The timings measured on 2xOpteron-242 (1.6 Ghz) with 4Gb RAM
Information in columns:
timins: JB: C program by Yanovich D.A.
FGb: the F4 implementation by J.-C.Faugere running under Maple 10
other timings are given for different GINV modules implementing selection strategies I ("deg") and II ("high" and "low") as described in paper "On Computing Janet Bases for Degree Compatible Orderings" for Janet (J) and Janet-like (JL) divisions
cardinality: JB: Janet basis
JLB: Janet-like basis
GB: Groebner basis
  timins (sec.) cardinality Hilbert polynomial
JB Maple(FGb) highSJ degJ highJ lowJ degJL highJL lowJL JB JLB GB
assur44 6.67 4.86 8.63 14.69 5.09 5.53 13.71 5.73 5.25 94 94 87 56
aubry2 29.02 1.13 15.92 67.24 15.23 19.21 56.79 27.32 28.51 135 123 79 168
augot 58.07                      
benchmark_D1 5.92 5.30 1.99 9.57 1.43 1.62 4.30 1.53 1.72 104 104 86 48
benchmark_i1 56.15 49.12 59.11 81.88 42.75 41.45 103.28 39.64 43.70 147 147 118 66
boon 0.00 0.04 0.00 0.01 0.00 0.00 0.01 0.01 0.00 12 12 12 8
butcher 0.04 0.06 0.03 0.10 0.04 0.06 0.10 0.04 0.05 52 52 27 1/2s^3 + 5s^2 - 3/2s + 8
butcher8 0.79 0.62 0.39 1.09 0.41 0.45 0.99 0.42 0.45 64 64 54 1/2s^3 + 5/2s^2 + 4s + 14
camera1s 0.08 0.53 0.11 0.08 0.10 0.10 0.07 0.09 0.08 35 32 26 20
caprasse 0.00 0.04 0.00 0.00 0.00 0.00 0.01 0.01 0.01 38 32 26 56
cassou 0.08 0.05 0.02 0.07 0.03 0.03 2.86 0.07 0.10 15 8 8 16s - 14
chandra4 0.00 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8 8 8 8
chandra5 0.00 0.06 0.00 0.01 0.01 0.00 0.00 0.01 0.00 16 16 16 16
chandra6 0.02 0.17 0.03 0.03 0.03 0.03 0.03 0.03 0.03 32 32 32 32
chemequ 0.01 0.16 0.02 0.02 0.02 0.02 0.02 0.02 0.03 18 18 18 16
chemequs 0.37 3.88 0.63 0.40 0.37 0.40 0.41 0.37 0.40 20 20 20 16
chemkin 12.28 6.22 10.75 16.22 9.80 8.92 15.78 9.17 9.65 117 116 90 80
cohn2 0.08 0.10 0.08 0.10 0.08 0.10 0.11 0.08 0.09 33 29 23 4s^2 + 6s - 1
cohn3 45.94 41.21 41.17 82.63 22.40 20.74 192.62 23.33 36.52 106 103 92 10s + 163
comb3000 0.00 0.10 0.01 0.01 0.01 0.00 0.01 0.01 0.01 34 22 20 16
comb3000s 0.03 0.44 0.03 0.04 0.03 0.03 0.04 0.03 0.04 34 22 20 16
conform1 0.00 0.02 0.00 0.01 0.00 0.00 0.00 0.00 0.00 10 10 10 16
cpdm5 1.59 0.84 1.61 2.00 2.05 2.06 1.94 2.13 2.06 83 83 77 213
cyclic5 0.00 0.02 0.00 0.01 0.01 0.01 0.01 0.00 0.02 23 21 20 70
cyclic6 0.14 0.10 0.13 0.25 0.14 0.16 0.25 0.14 0.16 46 45 45 156
cyclic7 50.15 10.00 76.37 87.76 72.89 64.33 77.71 69.73 67.32 210 210 209 924
cyclic8 9999.03 217.68 5825.85 14056.89 5376.18 3863.73 17232.79 4499.49 2975.51 384 383 372 144s + 760
d1 6.00 5.29 2.00 9.67 1.41 1.58 4.29 1.53 1.67 104 104 86 48
des18_3 0.17 0.63 0.19 0.19 0.19 0.19 0.18 0.19 0.21 104 76 39 46
des22_24 0.55 0.84 0.68 0.59 0.73 0.75 0.60 0.71 0.65 129 115 45 42
