Dingkang Wang  (中文版)
Key Lab of Mathematics Mechanization
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Address:  No.55 Zhongguancun East Road, 100190, Beijing
Email:  dwang(at)mmrc.iss.ac.cn


Research Interests: Computer Algebra, Mechanical Proving of Geometric Theorem, (Parametric) Groebner Basis
Selected Publications

Software
Education

    1990.9–1993.7,  Ph.D.,  Mathematics,  Institute of Systems Science, Chinese Academy of Sciences (CAS)

    Supervisor:  Wentsun Wu

    Dissertation:  Polynomial Equations Solving and Geometric Theorem Proving
    1987.9–1990.7,  M.Sci.,  Institute of Systems Science,   CAS
    1983.9–1987.7,  B.Sci.,  Department of Mathematics,  Peking University

Academic Experience

    2012.3–present,  Professor,  Academy of Mathematics and Systems Science, CAS
    1997.3–2012.3,  Associate Professor,  Academy of Mathematics and Systems Science, CAS
    1993.9–1997.3,  Assistant Professor,  Institute of Systems Science, CAS

简历

 

        I. 工作经历

        

        2012.3 - 现在：研究员 中国科学院数学与系统科学研究院

        

        1997.3-2012.3: 副研究员 中国科学院系统科学研究所

        

        1993.7-1997.3：助理研究员 中国科学院系统科学研究所

        

        II. 教育

        

            1993.7 理学博士

                1990.9-1993.7: 中国科学院系统科学研究所

                

            1990.7 理学硕士

                1987.9-1990.7: 中国科学院系统科学研究所

                

            1987.7 理学学士

                1983.9-1987.7 北京大学数学系计算数学专业

        

        



        I. 研究方向

        

        计算机代数

        几何定理自动证明

        符号计算的算法和软件

        

        II. 研究内容

        

        签名的Groenber基的相关算法

        参数Groenber基的计算

        几何定理自动证明的理论与算法

        矩阵分解（元素为多变元多项式)

        

论文与论著

 

        论著
        高小山，王定康，裘衷燕， 杨宏：方程求解与机器证明－基于MMP的问题求解. 科学出版社，2006
        S.C. Chou, X.S. Gao, Z.J. Liu, D.K. Wang, D.M. Wang, Chapter 20, Geometric Theorem Provers and Algebraic Equation Solvers ( Mathematics Mechanization and Applications ) 491-506. Academic Press, 2000.

