Timeline for Approximating Ehrhart Polynomial of Rational n-Tetrahedron
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2016 at 19:08 | comment | added | matthias beck | Yes, that's a typo: it should be $-n$, as you said. (Thanks for catching it!) | |
| Feb 27, 2016 at 19:58 | vote | accept | Jiro | ||
| Feb 27, 2016 at 16:20 | comment | added | Jiro | I see how this could work. Just a quick question, in your book p.151, (8.4), is this really $B_d^A(-t)$ or is it $B_d^A(-n)$? | |
| Feb 26, 2016 at 23:15 | comment | added | matthias beck | Yes, the pairwise co-prime case will still involve Bernoulli-Barnes polynomials--in fact, they give all coefficients in this case except the last one. | |
| Feb 25, 2016 at 22:30 | comment | added | Jiro | In terms of approximation, what I'm trying right now, is to replace the $T$ with an equilateral tetrahedron $T_e$ such that $d_e = d'_1 = \dots = d'_n$, where $d_e = \sqrt[n]{\prod_{i=1}^n d_i}$. The equilateral tetrahedron is very simple to scale and the leading coefficient is equal as the volumes of $T$ and $T_e$ are equal. I'm hoping that if the $d_i$'s are not too far away from $d_e$, the error won't be too big. Anyway to provide evidence that this doesn't go wrong horribly? | |
| Feb 25, 2016 at 22:30 | comment | added | Jiro | I've just found in an earlier paper that for pairwise co-prime $d_1, \dots, d_n$ all the coefficients (except $c_0$) are constant. This would be a possible restriction for me. Would the Bernoulli polynomials still helpful in this case? | |
| Feb 25, 2016 at 17:47 | history | answered | matthias beck | CC BY-SA 3.0 |