Timeline for Roots of a polynomial in several variables [closed]
Current License: CC BY-SA 2.5
10 events
when toggle format | what | by | license | comment | |
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Jan 30, 2016 at 10:10 | history | closed |
Peter LeFanu Lumsdaine Federico Poloni Alex Degtyarev Wolfgang user1688 |
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Jan 30, 2016 at 8:39 | review | Close votes | |||
Jan 30, 2016 at 10:10 | |||||
Jun 20, 2010 at 15:24 | comment | added | Olivier | Many thanks for your kind answers. I now understand that the question is too broad, and its solutions are far beyond my skills. I will work at narrowing my question, and come back here if I cannot find a solution by myself. Tnaks again, Olivier | |
Jun 18, 2010 at 20:22 | comment | added | Dan Piponi | It makes a big difference whether the coefficients are arbitrary approximately known reals, or simple constants that are known exactly. If you give more detail on this, and the type of polynomials, this might possibly turn into an MO question that gets modded up. | |
Jun 18, 2010 at 17:58 | comment | added | S. Carnahan♦ | I second Steve Huntsman's book recommendation. I'm afraid the question as it stands is a bit broad for MathOverflow - since the set of roots forms a complex hypersurface, it is difficult to algorithmically "find" all of them, except by descriptive means (e.g., using the polynomial itself, or computing interesting invariants of the zero set). | |
Jun 18, 2010 at 17:42 | comment | added | Steve Huntsman | ...If you truly need to learn about this stuff in any generality at all, a good way to start would be (to first acquaint yourself with the basic notions of abstract algebra like [groups], rings, fields, and ideals and then) check out this book: books.google.com/books?id=7eLkq0wQytAC | |
Jun 18, 2010 at 17:40 | comment | added | Steve Huntsman | The study zeros of polynomials is a vast and sophisticated subject called algebraic geometry. Usually the set of zeros is a curve or surface of some sort, called a variety (en.wikipedia.org/wiki/Algebraic_variety). One of the basic insights of algebraic geometry is that varieties correspond to algebraic objects called ideals (see the same wiki page). In practice these algebraic objects are what is used to perform computations on varieties... | |
Jun 18, 2010 at 16:46 | answer | added | Stopple | timeline score: 2 | |
Jun 18, 2010 at 16:19 | answer | added | Charles Matthews | timeline score: 1 | |
Jun 18, 2010 at 16:14 | history | asked | Olivier | CC BY-SA 2.5 |