        研究论文

    2019
    Dong Lu, Dingkang Wang and Fanghui Xiao: Factorizations for a Class of Multivariate Polynomial Matrices, Accepted by Multidimensional Systems and Signal Processing. 2019
    Banghe Li, Dingkang Wang: Hilbert problem 15 and Ritt-Wu method (II). Accepted by Journal of Systems Science and Complexity.
    Deepak Kapur, Dong Lu, Michael Monagan, Yao Sun and Dingkang Wang: Algorithms for Computing Greatest Common Divisors of Parametric Multivariate Polynomials. Accepted by Journal of Symbolic Computation. 2019
    Jian Bai, Yao Sun, Ting Li, Dingkang Wang: Applying Horner's Rule to Optimize Lightweight MDS Matrices. International Journal of Digital Crime and Forensics, 2019 Vol. 11 (4): 82-96. [PDF ]
    Ting Li, Yao Sun, Zhenyu Huang, Dingkang Wang, Dongdai Lin: Speeding Up the GVW Algorithm via a Substituting Method. Journal of Systems Science and Complexity, 2019 Vol. 32 (1): 205-233 [PDF]
    Dong Lu, Yao Sun, Dingkang Wang: A Survey on Algorithms for Computing Comprehensive Groebner Systems and Comprehensive Groebner Bases. Journal of Systems Science and Complexity, 2019 Vol. 32 (1): 234-255 [PDF]
    2018
    Jian Bai, Yao Sun, Dingkang Wang: On the Construction of Involutory MDS Matrics over F_{2^m}. Accepted by Journal of Systems Science and Complexity.
    Dong Lu, Dingkang Wang, Fanghui Xiao and Jie Zhou. Extending the GVW Algorithm to Local Ring, in Proceedings of ISSAC 2018, 271-278, July 16-19, New York, USA [PDF]
    Deepak Kapur, Dong Lu, Michael Monagan, Yao Sun and Dingkang Wang. An Efficient Algorithm for Computing Parametric Multivariate Polynomial GCD, in Proceedings of ISSAC 2018, 239-246, July 16-19, New York, USA [PDF]
    Ting Li, Yao Sun, Maodong Liao, Dingkang Wang: Preimage Attacks on the Round-reduced KECCAK with Cross-linear Structures, FSE 2018, IACR Transactions on Symmetric Cryptology, Vol. 2017, No. 4, pp. 39–57 [PDF]
    Dong Lu, Yao Sun, Dingkang Wang: A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials. Journal of Systems Science and Complexity, 2018 Vol. 31 (6): 1633-1646. [PDF]
    Jian Bai, Ting Li, Yao Sun, Dingkang Wang, and Dongdai Lin： The Lightest 4 × 4 MDS Matrices over GL(4,F2), Science China Series F: Information. 2018, 61(11): 119102 [PDF]
    2017
    Xiaodong Ma, Yao Sun, Dingkang Wang, Yushan Xue : On Checking Linear Dependence of Parametric Vectors, ICIC 2017: Intelligent Computing Theories and Application, LNCS 10362(2017) 188-196 [PDF]
    Deepak Kapur, Yao Sun, Dingkang Wang, Jie Zhou: The Generalized Rabinowitsch Trick, ACA 2015, in PROMS 198 (2017) 219-229. [PDF]
    Jie Zhou,Dingkang Wang, Yao Sun: Automated Reducible Geometric Theorem Proving and Discovery by Groebner Basis Method, Journal of Automated Reasoning, (2017) 59:331-344. [PDF]
    Dong Lu, Xiaodong Ma,Dingkang Wang: A New Algorithm for General Factorizations of Multivariate Polynomial Matrices, in Proceedings of ISSAC 2017, 277-284. July 25-28, Kaiserslautern Germany . [PDF]
    2016
    Jie Zhou,Dingkang Wang: Solving the Perspective-Three-Point Problem Using Comprehensive Groebner Systems, Journal of Systems Science and Complexity, 2016,29(5): 1446-1471. [PDF]
    Yao Sun, Zhenyu Huang, Dingkang Wang, Dongdai Lin: An improvement over the GVW algorithm for inhomogeneous polynomial systems, Finite Fields and Their Applications. Vol. 41, No. 4, (2016), 174 - 192. [PDF]
    Yao Sun, Zhenyu Huang, Dongdai Lin, Dingkang Wang: On Implementing the Symbolic Preprocessing Function over Boolean Polynomial Rings in Groebner Basis Algorithms Using Linear Algebra, Journal of Systems Science and Complexity. Vol. 29 No. 3 (2016) 789-804 [PDF]
    2014
    Jie Zhou, Dingkang Wang: A Method to Determine if Two Parametric Polynomial Systems Are Equal. ICMS 2014, LNCS 8592 (2014) 537-544. [PDF]
    2013
    Y.Sun and D.K. Wang: An Efficient Algorithm for Factoring Polynomials over Algebraic Extension Field. Science in China, Series A: Mathematics, Vol. 56, No. 6 (2013) 1155-1168. [PDF]
    Y.Sun and D.K. Wang: A New Proof for the Correctness of the F5 Algorithm. Science in China, Series A: Mathematics, Vol. 56, No. 4 (2013) 745-756. [PDF]
    D. Kapur, Y.Sun and D.K. Wang: An Efficient Method for Computing Comprehensive Groebner Bases. Journal of Symbolic Computation 52 (2013) 124–142. [PDF]
    D. Kapur, Y.Sun and D.K. Wang: An Efficient Algorithm for Computing a Comprehensive Groebner System of a Parametric Polynomial Systems. Journal of Symbolic Computation 49 (2013) 27–44. [PDF]
    2012
    Y.Sun, D.K. Wang, X.D. Ma and Y. Zhang: A Signature-Based Algorithm for Computing Groebner Bases in Solvable Polynomial Algebras. Proceedings of ISSAC 2012, 351-358. July 22-25, Grenoble, France. [PDF]
