Kant V4

  title={Kant V4},
  author={Mario Daberkow and Claus Fieker and J{\"u}rgen Kl{\"u}ners and Michael E. Pohst and K. Roegner and M. Sch{\"o}rnig and K. Wildanger},
  journal={J. Symb. Comput.},
The software package KANT V4 for computations in algebraic number elds is now available in version 4. In addition a new user interface has been released. We will outline the features of this new software package. 

KASH: Recent Developments

The computer algebra system KASH/KANT for number theory has evolved considerably and its new features are presented and the related components, QaoS (Querying Algebraic Objects System) and GiANT (Graphical Al algebraic Number Theory) are introduced.

A Database for Number Fields

A database for number fields is described that has been integrated into the algebraic number theory system Kant and gives efficient access to the tables of number fields that have been computed during the last years and is easily extended.

On the Computation of Hilbert Class Fields

Abstract Let k be an algebraic number field. We describe a procedure for computing the Hilbert class field Γ ( k ) of k , i.e., the maximal abelian extension unramified at all places. In the first

On solving norm equations in global function fields

This article develops general effective methods for that task in global function fields for the first time in algebraic number theory.

Kummer Curves and Their Fibre Products with Many Rational Points

  • M. Kawakita
  • Physics
    Applicable Algebra in Engineering, Communication and Computing
  • 2003
This method bases on the fine features of Kummer extensions and obtains new curves after practical searching by an efficient method of constructing curves with many rational points.

Factoring polynomials over global fields I

  • M. Pohst
  • Computer Science, Mathematics
    J. Symb. Comput.
  • 2005

An efficient algorithm for the computation of Galois automorphisms

We describe an algorithm for computing the Galois automorphisms of a Galois extension which generalizes the algorithm of Acciaro and Kluners to the non-Abelian case. This is much faster in practice

On the Resolution of Resultant Type Equations

This work makes the first attempt for the complete resolution of resultant type equations for monic quadratic polynomials satisfyingRes(P, Q) = a.



On the Computation of Hilbert Class Fields

Let k be an algebraic number eld. We describe a procedure for computing the Hilbert class eld ?(k) of k, i.e. the maximal abelian extension unramiied at all places. In the rst part of the paper we

Computations with relative extensions of number fields with an application to the construction of Hilbert class fields

We present new and improved algorithms for computations with relative extensions of algebraic number fields. Especially, the tasks of relative normal forms, relative bases, detection of subfields,

Algorithmic algebraic number theory

This chapter discusses the embedding of commutative orders into the maximal order of constructive algebraic number theory, and some of the methods used to derive these orders.

On Computing Subbelds

The purpose of this article is to determine all subbelds Q() of xed degree of a given algebraic number eld Q(). It is convenient to describe each subbeld by a pair (h;g) of polynomials in Qt] resp.

Solving Thue Equations of High Degree

Abstract We propose a general method for numerical solution of Thue equations, which allows one to solve in reasonable time Thue equations of high degree (provided necessary algebraic number theory

A course in computational algebraic number theory

  • H. Cohen
  • Computer Science, Mathematics
    Graduate texts in mathematics
  • 1993
The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.

Computational Algebraic Number Theory; Birkhauser; Basel

  • 1993

Computing Sub elds in Algebraic Number Fields

  • J. Aust. Math. Soc., Ser. A
  • 1990