These are the polynomials found on this page: http://magma.maths.usyd.edu.au/users/allan/gcdcomp.html The files for Sage can be found at http://sage.math.washington.edu/home/mhansen/multivariate_gcd_benchmarks.tar.bz2 . Timings were done on a 2.0 GHz Core 2 Duo Linux system.

For the Sage/Singular timings, I did the following:

sage: load fermat_gcd_1var.py
sage: time a = p1.gcd(p2, algorithm='ezgcd')

For the Maxima timings, I did the following:

sage: mp1 = maxima(p1)
sage: mp2 = maxima(p2)
sage: time a = mp1.gcd(mp2)

1 variable over QQ

File: fermat_gcd_1var.py

ezgcd

modular

maxima

p - 100

0.02

0.03

0.20

q - 1000

12.10

9.84

7.66

r - 10000

95.03

62.80

30.27

(Univariate)

p - 100

3.07

q - 1000

-

r - 2000

-

2 variables over QQ

File: fermat_gcd_2var.py

ezgcd

modular

maxima

p - 20

0.05

0.33

0.11

q - 40

0.33

9.47

0.66

r - 100

8.71

-

14.40

s - 160

89.57

-

3 variables over QQ

File: fermat_gcd_3var.py

ezgcd

modular

maxima

p - 20

0.30

-

1.42

q - 40

8.40

-

27.68

r - 60

92.03

-

4 variables over QQ

File: fermat_gcd_4var.py

ezgcd

modular

maxima

p - 10

0.13

-

1.04

q - 16

0.93

-

8.08

r - 20

2.82

-

33.96

s - 30

40.06

-

80.86

1 variable over GF(43051)

File: fermat_gcd_1var.py

ezgcd

modular

p - 100

0.03

0.03

q - 1000

10.65

8.33

r - 10000

75.74

85.41

2 variables over GF(43051)

File: fermat_gcd_mod_2var.py

ezgcd

modular

p - 20

0.25

0.25

q - 40

14.23

14.00

r - 100

-

-

s - 160

-

-

3 variables over GF(43051)

File: fermat_gcd_mod_3var.sage

ezgcd

modular

p - 10

0.84

0.86

q - 20

8.40

-

r - 60

92.03

-

4 variables over GF(43051)

File: fermat_gcd_4var.py

ezgcd

modular

p - 10

99.75

102.57

q - 16

r - 20

s - 30

MultivariateGCDBenchmarks (last edited 2008-11-14 13:42:04 by localhost)