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On non-binomial structure of cyclic 8-roots

  • Rostam SabetiEmail author
Original Paper Area 2

Abstract

Following pioneering works of Björck and Fröberg for identification of the solution set of cyclic 8-roots (\(IC_8\)), with sole usage of computer algebra system, we present another application of our heuristic numerical-symbolic method to identify solution set of cyclic 8-roots, a system with non-binomial prime ideals in the prime decomposition of \(\sqrt{IC_8}\) which consists of 1152 isolated zeros, eight ideals of second degree and eight of degree sixteen all of dimension one. We use a fact in the theory of algebraic curves to solve the problem of primality and dimensionality of the presented ideals. As a theme for future research, we propose typical prime ideals in the prime decompositions of \(\sqrt{IC_{16}}\) and \(\sqrt{IC_{18}}\) (two largest unknown systems) for future research and application of the method.

Keywords

Computational algebraic geometry Components of solutions Irreducible decomposition Symbolic-numerical algorithm 

Mathematics Subject Classification

Primary 14Q15 Secondary 65H10 68W30 13P05 

Notes

Acknowledgments

The valuable comments of the esteemed anonymous referees made this paper more enriched and they are very much appreciated.

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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science320 South Main St. Olivet CollegeOlivetUSA

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