Set complexity of construction of a regular polygon

11/15/2017

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by   Eugene Kogan, et al.

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Given a subset of C containing x,y, one can add x + y or x - y or xy or (when y0) x/y or any z such that z^2=x. Let p be a prime Fermat number. We prove that it is possible to obtain from {1} a set containing all the p-th roots of 1 by 16 p^2 above operations. This problem is different from the standard estimation of complexity of an algorithm computing the p-th roots of 1.