Handbook of theoretical computer science (vol. A)
Precise computation using range arithmetic, via C++
ACM Transactions on Mathematical Software (TOMS)
Algorithms in invariant theory
Algorithms in invariant theory
A course in computational algebraic number theory
A course in computational algebraic number theory
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We present an improvement of an algorithm given by GAUSS to compute a radical expression for a p-th root of unity. The time complexity of the algorithm is O (p3m6 log p), where m is the largest prime factor of p - 1.On current workstations the given implementation of the algorithm can be used to obtain radical expressions for p-th roots of unity for p up to about 100 in the general case and p up to about 250 if p - 1 has only small prime factors.Moreover, the algorithm allows the use of coarse grained parallel computation in various ways that would allow one to compute bigger examples on a network of workstations.