Archive for the ‘Computational Number Theory’ Category
Solving Certain Linear Systems over the Integers.
friday, june 17th, 2011We 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.
Rigorous Arithmetic in the Arakelov Divisor Class Group of a Number Field.
tuesday, july 27th, 2010This post presents a poster of mine presented at the poster session of the 9th Algorithmic Number Theory Symphoisum.
Finding Lattice Points, Finite Abelian Groups, and Explaining Algorithms.
friday, january 29th, 2010We 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.
Obtaining Infrastructures from Global Fields.
tuesday, july 21st, 2009We 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.
