Benchmarking for polynomial ideals

From Invo

All systems with rational coefficients, timings measured on machine 2xXeon-5410@2.33Ghz with 16Gb of RAM, running Gentoo 2008.0

Information in columns:

timings:
JB: C program by Yanovich D.A. [1]
Singular: version 3-1-4 [2]
Magma: version 2.19-1 [3]
Eder: F5 realization (incremental sba using F5's criteria) by Christian Eder (Singular-based) [4]
G2V: realization by Frank Volny (Singular-based) [5]
GINV: GINV 1.9 with lowJ strategy [6]
#JB: cardinality of Janet basis
#GB: cardinality of Groebner basis

* the timing exceeds 24 hours or runs out of memory.

JB Singular Magma F4 Magma Eder G2V GINV #JB #GB Hilbert polynomial
assur44 4.06 138.44 0.79 18111.37 704.32 * 3.6 94 87
butcher8 0.55 0.88 0.78 361.77 5317.23 0 0.3 64 54
chemequs 0.25 <1 s 0.58 1.64 0.68 1.32 0.3 20 20
chemkin 7.7 <1 s 5.22 146.22 0.06 1.32 4.3 117 90
cohn3 19.92 109.81 4.92 257.44 * * 11.4 106 92
cpdm5 0.94 1.22 0.14 4.73 0.9 9.71 0.8 83 77
cyclic7 31.83 * 1.22 27.32 * * 28.0 210 209
cyclic8 3012.68 * 38.12 3677.16 * * 1755.2 384 372
d1 3.13 2.19 1.41 9.94 8.02 336.08 1.0 104 86
des18_3 0.13 <1 s 0.42 2.09 6.07 12353.15 0.1 104 39
des22_24 0.33 <1 s 0.23 4.13 0.35 51.32 0.4 129 45
discret3 6483.4 41008.06 3640.38 11588.69 1853.80 19939.50 4282.6 164 147
dl 72.25 18.15 2.25 342995.86 1352.94 167939.43 43.0 538 323
eco10 29.63 56.10 1.17 27.41 298.10 101494.64 27.4 336 203
eco11 328.15 * 10.68 393.40 * * 278.4 662 389
eco12 2446.21 * 154.76 5463.33 * * 2531.2 1329 743
eco8 0.3 <1 s 0.05 0.45 0.20 29.23 0.3 86 59
eco9 2.55 2.03 0.24 2.94 3.70 1185.96 2.4 172 106
extcyc5 1.12 1.26 0.08 0.77 0.84 41.18 0.7 102 102
extcyc6 145.27 123101.92 7.86 188.93 * * 74.1 243 242
f744 2.69 1.16 0.26 0.2 * 396.55 1.4 162 87
f855 55.95 124.67 6.44 0.62 * * 18.9 264 148
fabrice24 37.09 1538.37 1.42 1514.95 373.35 2728.47 3.5 55 54
filter9 3.94 7.50 8.99 102.33 * * 2.0 232 153
hairer2 28.43 192.36 15.19 378.66 * * 43.3 453 128
hairer3 0.71 446.77 * * * * 1.0 1 1
hcyclic7 25.97 992.93 1.17 27.31 * * 47.0 1182 443
hcyclic8 1668.08 * 36.79 3698.82 * * 3338.0 4392 1182
hf744 6.26 3.32 0.25 107.68 180.19 60846.57 5.1 1244 204
hf855 465.01 505.72 6.33 * * * 395.6 4745 688
hietarinta1 0.61 2.15 0.52 1.32 * * 0.5 52 51
i1 31.91 15.00 5.96 70.82 210.68 * 24.2 147 118
ilias13 546.0 13114.38 55.79 52.00 * * 1486.0 285 246
ilias_k_2 77.24 9334.38 8.66 4482.93 * * 131.4 185 125
ilias_k_3 143.2 6088.77 13.49 3777.92 * * 273.6 205 140
jcf26 74.84 168.71 3.99 25819.35 * * 6.3 80 79
katsura10 1477.32 4396.77 41.92 * * 24255.37 1767.7 559 537
katsura7 1.11 1.57 0.16 18.33 0.17 4.00 1.1 79 74
katsura8 11.88 14.49 0.77 488.00 4.32 47.43 13.1 151 143
katsura9 130.72 246.34 5.29 17037.94 1505.29 914.62 155.2 287 272
kin1 5.07 12.15 5.42 57.14 * * 3.1 120 88
kotsireas 2.75 3.04 0.58 133.72 5.82 178.01 2.1 78 70
noon6 0.7 <1 s 0.15 0.78 0.05 4.67 0.8 399 187
noon7 12.96 0.72 1.15 10.70 0.21 48.55 20.2 1157 495
noon8 289.68 6.63 10.55 219.08 1.85 2842.34 669.1 3385 1338
noon9 15719.8 74.14 98.05 5276.06 19.39 * 88574.7 10001 3682
pinchon1 5.55 3.45 2.35 563.23 * * 5.8 145 108
rbpl 54.43 291.77 4.66 * * * 43.7 309 126
rbpl24 37.1 1585.07 1.43 1515.10 373.62 2734.41 3.4 55 54
redcyc6 0.1 <1 s 0.04 0.32 0.38 2.85 0.1 46 21
redcyc7 504.4 * 1.11 20.03 3757.30 1640.80 33.1 210 78
redeco10 8.63 3.66 0.38 8.83 0.58 286.71 10.3 384 257
redeco11 83.78 34.31 2.12 88.10 3.45 10709.72 102.8 768 513
redeco12 786.05 302.79 14.06 1018.33 29.73 * 952.4 1536 1025
reimer5 0.29 0.53 0.14 5.24 17.68 130.04 0.2 55 38
reimer6 8.4 150846.74 6.58 3828.62 * * 9.8 199 95
reimer7 546.01 * 659.69 * * * 1076.3 775 227
virasoro 4.61 13.51 0.32 335.48 8.03 95.12 4.8 136 128