Differences between revisions 1 and 22 (spanning 21 versions)
 ⇤ ← Revision 1 as of 2008-03-31 23:43:24 → Size: 241 Editor: MikeHansen Comment: ← Revision 22 as of 2008-11-14 13:42:04 → ⇥ Size: 2663 Editor: localhost Comment: converted to 1.6 markup Deletions are marked like this. Additions are marked like this. Line 1: Line 1: Describe MultivariateFactoringBenchmarks here. ## page was renamed from PolynomialGCDBenchmarks## page was renamed from MultivariateFactoringBenchmarks Line 3: Line 4: == 2 variables over ZZ ==|| ||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.pysage: 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: 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)