We present a (well-known) method to compute a solution to the linear system Ax=b over the integers, when it is known that the determinant of A is non-zero and that a solution with integral coefficients exists. We also provide a running time analysis.
Posts about Computational Number Theory.
This post presents a poster of mine presented at the poster session of the 9th Algorithmic Number Theory Symphoisum.
We compare the tasks of finding points of a lattice, computing the structure of finite abelian groups and explaining algorithms. We show up relations between these three topics and, as an example, depict the baby-step giant-step algorithm for order computation, as well as Terr's modification of this algorithm.
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.