Timeline for Algorithm to generate random polynomials which has root in Q(a) where a is another algebraic number
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 11, 2016 at 12:37 | comment | added | Pranjal Dutta | There is one problem. First of all we want to generate it 'randomly'. In order to that that if we take $a_0,..,a_n$ and take minimal poly of $a_0 \alpha + ..$ complexity of finding the minimal poly will increase very much (because the degree and coeffs will be much larger) . | |
| Apr 11, 2016 at 0:35 | comment | added | Gerry Myerson | The polynomial $x-17$ has exactly one root in the specified field, and while the polynomial may not be random, its root is (see, e.g., prasoondiwakar.com/wordpress/trivia/17-is-the-random-number). | |
| Apr 10, 2016 at 21:28 | comment | added | Dror Speiser | Take a basis of $\mathbb{Q}(\alpha)/\mathbb{Q}$ (say $1,\alpha,...$), choose rationals $a_0,a_1,...$ randomly somehow, and return the minimal polynomial of $a_0+a_1\alpha+...$. This polynomial will have a root in $\mathbb{Q}(\alpha)$. Note that it might have more than one root, depending, for example, on the galois group of $\mathbb{Q}(\alpha)/\mathbb{Q}$. | |
| Apr 10, 2016 at 20:12 | review | First posts | |||
| Apr 10, 2016 at 20:13 | |||||
| Apr 10, 2016 at 20:08 | history | asked | Pranjal Dutta | CC BY-SA 3.0 |