Thirteenth Algorithmic Number Theory Symposium ANTS-XIII University of Wisconsin, Madison July 16 – 20, 2018 Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII) July 16 – 20, 2018

Computation of triangular integral bases

Jens-Dietrich Bauch and Ha Thanh Nguyen Tran

Abstract: Let A be a Dedekind domain, K the fraction field of A, and f in A[x] a monic irreducible separable polynomial. For a given non-zero prime ideal p of A we present in this paper a new algorithm to compute a triangular p-integral basis of the extension L of K determined by f. This approach can be easily adopted to compute triangular p-integral basis of fractional ideals I of the integral closure of A in L. Along this process one can compute p-integral bases for a family of ideals contained in I as a by-product.

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