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An extended GCRD algorithm for parametric univariate polynomial matrices and application to parametric Smith form 期刊论文
JOURNAL OF SYMBOLIC COMPUTATION, 2023, 卷号: 115, 页码: 248-265
作者:  Wang, Dingkang;  Wang, Hesong;  Wei, Jingjing;  Xiao, Fanghui
收藏  |  浏览/下载：229/0  |  提交时间：2023/02/07
Extended greatest common right divisor  Parametric univariate polynomial matrix  Comprehensive Gr?bner system  Smith normal form  
Improved two-step Newton's method for computing simple multiple zeros of polynomial systems 期刊论文
NUMERICAL ALGORITHMS, 2022, 页码: 32
作者:  Li, Nan;  Zhi, Lihong
收藏  |  浏览/下载：174/0  |  提交时间：2022/04/02
Polynomial system  Simple multiple zero  Newton's method  Quadratic convergence  
Quantum Algorithm for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems 期刊论文
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2021, 页码: 40
作者:  Chen Yu-Ao;  Gao Xiao-Shan
收藏  |  浏览/下载：203/0  |  提交时间：2021/04/26
Block cipher AES  Boolean equation solving  condition number  hash function SHA-3  Keccak  HHL algorithm  MPKC  polynomial system solving  quantum algorithm  stream cipher Trivum  
Computing real radicals and S-radicals of polynomial systems 期刊论文
JOURNAL OF SYMBOLIC COMPUTATION, 2021, 卷号: 102, 页码: 259-278
作者:  El Din, Mohab Safey;  Yang, Zhi-Hong;  Zhi, Lihong
收藏  |  浏览/下载：469/0  |  提交时间：2020/09/23
Polynomial system  Real radical  S-radical ideal  Semi-algebraic set  Real algebraic geometry  
An Improvement of the Rational Representation for High-Dimensional Systems 期刊论文
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2020, 页码: 18
作者:  Xiao, Fanghui;  Lu, Dong;  Ma, Xiaodong;  Wang, Dingkang
收藏  |  浏览/下载：218/0  |  提交时间：2021/01/14
Comprehensive Grobner systems  high-dimensional polynomial system  rational representation  rational univariate representation  
A new deflation method for verifying the isolated singular zeros of polynomial systems 期刊论文
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 卷号: 376, 页码: 21
作者:  Cheng, Jin-San;  Dou, Xiaojie;  Wen, Junyi
收藏  |  浏览/下载：209/0  |  提交时间：2020/05/24
Polynomial system  Deflation method  Isolated singular zero  Interval verification  
A Survey on Algorithms for Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases 期刊论文
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2019, 卷号: 32, 期号: 1, 页码: 234-255
作者:  Lu Dong;  Sun Yao;  Wang Dingkang
收藏  |  浏览/下载：239/0  |  提交时间：2019/04/02
Comprehensive Grobner basis  comprehensive Grobner system  discovering geometric theorems mechanically  parametric polynomial system  quantifier elimination  
A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems 期刊论文
MATHEMATICS, 2018, 卷号: 6, 期号: 9, 页码: 18
作者:  Dou, Xiaojie;  Cheng, Jin-San
收藏  |  浏览/下载：225/0  |  提交时间：2019/01/11
over-determined polynomial system  isolated zeros  minimum point  sum of squares  interval methods  
Coupled modified KdV equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property 期刊论文
SCIENCE CHINA-MATHEMATICS, 2018, 卷号: 61, 期号: 6, 页码: 1063-1078
作者:  Chang, Xiangke;  He, Yi;  Hu, Xingbiao;  Li, Shihao;  Tam, Hon-wah;  Zhang, Yingnan
收藏  |  浏览/下载：233/0  |  提交时间：2018/07/30
integrable system  skew orthogonal polynomial  convergence acceleration algorithm  Laurent property  
Solving polynomial systems with noise over F-2: Revisited 期刊论文
THEORETICAL COMPUTER SCIENCE, 2017, 卷号: 676, 页码: 52-68
作者:  Huang, Zhenyu;  Lin, Dongdai
收藏  |  浏览/下载：179/0  |  提交时间：2018/07/30
Boolean polynomial system with noise  Max-PoSSo  ISBS method  Cold Boot attack  Serpent