NC algorithms for real algebraic numbers

Characterizing real algebraic numbers by a sign-sequence (according to Thom's lemma), using a variant of Ben Or Kozan and Reif algorithm for reducing the solving of systems of polynomial inequalities to the problem of counting real zeroes satisfying one polynomial inequality, and using a multivariate Sturm theory generalizing Hermite quadratic forms method for counting real zeroes, we prove that the computations on real algebraic numbers are in NC.

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