File:Zeroes of Cubic.svg
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 600 × 400 pixels. Other resolutions: 320 × 213 pixels | 640 × 427 pixels | 1,024 × 683 pixels | 1,280 × 853 pixels | 2,560 × 1,707 pixels.
Original file (SVG file, nominally 600 × 400 pixels, file size: 3 KB)
Captions
Captions
Add a one-line explanation of what this file represents
Summary
[edit]
| Description | Number of real zeroes of z^3+pz+q. For pairs (p,q) on the green curve the polynomial has a zero in common with its first derivative and therefore possesses at least one multiple zero. For pairs (p,q) off the line all zeroes are simple. To the left of the line (blue zone) there are three distinct real zeroes; to the right of the line (yellow zone) there is exactly one real zero. |
| Date | |
| Source | Own work |
| Author | Lieven Smits |
Licensing
[edit]
I, Lieven Smits, the copyright holder of this work, hereby publishes it under the following licenses:
|
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. |
  
|
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
| Attribution: I, Lieven Smits | ||
| ||
| This licensing tag was added to this file as part of the GFDL licensing update. |
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.
Attribution: I, Lieven Smits
- 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.
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 | 21:24, 11 July 2007 | | 600 × 400 (3 KB) | Lieven Smits (talk | contribs) | {{Information |Description=Number of real zeroes of z^3+pz+q. For pairs (p,q) on the green curve the polynomial has a zero in common with its first derivative and therefore possesses at least one multiple zero. For pairs (p,q) off the line all zeroes are |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on nl.wikipedia.org
