Timeline for Rational exponential expressions
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2010 at 12:53 | comment | added | fedja | The crucial difficulty is that all proofs of the sign preservation at infinity for Hardy functions I know have the following logical step in some form: if the derivative preserves sign near infinity, then the function itself preserves sign near infinity. This is completely useless from the computational standpoint because it doesn't allow you to figure out which of the 2 possible signs the function preserves in finite number of steps. The transseries approach clearly has a similar problem. You have to decide if infinitely many terms are equal before you can proceed to the next order terms. | |
| Jan 28, 2010 at 11:02 | comment | added | Charles Stewart | This "eventual trichotomy" property is something I had been thinking about: thank you for the reference (and cf. archive.org/details/ordersofinfinity00harduoft); I must clearly study the proof. I'll take a look at the transseries intro paper; this is a new field for me. | |
| Jan 27, 2010 at 18:17 | comment | added | Joel David Hamkins | In the case of multi-variable polynomials, the difference between the reals and the integers is the difference between decidability and undecidability. This is becasue Tarski's theorem shows that the decision problem for whether p(x1,...,xn) = 0 has a solution is decidable in the reals, but MRDP shows it is undecidable in the integers. But I agree that the question is likely decidable in the one-variable case. | |
| Jan 27, 2010 at 17:17 | comment | added | David E Speyer | I copied these links from the related question: mathoverflow.net/questions/3057/… | |
| Jan 27, 2010 at 17:16 | history | answered | David E Speyer | CC BY-SA 2.5 |