dessin1 0.17 0.64 0.18 0.20 0.18 0.20 0.17 0.20 0.20 104 76 39 46
dessin2 0.48 0.99 0.57 0.51 0.66 0.66 0.48 0.52 0.49 122 105 46 42
discret3 11374.4 11801.73 11772.97 7415.81 7945.25 15115.46 8467.31 10439.18 164 154 147 128
dl 247.1 6.06 200.64 412.91 101.69 101.06 491.86 105.97 133.61 538 491 323 468
ducos10                          
ducos7_3 33.58 1.89 18.24 68.23 25.39 29.95 52.72 27.25 40.29 135 122 80 168
ducos7_5 12464.30 2.48 3678.09 483.94 276.09 252.43 696.12 261.92 257.44 1 1 1 0
ducos8 29.29 2.50 66.29 41.34 66.59 101.90 42.66 18.64 29.36 176 23 11 384
eco10 44.86 4.46 55.76 70.99 81.77 73.38 83.13 73.21 68.27 336 279 203 256
eco11 465.36 58.62 523.86 864.73 832.02 743.31 843.11 813.17 845.07 662 561 389 512
eco12 3737.13 573.51 5173.68 9478.13 12958.02 13512.87 11691.61 11919.20 12179.72 1329 1109 743 1024
eco7 0.05 0.06 0.06 0.08 0.07 0.08 0.08 0.07 0.07 45 38 32 32
eco8 0.38 0.23 0.44 0.52 0.54 0.51 0.56 0.55 0.55 86 75 59 64
eco9 3.22 0.84 4.10 7.49 6.15 6.04 8.56 5.43 6.10 172 147 106 128
el44 2.11 0.14 0.51 1.50 0.35 0.73 26.81 0.34 0.67 26 22 14 12
el50                          
extcyc4 0.01 0.05 0.01 0.01 0.01 0.02 0.01 0.01 0.02 25 24 24 64
extcyc5 1.2 0.50 1.18 2.03 1.47 1.50 2.22 1.39 1.95 102 102 102 350
extcyc6 219.53 36.57 243.57 188.99 195.37 162.21 171.33 212.52 134.10 243 242 242 936
extcyc7 *                      
extcyc8                          
f633 0.06 0.11 0.06 0.10 0.08 0.10 0.10 0.09 0.10 153 149 47 16s^2 - 12s + 2
f744 4.43 0.46 2.24 10.13 2.52 3.05 10.26 2.51 3.15 162 159 87 40s - 30
f855 103.59 5.00 45.34 160.34 37.57 44.05 160.64 37.89 51.40 264 261 148 52s - 36
f966                          
fabrice24 60.92 7.27 9.31 134.91 5.05 5.45 137.36 5.00 5.48 55 55 54 40
filter9 18.62 3.29 1.20 7.20 1.04 3.58 6.40 1.09 2.95 232 226 153 192
geneig 0.01 0.07 0.02 0.02 0.01 0.02 0.02 0.01 0.01 16 16 16 10
hairer1 0.00 0.02 0.01 0.00 0.00 0.00 0.00 0.00 0.00 17 17 12 5s^2 - s + 2
hairer2 52.00 6.20 74.21 109.04 138.14 136.56 142.09 178.87 134.55 453 389 128 31s^2 - 40s + 10
hairer3 1.75 0.58 0.32 1.93 0.37 4.81 2.12 0.11 0.22 1 1 1 0
hairer4                          
hawes4                          
hcyclic5 0.00 0.05 0.01 0.02 0.01 0.01 0.01 0.00 0.01 52 44 38 120s - 480
hcyclic6 0.21 0.23 0.20 0.36 0.22 0.25 0.22 0.16 0.17 221 133 99 30s^2 + 84s - 1210
hcyclic7 56.12 18.40 69.61 100.19 79.38 89.59 68.17 58.93 64.28 1182 653 443 196s^2 - 546s - 7056
hcyclic8 5442.38 560.75 9175.63 6395.24 9871.78 7800.25 4204.18 7904.51 4967.98 4392 2359 1182 176/3s^3 - 392s^2 + 5944/3s - 23936
heart 0.00 0.06 0.00 0.01 0.00 0.01 0.01 0.00 0.00 10 10 9 4
hemmecke 0.56 0.04 0.03 0.94 0.04 0.05 0.00 0.01 0.00 983 14 9 2980s - 76460
