Timeline for Is there an algorithm for determining whether an expression involving nested radicals is rational?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| S Oct 27, 2019 at 10:16 | history | suggested | user21820 | CC BY-SA 4.0 |
added much simpler derivation for the incredible identity
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| Oct 27, 2019 at 3:51 | review | Suggested edits | |||
| S Oct 27, 2019 at 10:16 | |||||
| Oct 25, 2019 at 9:56 | comment | added | François Brunault | Why is the case of the value 0 different? In Pari/GP the command for detecting rationality is lindep([1,x]) which is a synonym for algdep(x,1). The case where x is a complex number very close to 0 is not different from the other ones. | |
| Oct 25, 2019 at 6:57 | comment | added | Esteban Crespi | @FrançoisBrunault you are right but in the case of value 0 you would use algdep(0,2) which is not very useful, I have added an example to clarify what I mean | |
| Oct 25, 2019 at 6:52 | history | edited | Esteban Crespi | CC BY-SA 4.0 |
Added an example
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| Oct 24, 2019 at 20:52 | comment | added | François Brunault | Regarding Pari/GP, I guess that you mean the algdep command, which indeed works well. But since here we only need to guess whether $\alpha$ is rational, we can even use lindep (LLL with 2 vectors) | |
| Oct 24, 2019 at 20:50 | comment | added | François Brunault | Computing a polynomial vanishing at $\alpha$ is possible without too much effort, using resultants for sums/products, and the obvious substition for radicals. Using numerical evaluation as you say, you can even find the minimal polynomial at each step. Actually this method may be the best thing to do in practice. (But to be certain we need something like interval arithmetic, at least for the operations of sums/products/radicals.) | |
| Oct 24, 2019 at 19:26 | history | answered | Esteban Crespi | CC BY-SA 4.0 |