基本信息
王定康  男  博导  中国科学院数学与系统科学研究院
电子邮件: dwang@mmrc.iss.ac.cn
通信地址: 北京市海淀区中关村东路55号
邮政编码: 100190

研究领域

几何定理自动证明与发现,参数Groebner基, 签名Groebner基算法,矩阵分解(其中元素是多变元多项式)

招生信息

   
招生专业
070104-应用数学
070101-基础数学
招生方向
机器证明,计算机代数
符号计算

教育背景

1990-09--1993-07   中国科学院系统科学研究所   博士
1987-09--1990-07   中国科学院系统科学研究所   硕士
1983-09--1987-07   北京大学   学士
学历
-- 研究生
学位
-- 博士

工作经历


工作简历
2012-03~现在, 中国科学院数学与系统科学研究院, 研究员
1997-03~2012-03,中国科学院系统科学研究所, 副研究员
1993-07~1997-02,中国科学院系统科学研究所, 助理研究员

教授课程

计算代数几何引论
代数计算理论
Groebner基的算法

专利与奖励

   
专利成果
( 1 ) 基于二次B样条曲线对G01代码的拟合及插补方法, 发明, 2009, 第 4 作者, 专利号: 200910082732.9

出版信息

  

发表论文
[1] Lu, Dong, Wang, Dingkang, Xiao, Fanghui. New remarks on the factorization and equivalence problems for a class of multivariate polynomial matrices. JOURNAL OF SYMBOLIC COMPUTATION[J]. 2023, 115: 266-284, http://dx.doi.org/10.1016/j.jsc.2022.07.005.
[2] Zheng Xiaopeng, Lu Dong, Wang Dingkang, Xiao Fanghui. New Results on the Equivalence of Bivariate Polynomial Matrices. JOURNAL OF SYSTEMS SCIENCE AND COMPLEXITY[J]. 2023, 36(1): 77-95, http://sciencechina.cn/gw.jsp?action=detail.jsp&internal_id=7551065&detailType=1.
[3] Lu, Dong, Wang, Dingkang, Xiao, Fanghui, Zheng, Xiaopeng. On General Factorization Problems of n-D Polynomial Matrices. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS[J]. 2023, 70(3): 1219-1223, http://dx.doi.org/10.1109/TCSII.2022.3223934.
[4] Lu, Dong, Wang, Dingkang, Xiao, Fanghui, Zheng, Xiaopeng. Equivalence and reduction of bivariate polynomial matrices to their Smith forms. JOURNAL OF SYMBOLIC COMPUTATION[J]. 2023, 118: 1-16, http://dx.doi.org/10.1016/j.jsc.2023.01.001.
[5] Wang, Dingkang, Wang, Hesong, Wei, Jingjing, Xiao, Fanghui. An extended GCRD algorithm for parametric univariate polynomial matrices and application to parametric Smith form. JOURNAL OF SYMBOLIC COMPUTATION[J]. 2023, 115: 248-265, http://dx.doi.org/10.1016/j.jsc.2022.07.006.
[6] Dong Lu, Dingkang Wang, Fanghui Xiao, Xiaopeng Zheng. A Property of Modules Over a Polynomial Ring With an Application in Multivariate Polynomial Matrix Factorizations. The 47th International Symposium on Symbolic and Algebraic Computationnull. 2022, [7] Xiao Fanghui, Lu Dong, Wang Dingkang. Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2022, 35(1): 413-426, https://www.webofscience.com/wos/woscc/full-record/WOS:000614789100008.
[8] Dingkang Wang, Jingjing Wei, Fanghui Xiao, Xiaopeng Zheng. Rational Univariate Representation of Zero-Dimensional Ideals with Parameters. The 47th International Symposium on Symbolic and Algebraic Computationnull. 2022, [9] Xiao, Fanghui, Lu, Dong, Ma, Xiaodong, Wang, Dingkang. An Improvement of the Rational Representation for High-Dimensional Systems. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2021, https://www.webofscience.com/wos/woscc/full-record/WOS:000587281000025.
