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Describe MultivariateFactoringBenchmarks here. ## page was renamed from PolynomialGCDBenchmarks
## page was renamed from MultivariateFactoringBenchmarks
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== 2 variables over ZZ ==
||<tablewidth="200px" tablestyle=""> ||ezgcd ||modular ||
||p - 20 ||0.05 ||0.33 ||
||q - 40 ||0.33 ||9.47 ||
||r - 100 ||8.71 ||- ||
||s - 160 ||89.57 ||- ||		 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 || || ||

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 anonymous)