THE INFRASTRUCTURE OF A GLOBAL FIELD OF ARBITRARY UNIT RANK
Felix Fontein · 2008
In the past, the infrastructure of a number or (global) function field has been used for computation of units. In the case of a one-dimensional infrastructure, i.e. in the case of unit rank one, one has a binary operation which is similar to multiplication, called a giant step, which was introduced by D. Shanks. In this paper, we show a general way to interpret infrastructure in the case of arbitrary unit rank, which gives a giant step. Moreover, we relate the infrastructure and the giant step to the arithmetic in the divisor class group. Finally, we give explicit algorithms in the function field case for computing, and show how the baby step-giant step method for unit computation generalizes to the case of arbitrary unit rank.