[10] Lu, Dong, Wang, Dingkang, Xiao, Fanghui. On factor left prime factorization problems for multivariate polynomial matrices. MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING[J]. 2021, 32(3): 975-992, http://dx.doi.org/10.1007/s11045-021-00768-x.
[11] Kapur, Deepak, Lu, Dong, Monagan, Michael, Sun, Yao, Wang, Dingkang. Algorithms for computing greatest common divisors of parametric multivariate polynomials. JOURNAL OF SYMBOLIC COMPUTATION[J]. 2021, 102: 3-20, http://dx.doi.org/10.1016/j.jsc.2019.10.006.
[12] Lu, Dong, Wang, Dingkang, Xiao, Fanghui. Factorizations for a class of multivariate polynomial matrices. MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING[J]. 2020, 31(3): 989-1004, https://www.webofscience.com/wos/woscc/full-record/WOS:000536473300010.
[13] Li, Banghe, Wang, Dingkang. Hilbert Problem 15 and Ritt-Wu Method (II). JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2020, 33(6): 2124-2138, https://www.webofscience.com/wos/woscc/full-record/WOS:000555391900006.
[14] 王定康. An Extended GCD Algorithm for Parametric Univariate Polynomials and Application to Parametric Smith Normal Form. Proceedings of ISSAC 2020[J]. 2020, [15] Bai, Jian, Sun, Yao, Wang, Dingkang. On the Construction of Involutory MDS Matrices overF2m. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2020, 33(3): 836-848, http://lib.cqvip.com/Qikan/Article/Detail?id=7102378921.
[16] Lu Dong, Sun Yao, Wang Dingkang. A Survey on Algorithms for Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2019, 32(1): 234-255, http://ir.amss.ac.cn/handle/2S8OKBNM/32584.
[17] Jian Bai, Yao Sun, Ting Li, Dingkang Wang. Applying Horner's Rule to Optimize Lightweight MDS Matrices. INTERNATIONAL JOURNAL OF DIGITAL CRIME AND FORENSICS (IJDCF). 2019, 11(4): http://kns.cnki.net/KCMS/detail/detail.aspx?QueryID=0&CurRec=1&recid=&FileName=SJIG3E0DAD0202587EB889CF70AB10C638F1&DbName=WWMERGEJ02&DbCode=WWME&yx=&pr=&URLID=&bsm=.
[18] Li Ting, Sun Yao, Huang Zhenyu, Wang Dingkang, Lin Dongdai. Speeding Up the GVW Algorithm via a Substituting Method. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2019, 32(1): 205-233, http://lib.cqvip.com/Qikan/Article/Detail?id=6100292587.
[19] Kapur Deepak, Lu Dong, Monagan Michael, Sun Yao, Wang Dingkang, Assoc Comp Machinery. An Efficient Algorithm for Computing Parametric Multivariate Polynomial GCD. ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATIONnull. 2018, 239-246, http://dx.doi.org/10.1145/3208976.3208980.
[20] Lu Dong, Wang Dingkang, Xiao Fanghui, Zhou Jie, Assoc Comp Machinery. Extending the GVW Algorithm to Local Ring. ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATIONnull. 2018, 271-278, http://dx.doi.org/10.1145/3208976.3208979.
[21] Bai, Jian, Li, Ting, Sun, Yao, Wang, Dingkang, Lin, Dongdai. The lightest 4 x 4 MDS matrices over GL(4, F-2). SCIENCE CHINA-INFORMATION SCIENCES[J]. 2018, 61(11): https://www.webofscience.com/wos/woscc/full-record/WOS:000444841700001.
