Kant V4

@article{Daberkow1997KantV,
  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.},
  year={1997},
  volume={24},
  pages={267-283}
}
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. 

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On solving norm equations in global function fields

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    Applicable Algebra in Engineering, Communication and Computing
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References

SHOWING 1-10 OF 15 REFERENCES

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