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.
Code coverage
General tests
Description
Test result
Runtime (min)
Basic tests
2
Simple root counting
2
Root counting for QSMs
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
❌
$20^6$
$20^{12}$
$1.087 \times 10^{11} \leq T \leq 2.854 \times 10^{13}$
