A benchmark for polynomial GCDs

GCD benchmark.md

Tool	Timing (s)
Symbolica	4.1
Mathematica	89
Sympy	3663

mm_gcd.m

a = (1 + 3*x1 + 5*x2 + 7*x3 + 9*x4 + 11*x5 + 13*x6 + 15*x7)^7 - 1
b = (1 - 3*x1 - 5*x2 - 7*x3 + 9*x4 - 11*x5 - 13*x6 + 15*x7)^7 + 1
g = (1 + 3*x1 + 5*x2 + 7*x3 + 9*x4 + 11*x5 + 13*x6 - 15*x7)^7 + 3
ag = Expand[a g]
bg = Expand[b g]
PolynomialGCD[ag, bg] - Expand[g]

symbolica_gcd.py

from symbolica import Expression as E
a = E.parse('(1 + 3*x1 + 5*x2 + 7*x3 + 9*x4 + 11*x5 + 13*x6 + 15*x7)^7 - 1').to_polynomial()
b = E.parse('(1 - 3*x1 - 5*x2 - 7*x3 + 9*x4 - 11*x5 - 13*x6 + 15*x7)^7 + 1').to_polynomial()
g = E.parse('(1 + 3*x1 + 5*x2 + 7*x3 + 9*x4 + 11*x5 + 13*x6 - 15*x7)^7 + 3').to_polynomial()
ag = a * g
bg = b * g
r = ag.gcd(bg) - g

sympy_gcd.py

from sympy.parsing.sympy_parser import parse_expr
from sympy import expand, gcd

a = parse_expr('(1 + 3*x1 + 5*x2 + 7*x3 + 9*x4 + 11*x5 + 13*x6 + 15*x7)**7 - 1')
b = parse_expr('(1 - 3*x1 - 5*x2 - 7*x3 + 9*x4 - 11*x5 - 13*x6 + 15*x7)**7 + 1')
g = parse_expr('(1 + 3*x1 + 5*x2 + 7*x3 + 9*x4 + 11*x5 + 13*x6 - 15*x7)**7 + 3')
ag = a * g
bg = b * g
r = gcd(ag, bg) - expand(g)