Constructive Differential Algebraic Geometry

Differential Chow Form and Differential Resultant

• X.S. Gao, W. Li, C.M. Yuan, Intersection Theory of Generic Differential Polynomials and Differential Chow Form. , {\em Arxiv preprint}, arXiv:1009.0148, 1-50, 2010..
• W. Li, X.S. Gao, C.M. Yuan, Sparse Differential Resultant, MM-Preprints, Vol.30, 1-19, 2011.

Closed-form Solutions of Differential Equations

• 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.
• 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.
• 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.
• R. Feng and X.S. Gao, Rational General Solutions of Algebraic Ordinary Differential Equations, Proc. ISSAC2004, 155-162, ACM Press, New York, 2004.

Decomposition of Differential and Difference Polynomials

• M. Zhang and X.S. Gao, Decomposition of ordinary difference polynomials, Journal of Symbolic Computation}, 44, 1394-1409, 2009.
• X.S. Gao and M. Zhang, Decomposition of Differential Polynomials, Applicable Algebra in Engineering, Communication and Computing, 19(1), 1-25, 2008.
• X.S. Gao and M. Zhang, Decomposition of Differential Polynomials with Constant Coefficients, Proc. ISSAC2004, 175-182, ACM Press, New York, 2004.

Characteristic Set Method: Differential Case

• X.S. Gao and S. C. Chou, A Zero Structure Theorem for Differential Parametric Systems, Journal of Symbolic Computation, Vol. 16, 585-595, 1993.
• 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.
• X.S. Gao, Implicitization for Differential Rational Parametric Equations, J. of Symbolic Computation, 811-824, 36(5), 2003..
• Y. Chen and X.S. Gao, Involutive Bases of Algebraic Partial Differential Equation Systems, Science in China (A), 33(2), 97-113, 2003.
• T. Chaolu and X.S. Gao, Nearly Differential Characteristic Set for Differential Polynomial System, Acta Mathematica Sinica, 45(6), 1041-1050, 2002.

Characteristic Set Method: Difference Case

• 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¨Cdifference 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.
• X.S. Gao and C. Yuan, Resolvent Systems of Difference Polynomial Ideals, Proc. ISSAC 2006, ACM Press, New York, 2006.

Automated Geometry Reasoning: Differential Geometry

• 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.
• 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.
• 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.