## page was renamed from PolynomialGCDBenchmarks
## page was renamed from MultivariateFactoringBenchmarks

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 ||   ||        ||