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(kill(all),0);
0$
(gcd_all_options(f,g) := append(makelist((gcd:option, gcd(f,g)), option, [ez, subres, red, spmod]),
makelist((gcd:option, gcd(g,f)), option, [ez, subres, red, spmod])),
check_gcd(f,g,expected_result) := block([gcds], gcds:gcd_all_options(expand(f), expand(g)),
if every (lambda ([e], equal (e, expected_result)), gcds)
then true
else FAILED_GCDS ('expected = expected_result, 'actual = gcds)),
0);
0$
/* Basic tests: numbers */
check_gcd(1, 1, 1);
true$
check_gcd(1, -1, 1);
true$
check_gcd(6, 2, 2);
true$
check_gcd(6, -2, 2);
true$
check_gcd(3/2, 1/2, 1/2);
true$
check_gcd(3/2, -1/2, 1/2);
true$
check_gcd(1+%i, 2+2*%i, 1+%i);
true$
check_gcd(1+%i, -1/2-1/2*%i, 1/2+1/2*%i);
true$
/* Basic tests: univariate polynomials */
check_gcd(x, 1, 1);
true$
check_gcd(6*x, 2, 2);
true$
check_gcd(2*x*(3*x-1), 2*x, 2*x);
true$
check_gcd(2*x*(3*x-1), 3*x-1, 3*x-1);
true$
check_gcd(2*x*(3*x-1), 6*x*(3*x-1), 2*x*(3*x-1));
true$
check_gcd(2*x*(3*x-1), 3*x+1, 1);
true$
/* Basic tests: multivariate polynomials */
check_gcd(y*x, 1, 1);
true$
check_gcd(6*y*x, 2, 2);
true$
check_gcd(2*y*(3*x-1)*(y+1), 2*y, 2*y);
true$
check_gcd(2*y*(3*x-1)*(y+1), (3*x-1)*(y-1), 3*x-1);
true$
check_gcd(2*y*(3*x-1)*(y+1), 2*y*(3*x-1)*(y-1), 2*y*(3*x-1));
true$
check_gcd(2*y*(3*x-1)*(y+1), 6*y*(3*x-1)*(y+1), 2*y*(3*x-1)*(y+1));
true$
check_gcd(2*y*(3*x-1)*(y+1), (3*x+1)*(y-1), 1);
true$
/* Randomized tests */
(random_polynomial(var) := product(random(3)+1+sum((random(4)-2)*var^i, i, 1, random(3)), j, 0, random(3)),
check_gcd_common_factor(f,g,common_factor,vars) :=
block([gcds], gcds: gcd_all_options (expand (f), expand (g)),
if every (lambda ([x], equal (remainder (x, common_factor), 0)), gcds)
then true
else FAILED_GCDS ('common_factor = common_factor, 'gcd_results = gcds)),
0);
0$
makelist(block([common_factor],
common_factor:random_polynomial(x),
check_gcd_common_factor(common_factor*random_polynomial(x),
common_factor*random_polynomial(x),
common_factor,
[x])),
10);
[true, true, true, true, true, true, true, true, true, true]$
makelist(block([common_factor],
common_factor:random_polynomial(x)*random_polynomial(y),
check_gcd_common_factor(common_factor*random_polynomial(x)*random_polynomial(y),
common_factor*random_polynomial(x)*random_polynomial(y),
common_factor,
[x, y])),
10);
[true, true, true, true, true, true, true, true, true, true]$
makelist(block([common_factor],
common_factor:random_polynomial(x)*random_polynomial(y)*random_polynomial(z),
check_gcd_common_factor(common_factor*random_polynomial(x)*random_polynomial(y)*random_polynomial(z),
common_factor*random_polynomial(x)*random_polynomial(y)*random_polynomial(z),
common_factor,
[x, y, z])),
10);
[true, true, true, true, true, true, true, true, true, true]$
/* SF bug 3832 and merge request 25 */
is(equal(gcd(expand((r^2-2*m+a^2)*(a^2*s^2+r^2)^3*(a^2*s^2+r^2-2*m)), expand((r^2-2*m+a^2)*(a^2*s^2+r^2)^2)),
expand((r^2-2*m+a^2)*(a^2*s^2+r^2)^2)));
true$
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