Algorithms for solving linear systems over cyclotomic fields

We consider the problem of solving a linear system Ax=b$Ax=b$ over a cyclotomic field. Cyclotomic fields are special in that we can easily find a prime p$p$ for which the minimal polynomial m(z)$m\left(z\right)$ for the field factors into a product of distinct linear factors. This makes it possible to develop fast modular algorithms.