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Posts about infrastructure.

This post presents a poster of mine presented at the poster session of the 9th Algorithmic Number Theory Symphoisum.
We show how to obtain n-dimensional infrastructures from global fields of unit rank n. We will also discuss how to obtain baby steps in these cases, and show graphical representations of certain two-dimensional infrastructures obtained from function fields.
We explain a general technique to obtain a reduction map, given X and d and, varying with the method of construction, additional information for every x in X. Moreover, we explain a technique on how to obtain n-dimensional infrastructures from certain lattices in (n+1)-dimensional space.
We will introduce n-dimensional infrastructures and briefly discuss reductions, f-representations and giant steps. We will also discuss how infrastructures can be obtained from finite abelian groups.
We introduce the notion of f-representations and relate them to reduction maps. Moreover, we equip a set of f-representations with a group operation which can be computed purely with baby steps, giant steps and relative distances.
We give the definition of one-dimensional infrastructures and construct baby and giant steps. Moreover, we show that one-dimensional infrastructures generalize finite cyclic groups. Finally, we give some remarks on our choice of the giant step definition.