[22] Lu Dong, Sun Yao, Wang Dingkang. A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2018, 31(6): 1633-1646, http://ir.amss.ac.cn/handle/2S8OKBNM/31875.
[23] Lu Dong, Ma Xiaodong, Wang Dingkang, ACM. A New Algorithm for General Factorizations of Multivariate Polynomial Matrices. PROCEEDINGS OF THE 2017 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC'17)null. 2017, 277-284, http://dx.doi.org/10.1145/3087604.3087607.
[24] Ting Li, Yao Sun, Maodong Liao, Dingkang Wang. Preimage Attacks on the Round-reduced Keccak with Cross-linear Structures. IACR TRANSACTIONS ON SYMMETRIC CRYPTOLOGY[J]. 2017, 39-57, https://doaj.org/article/fae4071b300140968565397bd54355c2.
[25] Zhou, Jie, Wang, Dingkang, Sun, Yao. Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method. JOURNAL OF AUTOMATED REASONING[J]. 2017, 59(3): 331-344, https://www.webofscience.com/wos/woscc/full-record/WOS:000409976900002.
[26] Ma Xiaodong, Sun Yao, Wang Dingkang, Xue Yushan, Huang DS, Jo KH, FigueroaGarcia JC. On Checking Linear Dependence of Parametric Vectors. INTELLIGENT COMPUTING THEORIES AND APPLICATION, ICIC 2017, PT IInull. 2017, 10362: 188-196, [27] Kapur Deepak, Sun Yao, Wang Dingkang, Zhou Jie, Kotsireas IS, MartinezMoro E. The Generalized Rabinowitsch Trick. APPLICATIONS OF COMPUTER ALGEBRAnull. 2017, 198: 219-229, [28] Sun Yao, Huang Zhenyu, Lin Dongdai, Wang Dingkang. On Implementing the Symbolic Preprocessing Function over Boolean Polynomial Rings in Grobner Basis Algorithms Using Linear Algebra. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2016, 29(3): 789-804, http://ir.amss.ac.cn/handle/2S8OKBNM/40482, http://www.irgrid.ac.cn/handle/1471x/6870171, http://ir.amss.ac.cn/handle/2S8OKBNM/40483.
[29] Zhou Jie, Wang Dingkang. Solving the Perspective-Three-Point Problem Using Comprehensive Grobner Systems. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY[J]. 2016, 29(5): 1446-1471, http://ir.amss.ac.cn/handle/2S8OKBNM/47551, http://www.irgrid.ac.cn/handle/1471x/6870664, http://ir.amss.ac.cn/handle/2S8OKBNM/47552.
[30] Sun, Yao, Huang, Zhenyu, Wang, Dingkang, Lin, Dongdai. An improvement over the GVW algorithm for inhomogeneous polynomial systems. FINITE FIELDS AND THEIR APPLICATIONS[J]. 2016, 41: 174-192, https://www.webofscience.com/wos/woscc/full-record/WOS:000381062900012.
[31] Jie Zhou, Dingkang Wang. A Method to Determine if Two Parametric Polynomial Systems Are Equal. Mathematical software - ICMS 2014 :. 2014, 535-544, [32] Kapur, Deepak, Sun, Yao, Wang, Dingkang. An efficient method for computing comprehensive Grobner bases. JOURNAL OF SYMBOLIC COMPUTATION[J]. 2013, 52: 124-142, https://www.webofscience.com/wos/woscc/full-record/WOS:000316648400008.
[33] Sun Yao, Wang DingKang. An efficient algorithm for factoring polynomials over algebraic extension field. SCIENCE CHINA-MATHEMATICS[J]. 2013, 56(6): 1155-1168, http://sciencechina.cn/gw.jsp?action=detail.jsp&internal_id=4864677&detailType=1.
