Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On computing the discriminant of an algebraic number field


Author: Theresa P. Vaughan
Journal: Math. Comp. 45 (1985), 569-584
MSC: Primary 11R29; Secondary 11Y40
MathSciNet review: 804946
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f(x)$ be a monic irreducible polynomial in $ {\mathbf{Z}}[x]$, and r a root of $ f(x)$ in C. Let K be the field $ {\mathbf{Q(r)}}$ and $ \mathcal{R}$ the ring of integers in K. Then for some $ k \in {\mathbf{Z}}$, $ \operatorname{disc}\,{\mathbf{r}} = {k^2}\,\operatorname{disc}\,\mathcal{R}$ . In this paper we give constructive methods for (a) deciding if a prime p divides k, and (b) if $ p\vert k$, finding a polynomial $ g(x) \in {\mathbf{Z}}[x]$ so that $ g(x)\nequiv 0\;\pmod p$ but $ g({\mathbf{r}})/p \in \mathcal{R}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11R29, 11Y40

Retrieve articles in all journals with MSC: 11R29, 11Y40


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1985-0804946-1
PII: S 0025-5718(1985)0804946-1
Article copyright: © Copyright 1985 American Mathematical Society