Selected Publications

 

Books

• X.S. Gao, D.K. Wang, Z. Qiu, and H. Yang, Equation Solving and Machine Proving - Problem Solving with MMP (in Chinese ), Science Press, Beijing, 2006.

Research Papers

2024

• Dong Lu, Dingkang Wang, Fanghui Xiao:On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices. Journal of Systems Science & Complexity, 2024, 37(3): 1295-1307 [PDF]
• Xiuquan Ding, Dingkang Wang, Fanghui Xiao, Xiaopeng Zheng: An Algorithm for Computing Greatest Common Right Divisors of Parametric Ore Polynomials. Proceedings of ISSAC 2024, 226-233, July 16-19, Raleigh, NC, USA. [PDF]
• Dong Lu, Dingkang Wang, Fanghui Xiao and Xiaopeng Zheng: Signature-based standard basis algorithm under the framework of GVW algorithm. accepted by Journal of Symbolic Computation.https://doi.org/10.1016/j.jsc.2024.102370 [PDF]
• Dingkang Wang, Jingjing Wei, Fanghui Xiao, Xiaopeng Zheng: Two Algorithms for Computing Rational Univariate Representations of Zero-Dimensional Ideals with Parameters, http://arxiv.org/abs/2403.16519

2023

• Dingkang Wang, Hesong Wang, Jingjing Wei and Fanghui Xiao: An Extended GCRD Algorithm for Parametric Univariate Polynomial Matrices and Application to Parametric Smith Form. Journal of Symbolic Computation 115 (2023) 248–265.[PDF].
• Dong Lu, Dingkang Wang, Fanghui Xiao:New Remarks on the Factorization and Equivalence Problems for a Class of Multivariate Polynomial Matrices. Journal of Symbolic Computation 115 (2023) 266–284.[PDF]
• Dong Lu, Dingkang Wang, Fanghui Xiao and Xiaopeng Zheng: Equivalence and reduction of bivariate polynomial matrices to their Smith forms. Journal of Symbolic Computation 118 (2023) 1–16.[PDF]
• Xiaopeng Zheng, Dong Lu, Dingkang Wang, Fanghui Xiao: New results on the equivalence of bivariate polynomial matrices. Journal of Systems Science and Complexity. 2023. Vol. 36(1):77-95.[PDF]
• Dong Lu, Dingkang Wang, Fanghui Xiao and Xiaopeng Zheng: On General Factorization Problems of n-D Polynomial Matrices. IEEE Transactions on Circuits and Systems II: Express Briefs. 2023. Vol. 70, No. 3: 1219-1223. [PDF]

2022

• Dong Lu, Dingkang Wang, Fanghui Xiao, Xiaopeng Zheng:A Property of Modules Over a Polynomial Ring With an Application in Multivariate Polynomial Matrix Factorizations. Proceedings of ISSAC 2022, 343-350, July 4-7, Villeneuve-d’Ascq, France [PDF]
• Dingkang Wang, Jingjing Wei, Fanghui Xiao and Xiaopeng Zheng: Rational Univariate Representation of Zero-Dimensional Ideals with Parameters. Proceedings of ISSAC 2022, 217-224, July 4-7, Villeneuve-d’Ascq, France [PDF]
• Fanghui Xiao, Dong Lu, Dingkang Wang: Solving Multivariate Polynomial Matrix Diophantine Equations with Groebner Basis Method, Journal of Systems Science and Complexity. 2022. Vol. 35(1):413-426 [PDF]

2021

• Dong Lu, Dingkang Wang, Fanghui Xiao:On Factor Left Prime Factorization Problems for Multivariate Polynomial Matrices, Multidimensional Systems and Signal Processing, 2021 Vol. (32), 975–992 [PDF]
• Deepak Kapur, Dong Lu, Michael Monagan, Yao Sun and Dingkang Wang: Algorithms for Computing Greatest Common Divisors of Parametric Multivariate Polynomials. Journal of Symbolic Computation 102 (2021) 3–20.[PDF]
• Fanghui Xiao, Dong Lu, Xiaodong Ma, Dingkang Wang: An Improvement of the Rational Representation for High-dimensional Systems. Journal of Systems Science and Complexity. 2021. Vol. 34(6):2410-2427 [PDF]

2020

• Dingkang Wang, Hesong Wang and Fanghui Xiao: An Extended GCD Algorithm for Parametric Univariate Polynomials and Application to Parametric Smith Normal Form.Proceedings of ISSAC 2020, 442-449, July 20-23, Kalamta, Greece [PDF]
• Dong Lu, Dingkang Wang and Fanghui Xiao: Further Results on the Factorization and Equivalence for Multivariate Polynomial Matrices. Proceedings of ISSAC 2020, 328-335, July 20-23, Kalamta, Greece [PDF]
• Jian Bai, Yao Sun, Dingkang Wang: On the Construction of Involutory MDS Matrices over F_{2^m}. Journal of Systems Science and Complexity, 2020 Vol. 33 (3): 836–848.[PDF]
• Dong Lu, Dingkang Wang and Fanghui Xiao: Factorizations for a Class of Multivariate Polynomial Matrices, Multidimensional Systems and Signal Processing, 2020 Vol. 31(3), 989-1004. [PDF ]
• Banghe Li, Dingkang Wang: Hilbert problem 15 and Ritt-Wu method (II). Journal of Systems Science and Complexity, 2020. Vol. 33(6): 2124-2138. [PDF]

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

• Dong Lu, Dingkang Wang, Fanghui Xiao and Jie Zhou: Extending the GVW Algorithm to Local Ring. 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. 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, 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] [Full version]

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. 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]

2008

• 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

• D.K.Wang, Y. Zhang: The Application of Normal Ascending Set in Solving Parametric Algebraic Equations，Acta Mathematica Sinica, Chinese Series, 29(2) 241－248 (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
• P. Li, X.F. Chen, D.K. Wang: On the Computation of Partitioned-Parametric Groebner Bases (In Chinese)，J. Sys. Sci. & Math. Scis., 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
• W.T. Wu, D.K. Wang: On the Surface Fitting Problems in CAGD. (In Chinese) Mathematics in Practice and Theory, 1994, 3.
• D.K. Wang: Mechanical Solution of a Group of Space Geometry Problems. Proceedings of the 1992 International Workshop on Mathematics Mechanization.