Timeline for Algorithm to detect if an element of a (commutative) ring is in a subring?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2013 at 15:49 | answer | added | Benjamin Steinberg | timeline score: 2 | |
| Jul 16, 2013 at 14:39 | comment | added | user37187 | The heart of the SAGBI idea seems to be the following. If we work in a polynomial ring in finitely many variables, then we can totally order the monomials, by lexicographically ordering the exponents. This is a well-ordering, so if you have a nice subset of your subring then you can attempt to do Euclid (always killing the monomial which is max wrt your order) and it will terminate. That seems to be it really, the problem being that you might not be able to find this nice subset. However because I have denominators my exponents are Z-valued so the algorithm may well not terminate. | |
| Jul 16, 2013 at 14:14 | comment | added | darij grinberg | Unfortunately I don't know the theory. | |
| Jul 16, 2013 at 14:12 | comment | added | user37187 | I can't find a clear reference for these bases but clearly this comment may ultimately be very useful, so thanks Darij. Do you know the theory? Is there more content to it than "lexicographically order the monomials and then hope?". Presumably! Two worrying points are: (1) the theory seems to be only for the case that the big ring is a polynomial ring and (2) apparently "a finite sagbi basis may not exist". Ideally I'd like to be able to see through the dust and decide whether these things have got a chance of helping. I will try to report back if I make any sense of things. | |
| Jul 16, 2013 at 12:49 | comment | added | darij grinberg | Maybe google for "sagbi bases". | |
| Jul 16, 2013 at 12:46 | review | First posts | |||
| Jul 16, 2013 at 13:41 | |||||
| Jul 16, 2013 at 12:44 | history | edited | user37187 | CC BY-SA 3.0 |
added more examples of things I don't know.
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| Jul 16, 2013 at 12:29 | history | asked | user37187 | CC BY-SA 3.0 |