𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Validated Computing in Algebraic Number Fields

✍ Scribed by MICHAEL E. POHST


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
341 KB
Volume
24
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Computing in the Field of Complex Algebr
✍ ADAM WOJCIECH STRZEBOΕƒSKI πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 371 KB

In this paper we present two methods of computing with complex algebraic numbers. The first uses isolating rectangles to distinguish between the roots of the minimal polynomial, the second method uses validated numeric approximations. We present algorithms for arithmetic and for solving polynomial e

On the Units of Algebraic Number Fields
✍ I. Yamaguchi; H. Takeuchi πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 99 KB

Let \(K\) be an algebraic number field and \(k\) be a proper subfield of \(K\). Then we have the relations between the relative degree \([K: k]\) and the increase of the rank of the unit groups. Especially, in the case of \(m\) th cyclotomic field \(Q\left(\zeta_{m}\right)\), we determine the number

GrΓΆbner Bases in Orders of Algebraic Num
✍ David Andrew Smith πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 281 KB

We prove that any order O of any algebraic number field K is a reduction ring. Rather than showing the axioms for a reduction ring hold, we start from scratch by well-ordering O, defining a division algorithm, and demonstrating how to use it in a Buchberger algorithm which computes a GrΓΆbner basis g