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Groebner Bases

The current version of this library ships with Maple. These timings are from 2016.

We used an Intel Core i5 4570 3.2 GHz with 8 GB DDR3-1600 running 64-bit Linux.

Groebner bases mod p are computed for the fastest machine prime supported by each software.

For mgb and Singular p=2^31-1, for Magma p=11863279, for FGb p=65521, and for Giac p=16777213.

Here are the benchmark systems.

Zp libmgb Magma 2.21-8 FGb 1.68 Giac 1.2.2 Singular 4.0.2
cyclic8 0.715 0.970 2.050 3.123 37.490
cyclic9 41.157 48.860 221.890 179.689 7113.800
katsura11 2.787 3.680 37.830 24.863 651.790
katsura12 16.269 21.080 314.640 184.403 5187.580
bayes148 15.754 16.520 891.400 1206.892 5.160
gametwo7 4.701 6.070 24.220 68.336 485.750
jason210 2.789 3.180 32.990 12.570 1.790
mayr42 36.755 30.780 196.530 4087.811 185.760
yang1 17.347 15.900 494.440 - 90.260
 
Q libmgb Magma 2.21-8 FGb 1.68 Giac 1.2.2 Singular 4.0.2
cyclic7 0.979 0.640 1.750 0.951 16.288
cyclic8 12.290 14.750 42.690 25.892 685.352
katsura9 4.740 2.270 7.870 3.858 203.529
katsura10 34.180 17.130 50.220 24.437 1635.524
alea6 50.620 114.680 88.470 52.433 1273.341
eco12 21.140 31.030 62.580 22.765 3333.936
jason210 19.530 4.790 62.270 23.831 47.273
noon9 42.330 45.430 157.480 126.898 1483.740