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On the coefficients of the polynomial in the number field sieve

Science China(Information Sciences) 2015年第11期58卷 182-190页

作者： YANG Min MENG QingShu WANG ZhangYi LI Li ZHANG HuanGuo International School of Software Wuhan University Computer School Wuhan University

Polynomial selection is very important in the number field sieve. If the number of relations a pair of polynomials can generate is closely correlated with the coefficients of the polynomials, we can select polynomials by checking the coefficients first, which can speed up the selection of good polynomials. In this paper, we aim to study the correlation between polynomial coefficients and the number of relations the polynomials can generate. By analyzing the zero roots, it is found that a polynomial with the ending coefficient containing more small primes usually can generate more relations than the one whose ending coefficient contains less. As a polynomial with more real roots usually can generate more relations, using the complete discrimination system,the requirements on the coefficients of a polynomial to obtain more real roots are analyzed. For instance, a necessary condition for a polynomial of degree d to have d distinct real roots is that the coefficient of degree d- 2should be negative or small enough. The result in the case d = 3 can be used directly in selecting polynomials generated by the nonlinear method, where d = 3 is already enough for practical purpose.

关键词： cryptography integer factorization number field sieve polynomial selection coefficients zero roots complete discrimination system

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New single traveling wave solution in birefringent fibers or crossing sea waves on the high seas for the coupled Fokas-Lenells system

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Journal of Ocean Engineering and Science 2023年第6期8卷 590-594页

作者： Zhao Li Jing Liu Xinyu Xie College of Computer Science Chengdu UniversityChengdu 610106PR China Officers College of PAP Chengdu 610213China

The main work of this paper is focused on construction the single traveling wave solution of the coupled Fokas-Lenells system,which is usually used to simulate the propagation of ultrashort optical pulses in birefringent fibers or crossing sea waves on the high ***,the coupled Fokas-Lenells system is simplified into a nonlinear ordinary differential equation by traveling wave transformation and linear ***,using the well-known complete discriminant system of third-order polynomials,some single traveling wave solutions of the coupled Fokas-Lenells system are obtained including implicit solutions,rational function solutions and Jacobian function solutions.

关键词： Coupled Fokas-Lenells system Traveling wave solution complete discrimination system

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SOLUTION CLASSIFICATION FOR THE NONPERSPECTIVE-THREE-POINT PROBLEM

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Journal of systems Science & Complexity 2006年第2期19卷 219-226页

作者： Jianliang TANG Wensheng CHEN Department of Mathematics College of Science Shenzhen University Shenzhen 518060 Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China. Department of Mathematics College of Science Shenzhen University Shenzhen 518060 China.

In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with the advance in imaging technologies for machine vision. These devise are not necessarily being designed to follow the perspective rule in order to satisfy some design criterion and,thus, the imaging rays may not pass through a common *** generalized imaging devices may not be perspective and, therefore, their poses cannot be estimated with traditional perspective *** the Wu-Ritt＇s zero decomposition method,the main component for the nonperspective-three-point problem is given. We prove that there are at most eight solutions in the general case and give the solution classification for the NP3P problem.

关键词： complete discrimination system Nonperspective-Three-Point Perspective-Three-Point Problem (P3P) revised sign lists Solution classification.

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