## STNB 2015 (29th year)

### Computation of triangular bases of integral closures

Hayden Stainsby

#### Abstract

In this presentation, we consider the problem of computing triangular bases of integral closures of one-dimensional local rings. MaxMin is an efficient algorithm which employs OM representations of prime ideals to compute local bases of fractional ideals of number fields and function fields. It generates bases which are guaranteed to be triangular and presents the same asymptotic computational complexity as existing methods based on OM representations. In practice, MaxMin is capable of computing triangular bases of large field extensions very quickly.

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