    X.D. Ma, Y.Sun and D.K. Wang: Computing Polynomial Univariate Representations of Zero-dimensional Ideals by Groebner Basis. Science in China, Series A: Mathematics, Vol. 55, No. 6 (2012) 1293-1302. [PDF]
    2011
    D. Kapur, Y. Sun, D.K. Wang: Computing Comprehensive Groebner Systems and Comprehensive Groebner Bases Simultaneously. Proceedings of ISSAC 2011, 193-200. June 8-11, San Jose, USA. [PDF]
    Y. Sun, D.K. Wang: A Generalized Criterion for Signature Related Groebner Basis Algorithms. Proceedings of ISSAC 2011, 337-344. June 8-11, San Jose, USA. [PDF]
    M. Zhang, W. Yan, C.M. Yuan, D.K. Wang and X.S.Gao, Curve fitting and optimal interpolation on CNC machines based on quadratic B-splines. Science China, Information Sciences, 54(7), 1407-1418, 2011. [PDF]
    X.D. Ma，Y. Sun and D.K. Wang: On Computing Groebner Bases in the Rings of Differential Operators. Science in China, Series A: Mathematics, Vol. 54, No. 6 (2011) 1077-1088. [PDF]
    Y. Sun and D.K. Wang: The F5 Algorithm in Buchberger's Style. Journal of Systems Sciences and Complexity. (2011) 24:1218-1231. [PDF]
    2010
    D.Kapur, Y. Sun. D.K. Wang: A New Algorithm for Computing Comprehensive Groebner Systems. Proceedings of ISSAC 2010, 29-36. July 25-28, Munich, Germany. [PDF]
    2009
    Y. Sun, D.K. Wang: The Implementation and Complexity Analysis of the Branch Groebner Bases Algorithm over Boolean Ring. COE Lecture Note Vol. 22: Kyushu University. The Joint Conference of ASCM 2009 and MACIS. 191-200 (2009). [PDF]
    Y. Sun, D.K. Wang: Branch Groebner Bases Algorithm over Boolean Ring. J. Sys. Sci. & Math. Scis. 29(9) (2009), 1266-1277. [PDF]
    B.H. Li, D.K. Wang: An Algorithm for Transforming Regular Chain into Normal Chain. In Computer Mathematics, LNAI 5081, ASCM 2007, 236-245. [PDF]
    2007
    D.K. Wang, Y. Zhang: An Algorithm for Decomposing a Polynomial System into Normal Ascending Sets. Science in China, Series A: Mathematics, Vol. 50, No. 10, (2007) 1441-1450. [PDF]
    X.F.Chen, P.Li, L.Lin, D.K.Wang: Proving Geometric Theorems by Partitioned -Parametric Groebner Bases, Automated Deduction in Geometry, LNAI 3763 34-43(2006), Springer. [PDF]
    1993-2006
    王定康，张岩：正规升列在参数代数方程组求解中的应用，数学学报，29(2) 2006
    F.D. Xie, Z.S. Lu, D.K.Wang: The Solutions of Toda Lattice and Volterra Lattice. Chaos, Solitons and Fractals 27(2006) 217-222.
    F.D.Xie, D.K.Wang, Z.S,Lu: An Approach to Directly Construct Exact Solutions of Nonlinear Differential-difference Equations. Nonlinear Analysis 62 (2005) 1490 – 1497
    李鹏，陈雪峰，王定康：分区参数Groebner基的计算，系统科学与数学, 25（2）129－138（2005）
    X.F.Chen and D.K.Wang: The Projection of Quasi Variety and Its Application on Geometric Theorem Proving, In: Automated Deduction in Geometry, LNAI 2930, Springer-Verlag, BerlinHeidelberg, 21-30 (2004) [PDF]
    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 ASCM 2003, (eds. Z. Li and W. Sit), 130-145, World Scientific, Singapore, 2003.
    Y.W. Wu, D.K. Wang, H.Yang, D.D. Lin: On Software Development of Characteristic Set Method, Journal of Systems Science and Systems Engineering. Vol 11, No.3 ( 2002) 371-379
    D.K. Wang: Zero Decomposition Algorithms for System of Polynomial Equations, Computer Mathematics, Proc. of the 4th Asian Symposium (2000) 67-70
    D.K. Wang: Inequality Mechanical Proving, Mathematics and Mathematics Mechanization. 173-183 2001
    X.S. Gao, D.K.Wang: On the Automatic Derivation of a Set of Geometric Formulae,Journal of Geometry. Vol. 53, 79-88, (1995)
    [PDF]
    D.K. Wang, L.H.Zhi: Software Development in MMRC，Proceedings of the Asian Technology Conference in Mathematics. 1995, 234-243
    吴文俊,王定康 CAGD中的曲面拼接问题，数学的实践与认识. 1994, 3.
    D.K. Wang: Mechanical Solution of a Group of Space Geometry Problems. Proceedings of the 1992 International Workshop on Mathematics Mechanization.
程序软件

 

    MMP (VC++) is a Mathematics-Mechanization Platform.
    wsolve is a package for solving system of polynomial equations on Maple.
    GBGC is a package for computing S-Groebner basis on Singular.
    CGS is a package for computing Comprehensive Groebner System on Magma.
    CGS&CGB is a package for computing Comprehensive Groebner Systems and Comprehensive Groebner Bases on Singular.
    Framework for GVW Implementation and Examples used in the paper "A framework for implementing the GVW algorithm efficiently".
    MatrixFactorization is a package for factorizing matrix with polynomial entries
    EHC is a package for computing extended Hensel construction of multivariable polynomials
    GVW on local ring is a package for computing standard basis by extending GVW algorithm for local ring
    parametric GCD is a package for computing GCD of multivariate polynomials with parameters