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Gr (?) Bner basis theory Hamiltonian cycle in polynomial decomposition and problems in the application

Author: LiKaiWang
Tutor: ChenXiaoSong
School: Central South University
Course: Computational Mathematics
Keywords: Gr (o ¨) bner base Zero-dimensional ideal Factorization Hamilton Circle
CLC: O153
Type: Master's thesis
Year: 2007
Downloads: 66
Quote: 0
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Abstract


The main thesis work is the application Gr (o | ¨) bner basis theory discussed higher multivariate polynomial with rational coefficients can be about sex , second-order polynomial matrix factorization and solution plan all the Hamilton Circle . This paper consists of five chapters , the first two chapters is to introduce Gr (o | ¨) bner basis theory . The first chapter is the introduction of articles to introduce the impact of computers on mathematics , algebra and computer algebra in calculating the basic concepts , commonly used mathematical software -Maple and Gr (o | ¨) bner basis theory formation. The second chapter describes multiple Gr (o | ¨) bner -based algorithms and Gr (o | ¨) bner based optimization algorithms and commutative rings polynomial ideal Gr (o | ¨) bner base . Article III Chapter Gr (o | ¨) bner base theory is applied to high-order multivariate polynomial factorization problems, have been factorization method to judge : the high-order multivariate polynomial equations factored into question based on polynomial equations constitute the ideal Gr (o | ¨) bner base G to make judgments, if G does not partakers type solution, the polynomial can not be decomposed ; G partakers type solution if the polynomial can be decomposed . And has been associated with some of the polynomial factorization specific nature . Also discussed the second multivariate polynomial matrix factorization , biodegradable necessary and sufficient condition is that it can be decomposed determinant , and discusses the use of ring Gr (o | ¨) bner base for second-order matrix factorization . Chapter article on the plan by the use of a piece of conceptual equivalence relation derived from any one plan proved Hamilton circle on the map to determine at least one dye solution ; plan if Hamilton on lap , then there must be a staining solution this makes the existence of Hamilton circle is one of the two colors dyed surface and the other two colors dyed surface junction edges. And take advantage of this nature , combined with Gr (o | ¨) bner basis method presents a plan can be found on all Hamilton circle algorithm, and finally the use of Gr (o | ¨) bner basis method to achieve this programming algorithms.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra )
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