def zzX_fateman_poly_F_3(n):
"""Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """
u = zzx_from_dict({n+1:1})
for i in xrange(1, n):
u = zzX_add_term([u], zzX_const(i, 1), n+1)
v = zzX_add_term(u, zzX_const(n-1, 2))
f = zzX_sqr(zzX_add_term([zzX_neg(v)], zzX_const(n, 1), n+1))
g = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n+1))
v = zzX_add_term(u, zzX_const(n-1, 1))
h = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n+1))
return zzX_mul(f,h), zzX_mul(g,h), h
def zzX_fateman_poly_F_2(n):
"""Fateman's GCD benchmark: linearly dense quartic inputs """
u = [1, 0]
for i in xrange(1, n):
u = [zzX_const(i, 1), u]
v = zzX_add_term(u, zzX_const(n - 1, 2))
f = zzX_sqr([zzX_const(n, 1), zzX_neg(v)])
g = zzX_sqr([zzX_const(n, 1), v])
v = zzX_add_term(u, zzX_const(n - 1, 1))
h = zzX_sqr([zzX_const(n, 1), v])
return zzX_mul(f, h), zzX_mul(g, h), h
def zzX_fateman_poly_F_2(n):
"""Fateman's GCD benchmark: linearly dense quartic inputs """
u = [1, 0]
for i in xrange(1, n):
u = [zzX_const(i, 1), u]
v = zzX_add_term(u, zzX_const(n-1, 2))
f = zzX_sqr([zzX_const(n, 1), zzX_neg(v)])
g = zzX_sqr([zzX_const(n, 1), v])
v = zzX_add_term(u, zzX_const(n-1, 1))
h = zzX_sqr([zzX_const(n, 1), v])
return zzX_mul(f,h), zzX_mul(g,h), h
def zzX_fateman_poly_F_3(n):
"""Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """
u = zzx_from_dict({n + 1: 1})
for i in xrange(1, n):
u = zzX_add_term([u], zzX_const(i, 1), n + 1)
v = zzX_add_term(u, zzX_const(n - 1, 2))
f = zzX_sqr(zzX_add_term([zzX_neg(v)], zzX_const(n, 1), n + 1))
g = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n + 1))
v = zzX_add_term(u, zzX_const(n - 1, 1))
h = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n + 1))
return zzX_mul(f, h), zzX_mul(g, h), h
def test_zzX_sqf():
assert zzX_sqf_p(f_0) == True
assert zzX_sqf_p(zzX_sqr(f_0)) == False
assert zzX_sqf_p(f_1) == True
assert zzX_sqf_p(zzX_sqr(f_1)) == False
assert zzX_sqf_p(f_2) == True
assert zzX_sqf_p(zzX_sqr(f_2)) == False
assert zzX_sqf_p(f_3) == True
assert zzX_sqf_p(zzX_sqr(f_3)) == False
assert zzX_sqf_p(f_5) == False
assert zzX_sqf_p(zzX_sqr(f_5)) == False
assert zzX_sqf_p(f_4) == True
assert zzX_sqf_part(f_4) == f_4
assert zzX_sqf_p(f_6) == True
assert zzX_sqf_part(f_6) == f_6
assert zzX_sqf_part(f_5) == [[[-1]], [[-1], [1, 0]]]
def test_zzX_sqf():
assert zzX_sqf_p(f_0) == True
assert zzX_sqf_p(zzX_sqr(f_0)) == False
assert zzX_sqf_p(f_1) == True
assert zzX_sqf_p(zzX_sqr(f_1)) == False
assert zzX_sqf_p(f_2) == True
assert zzX_sqf_p(zzX_sqr(f_2)) == False
assert zzX_sqf_p(f_3) == True
assert zzX_sqf_p(zzX_sqr(f_3)) == False
assert zzX_sqf_p(f_5) == False
assert zzX_sqf_p(zzX_sqr(f_5)) == False
assert zzX_sqf_p(f_4) == True
assert zzX_sqf_part(f_4) == f_4
assert zzX_sqf_p(f_6) == True
assert zzX_sqf_part(f_6) == f_6
assert zzX_sqf_part(f_5) == [[[-1]], [[-1], [1, 0]]]
def test_zzX_sqr():
assert zzX_sqr([[[]]]) == [[[]]]
assert zzX_sqr([[[2]]]) == [[[4]]]
def test_zzX_sqr():
assert zzX_sqr([[[]]]) == [[[]]]
assert zzX_sqr([[[2]]]) == [[[4]]]
