Together with Claus Fiecker I am developing Hecke, which is an open-source package for computational algebraic number theory written in julia. As part of the OSCAR computer algebra system, Hecke is supported by the DFG (SFB-TRR 195).
I am also one of the coauthors of Nemo and AbstractAlgebra, which are julia packages providing basic functionality mainly for matrices and polynomial rings over a variety of base rings.
The Magma implementation of the algorithms described in "Computing isomorphisms between lattices": Iso.zip (README).
The Magma implementation of the algorithms described in "Computational verification of Leopoldt’s conjecture and the Leading Term Conjectures for totally real fields": CheckLeopoldt.m.