On non-binomial structure of cyclic 8-roots

  • Rostam SabetiEmail author
Original Paper Area 2


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.


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

Mathematics Subject Classification

Primary 14Q15 Secondary 65H10 68W30 13P05 



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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