Originally, this code was and currently still is available in the ToricVarieties_project. To make this tool available to other computer algebra systems, the code has been moved to this repository at the beginning of 2023. For more background, see e.g. this article and references therein.
| Description |
Test result |
Runtime (min) |
| Basic tests |
 |
2 |
| Simple root counting |
 |
2 |
| Polytope |
$\overline{K}_{B_3}^3$ |
Elliptic curve |
Geometric multiplicity $\mu$
|
Total number of roots |
Estimate for number of triangulations $T$
|
Upper bound for number of configurations |
Runtime (min) |
Test result |
| 8 |
6 |
✔️ |
$12^3$ |
$12^8$ |
$3.867 \times 10^{13} \leq T \leq 2.828 \times 10^{16}$ |
$10^{24}$ |
2 |
 |
| 4 |
6 |
❌ |
$12^4$ |
$12^8$ |
$3.188 \times 10^{11}$ |
$10^{20}$ |
2 |
 |
| 134 |
6 |
❌ |
$12^4$ |
$12^8$ |
$7.538 \times 10^{10}$ |
$10^{19}$ |
2 |
 |
| 128, 130, 136, 236 |
6 |
❌ |
$12^4$ |
$12^8$ |
$3.217 \times 10^{11}$ |
$10^{20}$ |
1 |
 |
| 88 |
10 |
✔️ |
$20^5$ |
$20^{12}$ |
$5.231 \times 10^{10} \leq T \leq 1.246 \times 10^{14}$ |
$10^{30}$ |
3 |
 |
| 110 |
10 |
✔️ |
$20^5$ |
$20^{12}$ |
$5.239 \times 10^{8}$ |
$10^{24}$ |
4 |
 |
| 272, 274 |
10 |
✔️ |
$20^5$ |
$20^{12}$ |
$3.212 \times 10^{12} \leq T \leq 2.481 \times 10^{15}$ |
$10^{31}$ |
4 |
 |
| 387 |
10 |
✔️ |
$20^5$ |
$20^{12}$ |
$6.322 \times 10^{10} \leq T \leq 6.790 \times 10^{12}$ |
$10^{28}$ |
9 |
 |
| 798, 808, 810, 812 |
10 |
✔️ |
$20^5$ |
$20^{12}$ |
$1.672 \times 10^{10} \leq T \leq 2.515 \times 10^{13}$ |
$10^{29}$ |
12 |
 |
| 254 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$1.568 \times 10^{10}$ |
$10^{26}$ |
6 |
 |
| 52 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$1.248 \times 10^{8}$ |
$10^{24}$ |
7 |
 |
| 302 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$5.750 \times 10^{7}$ |
$10^{23}$ |
3 |
 |
| 786 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$9.810 \times 10^{8}$ |
$10^{24}$ |
74 |
 |
| 762 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$1.087 \times 10^{11} \leq T \leq 2.854 \times 10^{13}$ |
$10^{30}$ |
35 |
 |
| 417 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$1.603 \times 10^{9}$ |
$10^{25}$ |
34 |
 |
| 838 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$4.461 \times 10^{9}$ |
$10^{25}$ |
67 |
 |
| 782 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$3.684 \times 10^{9}$ |
$10^{25}$ |
124 |
 |
| 377, 499, 503 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$4.461 \times 10^{9}$ |
$10^{25}$ |
98 |
 |
| 1348 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$4.285 \times 10^{9}$ |
$10^{25}$ |
239 |
 |
| 882, 856 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$3.180 \times 10^{9}$ |
$10^{25}$ |
96 |
 |
| 1340 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$4.496 \times 10^{9}$ |
$10^{25}$ |
> 6 hours |
❌ |
| 1879 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$4.461 \times 10^{9}$ |
$10^{25}$ |
> 6 hours |
❌ |
| 1384 |
10 |
❌ |
$20^6$ |
$20^{12}$ |
$7.040 \times 10^{9}$ |
$10^{25}$ |
> 6 hours |
❌ |
(Runtimes are taken from #28.)
