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.
177 Citations
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- 2006
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.
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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.
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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…
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References
SHOWING 1-10 OF 15 REFERENCES
On the Computation of Hilbert Class Fields
- Mathematics
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
- MathematicsISSAC '95
- 1995
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
- MathematicsEncyclopedia of mathematics and its applications
- 1989
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
- Mathematics
- 1996
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
- Mathematics
- 1996
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
- Computer Science, MathematicsGraduate 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