Allan Steel (May 12, 2005)
This table compares some Computer Algebra systems for polynomial GCD computations.
The table is a copy of the table in Fermat is Overall Best in the World at Polynomial GCD, prepared in May 2004 by Daniel Robertz and Vladimir Gerdt and sent to Robert Lewis (and placed on his Fermat website), except for the new Magma V2.12 timings column which I have added (and some slight reformatting to fit things in).
Timings are for a 2.2GHz Opteron 248 (exactly as in the original table). See the original table above for details on the inputs. I thank Daniel Robertz for supplying me with the input in Magma format.
Note that the original table used Magma V2.9, which was released in mid 2002, so is rather old now.
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Characteristic 0
Magma 2.12 Magma 2.9 Fermat 3.4 Maple9 Singular 2.0.4
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1 variable
TD 100 0.000 0.010 0.000 0.007 < 0.100
TD 1000 0.040 0.050 0.160 0.391 7.800
TD 2000 0.110 0.210 0.720 1.605 60.850
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2 variables
TD 20 0.000 0.010 0.010 0.020 1.900
TD 40 0.000 0.110 0.070 0.100 276.000
TD 100 0.060 4.930 2.650 2.730 > 50000
TD 160 0.150 43.710 19.900 15.548 /
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3 variables
TD 20 0.010 0.210 0.100 0.772 6511.000
TD 40 0.100 6.740 2.600 50.777 /
TD 60 0.400 97.780 19.510 635.514 /
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4 variables
TD 10 0.010 0.160 0.040 0.406 /
TD 16 0.060 1.150 0.430 3.338 /
TD 20 0.140 4.170 1.570 16.061 /
TD 30 0.630 64.790 17.260 351.898 /
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Characteristic 43051
Magma 2.12 Magma 2.9 Fermat 3.4 Maple9 Singular 2.0.4
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1 variable
TD 100 0.000 0.000 0.000 0.001 0.000
TD 1000 0.020 0.030 0.020 0.025 0.360
TD 2000 0.040 0.080 0.070 0.091 1.340
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2 variables
TD 20 0.000 0.000 0.000 0.010 0.410
TD 40 0.000 0.050 0.060 0.029 23.940
TD 100 0.040 1.540 2.340 0.253 5489.070
TD 160 0.140 9.990 17.400 1.087 91107.230
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3 variables
TD 20 0.000 0.010 0.000 0.112 1.960
TD 40 0.010 0.130 0.080 3.452 /
TD 60 0.100 3.040 1.670 240.441 /
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4 variables
TD 10 0.010 0.100 0.040 0.773 256.600
TD 16 0.050 0.810 0.340 11.721 /
TD 20 0.110 2.700 1.150 54.394 /
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[TD = Total Degree]