Timeline for Varieties invariant under affine transformations
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2013 at 17:17 | vote | accept | Michael | ||
| Dec 18, 2013 at 17:16 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Corrected my use of 'Euclidean' and explained the use of a 'division' algorithm more clearly
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| Dec 18, 2013 at 16:56 | comment | added | Robert Bryant | @KConrad: You are right; I'm not using 'Euclidean' in its standard sense, which is not a good idea. I just meant that there is an effective (multivariate) division algorithm for this ring, using, say, a total monomial ordering, à la Buchberger's algorithm using Gröbner bases. I'll edit my answer to reflect this. | |
| Dec 18, 2013 at 16:48 | comment | added | KConrad | What do you mean at the end by saying "$k[x^1,\dots,x^n]$ is a Euclidean ring"? The ring of polynomials in more than one variable over a field is not a Euclidean domain (i.e., no division algorithm) since it is not a PID. Maybe you just had in mind that the coefficient ring $k$ is a field (a trivial type of Euclidean domain). | |
| Dec 18, 2013 at 16:46 | history | edited | KConrad | CC BY-SA 3.0 |
deleted 1 characters in body
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| Dec 18, 2013 at 16:42 | history | edited | Robert Bryant | CC BY-SA 3.0 |
improved the exposition of the relation between the full affine symmetry group and its identity component
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| Dec 18, 2013 at 11:38 | history | edited | Robert Bryant | CC BY-SA 3.0 |
added some clarifying comments about the connected components of the symmetry group
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| Dec 18, 2013 at 11:28 | history | answered | Robert Bryant | CC BY-SA 3.0 |