Timeline for Does there exist a general theory of "arithmetic complexity"/"arithmetic height"?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2010 at 18:51 | history | edited | Sam Derbyshire | CC BY-SA 2.5 |
Comment about computational effectivity
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| Mar 9, 2010 at 18:10 | history | edited | Sam Derbyshire |
Added a tag
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| Mar 9, 2010 at 18:03 | history | edited | Sam Derbyshire | CC BY-SA 2.5 |
Typo
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| Mar 9, 2010 at 17:40 | comment | added | Sam Derbyshire | But the thing is, I think you should be able to get away without computing it: there should be finitely many algebraic numbers up to a certain bound of h(a) (I probably got the wrong definition for this), so you can check all possibilities and see which ones agree up to the desired precision, and which of those have the lowest height. | |
| Mar 9, 2010 at 14:10 | answer | added | kakaz | timeline score: 1 | |
| Mar 9, 2010 at 0:57 | history | edited | Sam Derbyshire | CC BY-SA 2.5 |
Typos
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| Mar 9, 2010 at 0:51 | comment | added | Bjorn Poonen | Although your formula for h(a) looks explicit, you can't actually use it directly if all you have is a decimal approximation to a. You first need to figure out the minimal polynomial of a over Q. And that is exactly what LLL is good for, as pointed out by Kevin. | |
| Mar 9, 2010 at 0:15 | answer | added | Kevin Buzzard | timeline score: 8 | |
| Mar 9, 2010 at 0:10 | history | edited | Sam Derbyshire | CC BY-SA 2.5 |
Added a possible arithmetic height function - the logarithmic height
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| Mar 8, 2010 at 23:37 | answer | added | Neel Krishnaswami | timeline score: 1 | |
| Mar 8, 2010 at 23:30 | answer | added | Joel David Hamkins | timeline score: 5 | |
| Mar 8, 2010 at 23:19 | history | asked | Sam Derbyshire | CC BY-SA 2.5 |