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RootCounter

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

codecov

General tests

Description Test result Runtime (min)
Basic tests BasicTests 2
Simple root counting SimpleRootCounting 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 Polytope8
4 6 $12^4$ $12^8$ $3.188 \times 10^{11}$ $10^{20}$ 2 Polytope4
134 6 $12^4$ $12^8$ $7.538 \times 10^{10}$ $10^{19}$ 2 Polytope134
128, 130, 136, 236 6 $12^4$ $12^8$ $3.217 \times 10^{11}$ $10^{20}$ 1 Polytope128
88 10 ✔️ $20^5$ $20^{12}$ $5.231 \times 10^{10} \leq T \leq 1.246 \times 10^{14}$ $10^{30}$ 3 Polytope88
110 10 ✔️ $20^5$ $20^{12}$ $5.239 \times 10^{8}$ $10^{24}$ 4 Polytope110
272, 274 10 ✔️ $20^5$ $20^{12}$ $3.212 \times 10^{12} \leq T \leq 2.481 \times 10^{15}$ $10^{31}$ 4 Polytope272
387 10 ✔️ $20^5$ $20^{12}$ $6.322 \times 10^{10} \leq T \leq 6.790 \times 10^{12}$ $10^{28}$ 9 Polytope387
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 Polytope798
254 10 $20^6$ $20^{12}$ $1.568 \times 10^{10}$ $10^{26}$ 6 Polytope254
52 10 $20^6$ $20^{12}$ $1.248 \times 10^{8}$ $10^{24}$ 7 Polytope52
302 10 $20^6$ $20^{12}$ $5.750 \times 10^{7}$ $10^{23}$ 3 Polytope302
786 10 $20^6$ $20^{12}$ $9.810 \times 10^{8}$ $10^{24}$ 74 Polytope786
762 10 $20^6$ $20^{12}$ $1.087 \times 10^{11} \leq T \leq 2.854 \times 10^{13}$ $10^{30}$ 35 Polytope762
417 10 $20^6$ $20^{12}$ $1.603 \times 10^{9}$ $10^{25}$ 34 Polytope417
838 10 $20^6$ $20^{12}$ $4.461 \times 10^{9}$ $10^{25}$ 67 Polytope838
782 10 $20^6$ $20^{12}$ $3.684 \times 10^{9}$ $10^{25}$ 124 Polytope782
377, 499, 503 10 $20^6$ $20^{12}$ $4.461 \times 10^{9}$ $10^{25}$ 98 Polytope377
1348 10 $20^6$ $20^{12}$ $4.285 \times 10^{9}$ $10^{25}$ 239 Polytope1348
882, 856 10 $20^6$ $20^{12}$ $3.180 \times 10^{9}$ $10^{25}$ 96 Polytope882
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.)