The Application of Wu’s Method of Characteristic Set in Solving Sudoku Problem

2019 ◽  
Vol 09 (03) ◽  
pp. 403-409
Author(s):  
晓宁 许
Keyword(s):  
Characteristic Set ◽  
Wu’S Method ◽  
Wu's Method

scholarly journals Applications of Differential Form Wu’s Method to Determine Symmetries of (Partial) Differential Equations

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 378 ◽  
Author(s):  
Temuer Chaolu ◽  
Sudao Bilige
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Polynomial ◽  
Decomposition Algorithm ◽  
Partial Differential ◽  
Wu’S Method ◽  
Classical Symmetry ◽  
Symmetries Of Differential Equations ◽  
Wu's Method ◽  
Nonclassical Symmetry

In this paper, we present an application of Wu’s method (differential characteristic set (dchar-set) algorithm) for computing the symmetry of (partial) differential equations (PDEs) that provides a direct and systematic procedure to obtain the classical and nonclassical symmetry of the differential equations. The fundamental theory and subalgorithms used in the proposed algorithm consist of a different version of the Lie criterion for the classical symmetry of PDEs and the zero decomposition algorithm of a differential polynomial (d-pol) system (DPS). The version of the Lie criterion yields determining equations (DTEs) of symmetries of differential equations, even those including a nonsolvable equation. The decomposition algorithm is used to solve the DTEs by decomposing the zero set of the DPS associated with the DTEs into a union of a series of zero sets of dchar-sets of the system, which leads to simplification of the computations.

Solving colored Yang-Baxter equation by Wu's method

2009 ◽  
Vol 29 (5) ◽  
pp. 1267-1294 ◽  
Author(s):  
Xin'an Ren ◽  
Shikun Wang ◽  
Ke Wu
Keyword(s):  
Baxter Equation ◽  
Wu’S Method ◽  
Wu's Method

A Wu‘s Method Based Parallelization Design and Implementation for Algebraic Cryptanalysis

2014 ◽  
Vol 530-531 ◽  
pp. 641-645
Author(s):  
Huai Zhe Zhou ◽  
Hai He Ba ◽  
Jiang Chun Ren ◽  
Tao Xie ◽  
Min Zhu ◽  
...  
Keyword(s):  
Large Scale ◽  
Computing Time ◽  
Polynomial Equation ◽  
Wu’S Method ◽  
Algebraic Cryptanalysis ◽  
Wu's Method ◽  
Efficient Data ◽  
Computing Performance ◽  
Balance Mechanism ◽  
Serial Algorithm

Wus method is one of the effective methods for solving large-scale polynomial equation systems in algebraic cryptanalysis. But it will take a lot of time to solve polynomial equations with a serial algorithm of Wu’s method. In order to eliminate the bottleneck of computing time overheads, we proposes an efficient data parallelization scheme based on Wu‘s method. And a load balance mechanism applied to our scheme, which greatly improves computing-performance of Wu’s method and enhances its ability to meet challenges of algebraic cryptanalysis.

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