Timeline for Is the regularity of finitely generated rings decidable?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2014 at 15:49 | comment | added | Damien Robert | @Yasuda: you can do Gröbner basis over R when you know how to do linear algebra over R (see for instance the survey "Grobner Bases with Coefficients in Rings" by Franz Paue). So in particular when R is an euclidean domain like $\mathbb{Z}$ (of course in practice it will be a lot slower than over a field, and over fields Gröbner basis computation can be quite long already...) At least over $\mathbb{Z}$ it is implemented by Singular (hence Sage) and Magma. | |
| Oct 19, 2014 at 11:23 | vote | accept | Takehiko Yasuda | ||
| Oct 18, 2014 at 12:04 | comment | added | Takehiko Yasuda | I like your strategy, which sounds quite probable! But let me ask a question to understand better. I think that many algorithms for polynomial rings over fields are based on the Gröbner basis theory. I don't know to what extent it is generalized to polynomial rings over integers. For instance, is there an algorithm to tell whether an ideal of $\mathbb{Z}[x_1,\dots,x_n]$ with explicit generators is equal to the entire ring? Can you also mention a few softwares to which some of algorithms you suggested might be implemented? | |
| Oct 17, 2014 at 16:52 | review | First posts | |||
| Oct 17, 2014 at 16:53 | |||||
| Oct 17, 2014 at 16:50 | history | answered | Count Dracula | CC BY-SA 3.0 |