Comparison of different computational strategies in GINV

From Invo

The timings measured in run on machine 2xXeon-5410@2.33Ghz with 16Gb of RAM, running Gentoo 2008.0

Information in columns:

cardinality: JB: Janet basis
JLB: Janet-like basis
GB:Groebner basis

* means that the timing exceeds 24 hours or there was not enough memory to compute the example.

degJ degJL highJ highJL lowJ lowJL JB JLB GB Hilbert polynomial
assur44 8.1 7.9 3.8 4.3 3.6 3.3 94 94 87
aubry2 21.4 22.9 5.5 8.8 6.8 9.9 135 123 79
augot 6.0 4.5 0.3 80.6 1.5 151.8 249 9 9
benchmark_D1 5.8 2.6 0.9 1.0 0.9 1.0 104 104 86
benchmark_i1 46.2 58.8 24.9 25.6 24.3 26.6 147 147 118
butcher8 0.7 0.7 0.2 0.2 0.3 0.3 64 64 54
chemequs 0.3 0.3 0.2 0.2 0.3 0.3 20 20 20
chemkin 7.5 8.2 4.7 5.0 4.3 4.7 117 116 90
cohn3 152.6 185.4 13.4 21.9 11.4 21.7 106 103 92
cpdm5 0.8 0.8 0.8 0.8 0.8 0.8 83 83 77
cyclic7 37.2 38.1 32.3 29.1 28.0 25.3 210 210 209
cyclic8 3774.2 3686.8 2090.8 1734.2 1755.2 1419.2 384 383 372
d1 5.8 2.6 0.9 1.0 1.0 1.0 104 104 86
des18_3 0.1 0.1 0.1 0.1 0.1 0.1 104 76 39
des22_24 0.3 0.3 0.4 0.4 0.4 0.4 129 115 45
discret3 6745.1 8557.2 4052.0 5589.7 4282.6 5725.8 164 154 147
dl 145.5 193.6 40.7 51.5 43.0 48.5 538 491 323
ducos7_3 25.0 21.7 7.7 10.4 9.4 13.6 135 122 80
ducos7_5 302.7 * 432.4 449.3 474.3 494.6 1 1 1
ducos8 23.3 24.0 32.5 9.6 56.8 12.5 176 23 11
eco10 29.1 33.2 28.2 29.3 27.4 29.1 336 279 203
eco11 363.4 377.6 287.8 310.9 278.4 304.7 662 561 389
eco12 3452.8 3837.7 2521.7 2770.1 2531.2 2730.9 1329 1109 743
eco8 0.3 0.3 0.3 0.3 0.3 0.3 86 75 59
eco9 3.5 3.8 2.4 2.6 2.4 2.6 172 147 106
extcyc5 1.1 1.3 0.6 0.9 0.7 0.9 102 102 102
extcyc6 103.3 88.4 96.1 94.2 74.1 69.4 243 242 242
f744 5.8 5.7 1.4 1.4 1.4 1.4 162 159 87
f855 63.3 63.8 17.0 17.1 18.9 19.0 264 261 148
fabrice24 37.3 37.3 3.4 3.4 3.5 3.5 55 55 54
filter9 4.1 3.7 0.7 0.8 2.0 1.8 232 226 153
hairer2 49.1 48.3 43.3 43.2 43.3 42.9 453 389 128
hairer3 * * * 0.1 1.0 0.1 1 1 1
hcyclic7 51.9 29.1 34.8 34.6 47.0 28.2 1182 653 443
hcyclic8 2897.1 1610.9 2497.7 2008.0 3338.0 2106.4 4392 2359 1182
hf744 10.7 11.1 4.3 4.3 5.1 5.1 1244 1242 204
hf855 515.0 528.8 326.4 278.7 395.6 323.1 4745 4742 688
hietarinta1 0.7 0.7 0.2 0.2 0.5 0.5 52 52 51
i1 46.1 58.9 24.9 25.6 24.2 26.6 147 147 118
ilias13 3404.8 1063.5 1163.1 1204.9 1486.0 1500.7 285 285 246
ilias_k_2 248.4 265.5 276.7 274.5 131.4 132.8 185 183 125
ilias_k_3 308.0 322.8 502.2 502.8 273.6 273.5 205 202 140
jcf26 114.9 115.1 6.3 6.4 6.3 6.5 80 80 79
katsura10 1618.9 1618.5 1796.1 1794.6 1767.7 1769.4 559 559 537
katsura7 1.1 1.1 1.1 1.1 1.1 1.1 79 79 74
katsura8 12.1 12.3 13.4 13.4 13.1 13.0 151 151 143
katsura9 142.3 142.7 158.7 158.7 155.2 154.9 287 287 272
kin1 8.3 8.7 3.1 3.1 3.1 3.2 120 120 88
kotsireas 4.3 5.0 2.8 3.0 2.1 2.3 78 78 70
matrix 3.3 3.3 0.9 0.9 1.1 1.0 1324 1249 161
mckay 78490.9 80937.5 5315.5 5315.1 2482.2 2481.1 126 63 51
noon6 0.9 1.2 0.8 1.1 0.8 1.2 399 234 187
noon7 24 30.2 20.0 29.1 20.2 32.4 1157 651 495
noon8 586.6 1429.8 814.8 1619.6 669.1 1682.8 3385 1818 1338
noon9 49195 104796.9 76141.5 93475.4 88574.7 179382.4 10001 5108 3682
pinchon1 7.6 7.1 5.7 5.7 5.8 5.6 145 122 108
rbpl 46.3 42.2 43.9 40.3 43.7 40.2 309 148 126
rbpl24 37.2 37.4 3.4 3.4 3.4 3.6 55 55 54
redcyc6 0.2 0.1 0.1 0.1 0.1 0.1 46 31 21
redcyc7 448.3 24790.2 30.1 31.9 33.1 33.0 210 126 78
redeco10 10.1 10.3 10.2 10.3 10.3 10.1 384 384 257
redeco11 104.3 104.5 103.5 103.9 102.8 103.4 768 768 513
redeco12 949.8 959.1 964.1 963.9 952.4 953.4 1536 1536 1025
redeco9 1.1 1.1 1.1 1.1 1.1 1.1 192 192 129
reimer5 0.2 0.2 0.3 0.2 0.2 0.2 55 42 38
reimer6 11.2 7.7 9.6 7.5 9.8 7.5 199 118 95
reimer7 1146.6 543.8 1026.7 588.4 1076.3 601.2 775 337 227
virasoro 4.2 4.2 4.7 4.6 4.8 4.7 136 136 128