[34] Kapur, Deepak, Sun, Yao, Wang, Dingkang. An efficient algorithm for computing a comprehensive Grobner system of a parametric polynomial system. JOURNAL OF SYMBOLIC COMPUTATION[J]. 2013, 49: 27-44, https://www.webofscience.com/wos/woscc/full-record/WOS:000312476000003.
[35] Sun Yao, Wang DingKang. A new proof for the correctness of the F5 algorithm. SCIENCE CHINA-MATHEMATICS[J]. 2013, 56(4): 745-756, http://ir.amss.ac.cn/handle/2S8OKBNM/44781, http://www.irgrid.ac.cn/handle/1471x/6870467, http://ir.amss.ac.cn/handle/2S8OKBNM/44782.
[36] 王定康. A Signature-Based Algorithm for Computing Groebner Bases in Solvable Polynomial Algebras. Proceedings of ISSAC 2012. 2012, [37] Ma XiaoDong, Sun Yao, Wang DingKang. Computing polynomial univariate representations of zero-dimensional ideals by Grobner basis. SCIENCE CHINA-MATHEMATICS[J]. 2012, 55(6): 1293-1302, http://lib.cqvip.com/Qikan/Article/Detail?id=42195958.
[38] Ma XiaoDong, Sun Yao, Wang DingKang. On computing Grobner bases in rings of differential operators. SCIENCE CHINA-MATHEMATICS[J]. 2011, 54(6): 1077-1087, https://www.webofscience.com/wos/woscc/full-record/WOS:000292612300001.
[39] Zhang Mei, Yan Wei, Yuan ChunMing, Wang DingKang, Gao XiaoShan. Curve fitting and optimal interpolation on CNC machines based on quadratic B-splines. SCIENCE CHINA-INFORMATION SCIENCES[J]. 2011, 54(7): 1407-1418, http://lib.cqvip.com/Qikan/Article/Detail?id=38373983.
[40] Sun, Yao, Wang, Dingkang. The F5 algorithm in Buchberger's style. JOURNALOFSYSTEMSSCIENCECOMPLEXITY[J]. 2011, 24(6): 1218-1231, http://lib.cqvip.com/Qikan/Article/Detail?id=40670847.
[41] 孙瑶, 王定康. 布尔环上的分支Groebner基算法. 系统科学与数学[J]. 2009, 1266-1277, http://lib.cqvip.com/Qikan/Article/Detail?id=31787397.
[42] Dingkang Wang, Yan Zhang. An algorithm for decomposing a polynomial system into normal ascending sets. SCIENCE IN CHINA SERIES A-MATHEMATICS[J]. 2007, 50(10): 1441-1450, http://ir.amss.ac.cn/handle/2S8OKBNM/45804, http://www.irgrid.ac.cn/handle/1471x/6870537, http://ir.amss.ac.cn/handle/2S8OKBNM/45805.
[43] 李鹏, 陈雪峰, 王定康. 分区参数Groener基的计算. 系统科学与数学[J]. 2005, 25(2): 129-138, http://lib.cqvip.com/Qikan/Article/Detail?id=15501560.
发表著作
(1) 方程求解与机器证明-基于MMP的问题求解, 科学出版社, 2006-10, 第 2 作者

科研活动

   
科研项目
( 1 ) 数学机械化方法及其在数字化设计制造中的应用, 参与, 国家级, 2011-01--2015-12
( 2 ) 数学机械化及其在信息技术中应用, 参与, 国家级, 2012-01--2014-12
( 3 ) 基于签名的Groebner基算法及其应用, 主持, 国家级, 2014-01--2017-12

指导学生

已指导学生

王继斌  硕士研究生  070104-应用数学  

樊炜  博士研究生  070104-应用数学  

张文哲  硕士研究生  070104-应用数学  

马晓栋  博士研究生  070104-应用数学  

周洁  博士研究生  070104-应用数学  

白剑  博士研究生  070104-应用数学  

鲁东  博士研究生  070104-应用数学  

杨润河  硕士研究生  070104-应用数学  

肖方慧  博士研究生  070104-应用数学  

魏婧婧  硕士研究生  070104-应用数学  

王贺松  博士研究生  070104-应用数学  

现指导学生

丁修权  硕士研究生  070104-应用数学  

郑晓鹏  博士研究生  070104-应用数学