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Summary
| Description |
English: A fundamental domain of the maximal order of the field K obtained by adjoining to Q a root of f(x) = x3 − x2 − 2x + 1. This field is a Galois extension of degree 3. Its discriminant is 49=72. Accordingly, the volume of the fundamental domain is 7. A basis for its lattice is (approximately) {(1,1,1),(−1.2469796037,0.4450418679,1.8019377358),(1.8019377358,−1.2469796037,0.4450418679)}. Computed using PARI/GP. Plotted using Mathematica. |
| Date | |
| Source | Own work |
| Author | RobHar |
| Other versions | File:Discriminant49CubicFieldFundamentalDomain.svg (svg version without shading) |
This diagram was created with
Mathematica.
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the
Creative Commons
Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:41, 13 June 2010 |
| 802 × 670 (10 KB) | RobHar | bigger numbers, remove zeroes, fewer ticks |
| 02:46, 13 June 2010 |
 | 940 × 782 (11 KB) | RobHar | {{Information |Description={{en|1=A fundamental domain of the maximal order of the field ''K'' obtained by adjoining to '''Q''' a root of ''f''(''x'') = ''x''<sup>3</sup> − ''x''<sup>2</sup> − 2''x'' + 1 |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Global file usage
The following other wikis use this file:
- Usage on fr.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ru.wikipedia.org
Size of this preview:
718 × 600 pixels. Other resolutions:
287 × 240 pixels |
575 × 480 pixels |
802 × 670 pixels.
Original file (802 × 670 pixels, file size: 10 KB, MIME type: image/png)
| This is a file from the
Wikimedia Commons. Information from its
description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
| Description |
English: A fundamental domain of the maximal order of the field K obtained by adjoining to Q a root of f(x) = x3 − x2 − 2x + 1. This field is a Galois extension of degree 3. Its discriminant is 49=72. Accordingly, the volume of the fundamental domain is 7. A basis for its lattice is (approximately) {(1,1,1),(−1.2469796037,0.4450418679,1.8019377358),(1.8019377358,−1.2469796037,0.4450418679)}. Computed using PARI/GP. Plotted using Mathematica. |
| Date | |
| Source | Own work |
| Author | RobHar |
| Other versions | File:Discriminant49CubicFieldFundamentalDomain.svg (svg version without shading) |
This diagram was created with
Mathematica.
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the
Creative Commons
Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
|
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:41, 13 June 2010 |
| 802 × 670 (10 KB) | RobHar | bigger numbers, remove zeroes, fewer ticks |
| 02:46, 13 June 2010 |
| 940 × 782 (11 KB) | RobHar | {{Information |Description={{en|1=A fundamental domain of the maximal order of the field ''K'' obtained by adjoining to '''Q''' a root of ''f''(''x'') = ''x''<sup>3</sup> − ''x''<sup>2</sup> − 2''x'' + 1 |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Global file usage
The following other wikis use this file:
- Usage on fr.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ru.wikipedia.org