hf744 21.82 1.24 6.59 20.55 7.99 13.77 21.12 7.98 11.47 1244 1242 204 1/60s^5 + 17/12s^4 + 35/4s^3 + 487/12s^2 - 10103/30s + 570
hf855 1992.07 55.90 596.21 906.15 821.12 1105.27 932.55 628.41 874.00 4745 4742 688 1/360s^6 + 47/120s^5 + 395/72s^4 + 425/24s^3 - 5962/45s^2 - 151/10s + 749
hietarinta1 0.71 0.34 0.50 1.06 0.37 1.10 1.10 0.38 0.96 52 52 51 3/2s^2 + 23/2s + 1
hunecke 0.00 0.04 0.00 0.00 0.00 0.01 0.00 0.00 0.00 15 14 9 5/2s^3 - 5/2s^2 - 5s + 24
i1 54.49 48.99 59.13 88.00 42.51 41.97 103.71 39.37 44.54 147 147 118 33s^2 - 40s + 19
ilias12                          
ilias13 723.07 183.44 6585.12 6577.81 2036.98 2529.96 2058.79 2011.34 2593.16 285 285 246 468
ilias_k_2 208.02 28.06 1242.93 479.12 349.44 208.16 495.06 350.64 215.40 185 183 125 144
ilias_k_3 275.22 51.93 1777.51 597.28 813.70 429.22 603.66 809.95 427.09 205 202 140 168
issac97 0.00 0.06 0.01 0.00 0.00 0.00 0.00 0.01 0.00 12 12 12 16
jcf26 121.86 14.66 19.09 254.02 10.28 10.31 251.81 9.81 10.38 80 80 79 40
katsura10 3732.74 576.36 4104.93 4784.14 7195.53 6078.84 4444.97 7558.93 6294.32 559 559 537 1024
katsura6 0.17 0.22 0.18 0.20 0.21 0.20 0.18 0.20 0.20 43 43 41 64
katsura7 1.83 1.22 1.96 2.05 2.28 2.27 2.16 2.43 2.33 79 79 74 128
katsura8 22.24 7.80 26.62 30.87 34.86 32.45 30.57 31.31 28.50 151 151 143 256
katsura9 271.00 56.54 314.32 348.08 390.53 353.25 307.69 380.82 320.10 287 287 272 512
kin1 8.32 18.19 7.82 13.74 4.71 5.12 14.12 4.66 5.25 120 120 88 48
kinema 0.15 0.28 0.12 0.17 0.13 0.13 0.17 0.14 0.15 45 45 39 40
kotsireas 4.68 2.80 5.81 9.58 4.71 4.60 9.47 5.07 5.04 78 78 70 108s - 257
ku10 0.00 0.04 0.00 0.01 0.00 0.00 0.01 0.01 0.00 10 10 10 2
lanconelli 0.00 0.04 0.01 0.00 0.00 0.00 0.00 0.00 0.01 10 8 6 1/630s^7 + 1/40s^6 + 8/45s^5 + 3/4s^4 + 359/180s^3 + 129/40s^2 + 1187/420s + 1
lichtblau 0.08 1.22 0.11 0.08 0.08 0.08 0.09 0.08 0.09 16 16 16 11s + 1
liu 0.00 0.02 0.00 0.00 0.00 0.00 0.01 0.01 0.00 19 19 12 8s^2 - 8s + 8
lorentz 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 13 13 12 11
matrix 12.54 0.55 0.92 6.69 0.67 1.79 5.85 0.85 2.23 1324 1249 161 1/1440s^8 + 1/72s^7 + 8/45s^6 + 113/144s^5 + 3259/1440s^4 + 617/144s^3 + 607/120s^2 + 41/12s + 3
mckay 132778.00 7.40 * * 6624.61 3895.01 * 6648.29 3914.28 126 63 51 10s + 34
mckay.gls50mod                          
mickey 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 2 2 4
morgenstern 0.01 0.05 0.01 0.02 0.02 0.01 0.01 0.02 0.01 72 69 27 4/3s^4 + 20/3s^2 + 0s + 2
noon5 0.06 0.16 0.05 0.09 0.06 0.07 0.08 0.08 0.09 137 84 72 233
noon6 0.98 0.86 1.17 1.76 1.43 1.42 1.97 1.97 2.11 399 234 187 717
noon7 24.13 6.65 28.50 46.62 42.42 42.19 65.50 69.33 79.56 1157 651 495 2173
