II. Proving Theorems with FullAngles,
J. of Automated Reasoning, 17, 349370, 1996.

S.C. Chou, X.S. Gao, and J.Z. Zhang,
An Introduction to Geometry Expert,
Proc. CADE13, p. 235239, 1996, L.N.A.I. No. 1104,
(eds. M. A. McRobbie and J. K. Slaney), SpringerVerlag.
1995

S.C. Chou, X.S. Gao, J.Z. Zhang,
Automated Production of Traditional Proofs in Solid Geometry,
Journal of Automated Reasoning,
14, p.257291, 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.109137.

X.S. Gao and S.C. Chou, The Computer Searches for Pascal Conics, Journal of
Computers and Mathematical Applications, Vol. 29, No. 2, pp. 6371,
1995.
 X.S. Gao and D.K. Wang,
On the Automatic Derivation of a Set of Geometric Formulae,
Journal of Geometry, vol. 53, p.7988, 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 CADE12, Nancy, France, June 1994, 222236.
1993

X.S. Gao and S. C. Chou,
A Zero Structure Theorem for Differential Parametric Systems,
Journal of Symbolic Computation, Vol. 16, 585595, 1993.

X.S. Gao and S. C. Chou,
The Dimension of Ascending Chains,
Chinese Science Bulletin, Vol. 38, No.5, 1993, 396399.

S. C. Chou and X.S. Gao,
Automated Reasoning in Differential Geometry and Mechanics: Part I.
An Improved Version of RittWu's Decomposition Algorithm
,
Journal of Automated Reasoning, 10: 161172, 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: 173189, 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.186192, 1993.

S.C. Chou, X.S. Gao, J.Z. Zhang,
``Automated Geometry Theorem Proving
by Vector Calculation'', Proceedings of ISSAC93, 284291.

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, 4856.
1992

S.C. Chou and X.S. Gao,
Implicitization of Rational Parametric Equations,
Journal of Symbolic Computation, 1992, 14, 459470.

S.C. Chou and X.S. Gao,
On the Parameterization of Algebraic Curves,
Journal of Applicable Algebra in Engineering,
Communication and Computing, 3, 2738 (1992).

S.C. Chou and X.S. Gao,
Proving Geometry Statements of Constructive Type,
in Proceedings of CADE11, Lecture Notes in Computer
Science, Vol. 607, 2034, SpringerVerlag, 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, 139181.
An international journal.

Transformation Theorems among CaleyKlein Geometries,
J. of Sys. Sci. and Math. Sci., 1992, 3: 260273.

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 (NorthHolland),
Beijing, p112, 1992.

SC Chou and XS Gao,
Solving Parametric Algebraic Systems, in
the Proceedings of ISSAC'92 , Berkeley, 335341, 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.117, 1992.
1991

X.S. Gao and S.C. Chou,
Computations with Parameter Equations,
in Prof. ISSAC'91, Germany, ACM Press, 122127, 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), 125136.
An international journal.

X.S. Gao, The Discriminant Systems of Univariate Polynomials and Their Computations,
Chinese Quarterly Journal of Mathematics, No2., p1p11, 1991.

X.S. Gao, Transcendental Functions and Mechanical
Theorem Proving in Elementary Geometries,
Journal of Automated Reasoning, 6:403417, 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, 265270.

S.C. Chou and X.S. Gao,
RittWu's Decomposition Algorithm and Geometry
Theorem Proving in Proceedings of CADE10, Lecture Notes
in Artificial Intelligence 449, SpringerVerlag, 1990, 207220.

X.S. Gao,
The Minimal Characteristic Basis of a Differential Polynomial Ideal,
Chinese Science Bulletin, vol. 35, No. 6, 1990, 455458.

X.S. Gao,
The Minimal Characteristic Basis of a Polynomial Ideal,
J. Sys Sci \& Math Sci, No.2, 1989, 236242.

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,
WSUCS962, 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
Page Maintained by xgao@mmrc.iss.ac.cn