Abstract
Following pioneering works of Bjorck and Froberg 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.
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