科研之友
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摘要
In 1992, Goran Bjorck and Ralf Froberg completely characterized the solution set of cyclic-8. In 2001, Jean-Charles Faugere determined the solution set of cyclic-9, by computer algebra methods and Grobner basis computation. In this paper, a new theory in matrix analysis of rank-deficient matrices together with algorithms in numerical algebraic geometry enables us to present a symbolic-numerical algorithm to derive exactly the defining polynomials of all prime ideals of positive dimension in primary decomposition of cyclic-12. Empirical evidence together with rigorous proof establishes the fact that the positive-dimensional solution variety of cyclic-12 just consists of 72 quadrics of dimension one.
- 出版日期2011
