C. Comparison with other programs

In this section we present experimental results on comparison of GINV with package JB and Magma (see http://arXiv.org/math.AC/0603161 for references and more details).

The below timing were obtained on the following machines:

JB:
2xOpteron-242 (1.6 Ghz) with 4Gb of RAM running under Gentoo Linux 2004.3 with gcc-3.4.2 compiler.
GINV:
Turion-3400 (1.8 Ghz) with 2Gb of RAM running under Gentoo Linux 2005.1 with gcc-3.4.4 compiler.
Magma:
dual processor Pentium III (1 Ghz) with 2 GB of RAM running under SuSE Linux 8.0 (kernel 2.4.18-64GB-SMP) with gcc-2.95.3 compiler.
All timings in the table are given in seconds, and (*) shows that the example was not computed because of the memory overflow.

Benchmarking
Example Algorithm I Algorithm I Algorithm II Algorithm II Magma Magma
(JB) (GINV) high (GINV) low (GINV) V2.11-8 V2.12-17
assur44 10.35 14.20 6.33 6.4 4.56 4.99
butcher8 1.06 1.02 0.38 0.39 4.68 5.00
chemequs 0.67 0.61 0.57 0.6 12.80 11.99
chemkin 17.83 16.87 10.95 9.95 32.34 29.83
cohn3 76.72 107.14 30.21 25.47 37.73 39.20
cpdm5 1.78 1.57 1.69 1.68 0.69 0.70
cyclic6 0.12 0.19 0.14 0.14 0.09 0.08
cyclic7 58.72 60.94 68.59 65.28 6.64 7.08
cyclic8 12056.24 14046.26 5826.18 4424.96 235.73 245.65
d1 8.77 12.58 1.99 2.08 28.49 8.29
des18_3 0.19 0.18 0.19 0.19 1.81 1.89
des22_24 0.68 0.62 0.77 0.79 1.37 1.46
discret3 23322.8 20956.31 12642.49 13521.65 33658.09 19369.53
dl 270.17 278.89 80.77 89.52 14.57 11.95
eco8 0.40 0.44 0.44 0.46 0.20 0.20
eco9 3.22 5.60 4.99 5.08 1.25 1.20
eco10 52.56 56.70 65.71 68.06 7.07 6.91
eco11 765.98 741.74 718.53 679.3 62.33 51.08
extcyc5 1.35 1.53 1.46 1.37 0.37 0.38
extcyc6 324.70 184.49 276.06 155.64 45.36 47.96
extcyc7 * * * * 8242.00 8492.13
f744 4.88 7.71 2.22 2.68 1.47 1.38
f855 132.97 139.79 37.64 38.45 48.63 37.06
fabrice24 108.52 116.77 8.2 7.7 9.45 8.70
filter9 20.97 5.76 1.13 1.6 80.04 56.67
hairer2 62.91 108.17 126.69 125.43 92.07 85.86
hairer3 1.96 0.92 0.32 1.4 * *
hcyclic7 64.17 53.87 65.81 73.0 6.26 6.76
hcyclic8 6024.97 4316.59 * 7560.99 229.70 237.12
hf744 22.17 8.58 7.18 11.26 1.39 1.32
hf855 2157.88 534.08 806.51 988.38 48.15 36.69
hietarinta1 0.77 0.71 0.38 0.53 2.63 2.15
i1 98.24 122.36 58.29 58.21 55.07 42.35
ilias13 1167.18 5851.97 3013.1 2469.62 336.21 309.64
ilias_k_2 323.59 669.68 445.51 270.21 55.41 54.71
ilias_k_3 452.32 846.19 1162.7 622.14 90.67 89.97
jcf26 224.96 211.24 16.44 14.65 31.64 25.59
katsura7 2.15 1.77 2.08 1.98 0.72 0.79
katsura8 27.48 24.66 28.8 27.09 4.7 5.06
katsura9 337.52 294.59 340.45 311.98 33.47 34.87
katsura10 4790.55 4983.11 7220.29 6204.95 287.38 292.02
kin1 15.18 20.32 7.11 7.11 50.56 45.33
kotsireas 6.33 37.94 4.93 4.27 3.45 3.67
noon6 0.97 1.29 1.27 1.29 0.60 0.62
noon7 28.87 32.58 37.52 38.52 4.93 4.77
noon8 1552.26 2292.84 3322.62 3152.57 43.65 42.80
pinchon1 10.37 0.04 0.01 0.01 4.09 3.54
rbpl 210.94 177.51 173.8 173.98 38.33 35.79
rbpl24 108.78 116.78 8.23 7.7 9.62 8.74
redcyc6 0.16 0.17 0.13 0.14 0.10 0.10
redcyc7 913.75 1048.69 48.19 48.61 5.73 6.36
redeco10 18.51 18.66 23.91 22.4 2.33 2.40
redeco11 178.32 187.36 253.34 228.41 14.56 14.85
redeco12 1735.95 2172.75 4666.8 3385.97 101.51 103.02
reimer5 0.22 0.36 0.34 0.38 0.74 0.70
reimer6 9.69 21.60 24.19 23.96 42.13 42.40
reimer7 719.37 3808.91 4756.4 4314.12 5216.53 5032.73
virasoro 9.69 8.90 10.96 10.68 1.72 1.77