noon8 1237.66 66.49 1235.00 2564.97 3709.50 3281.98 5748.63 7086.76 6834.83 3385 1818 1338 6545
noon9 72426.90                      
pinchon1 8.54 2.47 10.63 15.83 13.15 13.17 14.99 12.50 13.66 145 122 108 78
puma 0.00 0.08 0.00 0.01 0.01 0.00 0.00 0.01 0.00 32 19 16 16
quadfor2 0.00 0.02 0.00 0.00 0.00 0.00 0.01 0.00 0.00 4 4 4 2s + 1
quadgrid 0.00 0.04 0.01 0.01 0.00 0.00 0.01 0.00 0.01 8 8 8 5s - 0
rabmo 0.72 0.18 2.06 0.62 2.08 2.86 0.56 2.38 3.26 28 28 20 16
rbpl 155.70 30.10 170.32 157.83 156.02 155.63 157.59 128.69 152.71 309 148 126 10/3s^3 + 37s^2 - 427/3s + 137
rbpl24 60.84 7.29 9.32 133.16 5.11 5.37 134.37 5.07 5.52 55 55 54 40
redcyc5 0.01 0.02 0.01 0.01 0.01 0.00 0.01 0.01 0.01 23 14 10 70s - 210
redcyc6 0.17 0.15 0.27 0.14 0.17 0.26 0.15 0.17 46 31 21 156s - 588
redcyc7 510.31 2.18 57.65 749.17 51.12 55.56 56234.83 47.22 63.69 210 126 78 924s - 5257
redcyc8                          
redeco10 15.09 2.24 19.01 25.52 30.19 29.03 22.35 26.59 24.51 384 384 257 256
redeco11 145.88 11.83 193.96 250.43 299.67 283.29 249.51 311.78 254.73 768 768 513 512
redeco12 1370.75 80.86 1948.09 2642.87 5466.67 3662.07 2631.55 6098.63 4267.28 1536 1536 1025 1024
redeco7 0.02 0.04 0.02 0.03 0.02 0.03 0.02 0.02 0.03 48 48 33 32
redeco8 0.17 0.15 0.18 0.21 0.23 0.23 0.21 0.22 0.22 96 96 65 64
redeco9 1.62 0.55 1.82 2.30 2.59 2.48 2.30 2.37 2.30 192 192 129 128
reif 0.00 0.05 0.01 0.01 0.05 0.01 0.02 0.05 0.01 1 1 1 0
reimer4 0.01 0.05 0.01 0.04 0.02 0.02 0.03 0.02 0.01 19 17 17 36
reimer5 0.22 0.18 0.34 0.42 0.53 0.40 0.36 0.45 0.36 55 42 38 144
reimer6 10.54 3.21 18.94 29.35 28.72 29.87 19.70 21.24 22.30 199 118 95 576
reimer7 765.97 75.88 2324.00 3963.38 5275.00 4584.26 2236.61 3358.18 2865.22 775 337 227 2880
reimer8                          
rose 0.00 0.07 0.00 0.01 0.01 0.01 0.01 0.01 0.01 45 29 18 136
s9_1 0.00 0.04 0.00 0.01 0.00 0.00 0.00 0.00 0.00 15 15 15 10
solotarev 0.00 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 10 9 9 6
sparse5 0.00 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 31 5 5 160
speer 0.07 0.16 0.07 0.17 0.08 0.08 0.24 0.07 0.09 49 49 44 1/3s^3 + 35s^2 - 451/3s + 218
tangents 0.04 0.11 0.03 0.04 0.04 0.04 0.04 0.03 0.04 25 25 25 24
test 0.00 0.02 0.00 0.00 0.00 0.01 0.00 0.00 0.00 23 7 5 13s - 2
uteshev_bikker 0.02 0.16 0.02 0.02 0.02 0.02 0.02 0.02 0.02 17 17 17 36
vermeer 0.01 0.04 0.02 0.02 0.01 0.02 0.03 0.01 0.02 36 25 20 30s - 50
vernov1                          
virasoro 8.13 2.38 9.82 10.01 13.10 12.98 11.55 11.35 13.20 136 136 128 256
wang16 0.01 0.05 0.01 0.02 0.01 0.02 0.01 0.01 0.01 20 20 18 24
wright 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 31 5 5 32


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