LiDIA : a library for computational number theory

Abstract

In this paper we describe LiDIA, a new library for computational number theory. Why do we work on a new library for computational number theory when such powerful tools as Pari [1], Kant [11], Simath [10] already exist? In fact, those systems are very useful for solving problems for which there exist efficient system routines. For example, using Pari or Kant it is possible to compute invariants of algebraic number fields and Simath can be used to find the rank of an elliptic curve over Q. However, building complicated and efficient software on top of existing systems has in our experience turned out to be very difficult. Therefore, the software of our research group is developed independently of other computer algebra systems.