Skip to main content Accessibility help
×
Home
Hostname: page-component-59b7f5684b-j5sqr Total loading time: 0.24 Render date: 2022-09-27T02:11:57.082Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

A Database for Field Extensions of the Rationals

Published online by Cambridge University Press:  01 February 2010

Jürgen Klüners
Affiliation:
Universität Heidelberg, IWR, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany, klueners@iwr.uni-heidelberg.de, http://www.iwr.uni-heidelberg.de/~Juergen.Klueners
Gunter Malle
Affiliation:
FB Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany, malle@mathematik.uni-kassel.de, http://www.mathematik.uni-kassel.de/~malle/

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2001

References

1.Acciaro, V. and Klüners, J., ‘Computing local Artin maps, and solvability of norm equations’, J. Symb. Comput. 30 (2000) 239252.CrossRefGoogle Scholar
2.Beckmann, S., ‘IS every extension of ℚ the specialization of a branched covering?’, J. Algebra 164 (1994) 430451.CrossRefGoogle Scholar
3.Belabas, K., ‘A fast algorithm to compute cubic fields’, Math. Comput. 66 (1997) 12131237.CrossRefGoogle Scholar
4.Berge, A., Martinet, J. and Olivier, M., ‘The computation of sextic fields with a quadratic subfield’, Math. Comput. 54 (1990) 869884.CrossRefGoogle Scholar
5.Böge, S., ‘Witt-Invariante und ein gewisses Einbettungsproblem’, J. Reine Angew. Math. 410 (1990) 153159.Google Scholar
6.Buchmann, J., Ford, D. and Pohst, M., ‘Enumeration of quartic fields of small discriminant’, Math. Comput. 61 (1993) 873879.CrossRefGoogle Scholar
7.Cohen, H., A course in computational algebraic number theory (Springer, Berlin, 1993).CrossRefGoogle Scholar
8.Cohen, H., Advanced topics in computational number theory (Springer, Berlin, 2000).CrossRefGoogle Scholar
9.Cohen, H., Diaz, F. Diaz Y and Olivier, M., ‘Tables of octic fields with a quartic subfield’, Math. Comput. 68 (1999) 17011716.CrossRefGoogle Scholar
10.Daberkow, M., Fieker, C., Klüners, J., Pohst, M., Roegner, K., Schörnig, M. and Wildanger, K., ‘KANT V4’, J. Symb. Comput. 24 (1997) 267283.CrossRefGoogle Scholar
11.Diaz, F. Diaz Y, ‘Valeurs minima du discriminant pour certains types de corps de degré 7’, Ann. Inst. Fourier 34 (1984) 2938.CrossRefGoogle Scholar
12.Diaz, F. Diaz Y, ‘Petits discriminants des corps de nombres totalement imaginaires de degré 8’. J. Number Theory 25 (1987) 3452.CrossRefGoogle Scholar
13.Diaz, F. Diaz Y, ‘Discriminant minimal et petits discriminants des corps de nombres de degré 7 avec cinq places réelles’, J. London Math. Soc. (2) 38 (1988) 3346.CrossRefGoogle Scholar
14.Diaz, F. Diaz Y and Olivier, M., ‘Imprimitive ninth-degree number fields with small discriminants’, Math. Comput. 64, microfiche suppl. (1995) 305321.CrossRefGoogle Scholar
15.Fieker, C., ‘Computing class fields via the Artin map’, Math. Comput. 70 (2001) 12931303.CrossRefGoogle Scholar
16.Fieker, C. and Klüners, J., ‘Minimal discriminants for fields with Frobenius groups as Galois groups', IWR-Preprint 2001-33, Universität Heidelberg, 2001.Google Scholar
17.Ford, D. and Pohst, M., ‘The totally real A5 extension of degree 6 with minimum discriminant’, Exp. Math. 1 (1992) 231235.CrossRefGoogle Scholar
18.Ford, D. and Pohst, M., ‘The totally real A6 extension of degree 6 with minimum discriminant’, Exp. Math. 2 (1993) 231232.CrossRefGoogle Scholar
19.Ford, D., Pohst, M., Daberkow, M. and H. Nasser, ‘The S5 extensions of degree 6 with minimum discriminant’, Exp. Math. 7 (1998) 121124.CrossRefGoogle Scholar
20.Haran, D. and Jarden, M., ‘The absolute Galois group of a pseudo real closed field’, Ann. Sc. Norm. Super. Pisa 12 (1985) 449489.Google Scholar
21.Klüners, J. and Malle, G., ‘Explicit Galois realization of transitive groups of degree up to 15’, J. Symb. Comput. 30 (2000) 675716.CrossRefGoogle Scholar
22.Koch, H., Number theory-algebraic numbers and functions (Amer. Math. Soc, Providence, RI, 2000).Google Scholar
23.Malle, G., ‘Multi-parameter polynomials with given Galois group’, J. Symb. Comput. 30(2000) 717731.CrossRefGoogle Scholar
24.Malle, G. and Matzat, B. H., Inverse Galois theory (Springer, Berlin, 1999).CrossRefGoogle Scholar
25.Narkiewicz, W., Elementary and analytic theory of algebraic numbers (Springer, Berlin, 1989).Google Scholar
26.Olivier, M., ‘Corps sextiques primitifs. IV’, Semin. Theor. Nombres Bordx. (II) 3 (1991) 381404.CrossRefGoogle Scholar
27.Olivier, M., ‘The computation of sextic fields with a cubic subfield and no quadratic subfield’, Math. Comput. 58 (1992) 419432.CrossRefGoogle Scholar
28.Pohst, M., Martinet, J. and Diaz, F. Diaz Y, ‘The minimum discriminant of totally real octic fields’, J. Number Theory 36 (1990) 145159.CrossRefGoogle Scholar
29.Pohst, M., ‘The minimum discriminant of seventh degree totally real algebraic number fields’, Number theory and algebra (Academic Press, New York, 1977) 235240.Google Scholar
30.Pohst, M., ‘On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields’, J. Number Theory 14 (1982) 99117.CrossRefGoogle Scholar
31.Schwarz, A., Pohst, M. and Diaz, F. Diaz Y, ‘A table of quintic number fields’, Math. Comput. 63 (1994) 361376.CrossRefGoogle Scholar
32.Serre, J.-P., Topics in Galois theory (Jones and Bartlett, Boston, 1992).Google Scholar
Supplementary material: File

Kluners and Malle Appendix

Appendix

Download Kluners and Malle Appendix(File)
File 4 MB
You have Access
33
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A Database for Field Extensions of the Rationals
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A Database for Field Extensions of the Rationals
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A Database for Field Extensions of the Rationals
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *