Timeline for computability and geometry
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 2, 2011 at 13:00 | comment | added | Henry Cohn | @Will Jagy: Do you know what Lam meant? Here's a weak version. Let $E$ be the set of expressions for constructible numbers (you can use rational numbers, arithmetic operations, and square roots; no division by zero or square roots of negative numbers), and let $e : E \to \mathbb{R}$ be the evaluation map. Then we want a computable function $f : E \to E$ such that for $\alpha,\beta in E$, we have $e(\alpha) = e(\beta)$ if and only if $f(\alpha) = f(\beta)$, and $f(f(\alpha)) = f(\alpha)$. Such a function does exist, but I imagine Lam meant there's no canonical choice of canonical form? | |
| Jul 6, 2010 at 9:00 | answer | added | grshutt | timeline score: 1 | |
| Jul 5, 2010 at 21:28 | answer | added | Joel David Hamkins | timeline score: 4 | |
| Jul 5, 2010 at 21:09 | vote | accept | Davide | ||
| Jul 5, 2010 at 21:09 | |||||
| Jul 5, 2010 at 19:58 | answer | added | Igor Pak | timeline score: 5 | |
| Jul 5, 2010 at 18:50 | comment | added | Will Jagy | I once asked T. Y. Lam a related question, he was firm in saying there is no canonical form possible for numbers in the "constructible numbers," meaning the smallest field extension of the rationals such that the square root of any positive element is also in the field. | |
| Jul 5, 2010 at 15:55 | comment | added | Joseph O'Rourke | This paper of Pippenger's is often cited in this context, but I haven't read it myself: "Computational complexity in algebraic function fields," 1979. portal.acm.org/citation.cfm?id=1382433.1382606 | |
| Jul 5, 2010 at 15:35 | history | asked | Davide | CC BY-SA 2.5 |