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Numerical-symbolic exact irreducible decomposition of cyclic-12

Part of: Nonlinear algebraic or transcendental equations Computational aspects and applications Algorithms - Computer Science Computational aspects in algebraic geometry

Published online by Cambridge University Press:  01 August 2011

Rostam Sabeti
Rostam Sabeti*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA (email: [email protected])

Abstract

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In 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 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.

MSC classification

Secondary: 65H10: Systems of equations 68W30: Symbolic computation and algebraic computation 13P05: Polynomials, factorization 14Q99: None of the above, but in this section
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 155 - 172
Copyright
Copyright © London Mathematical Society 2011

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