Numerical-symbolic exact irreducible decomposition of cyclic-12

Rostam Sabeti
2011 LMS Journal of Computation and Mathematics  
AbstractIn 1992, Göran Björck and Ralf Fröberg completely characterized the solution set of cyclic-8. In 2001, Jean-Charles Faugère determined the solution set of cyclic-9, by computer algebra methods and Gröbner 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
more » ... f 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.
doi:10.1112/s146115701000001x fatcat:itim62zq7zed7nculzdlt4zbya