| Let A be a unique factorization domain that is finitely generated as an algebra over a field k of characteristic 0, and let K be the field of fractions of A. An algorithm is presented for computing the integral closure of A in the ring extension L = K [ X]/(f) where f ∈ A[X] is monic and has no repeated roots in an algebraic closure of K. This task is accomplished by replacing the ring A with suitable complete discrete valuation rings that arise from localizations at height 1 prime ideals of A. In that setting, Henselization techniques, Newton Polygon factorizations, and Chinese Remainder Theorem decompositions are employed to compute an integrally closed separable extension that is then used to recover the desired normalization by algebraic descent. A partial implementation of the procedures used in the algorithm to MAPLE is given along with several examples. |
