def test_zzX_values():
assert zzX_zero(0) == 0
assert zzX_zero(1) == []
assert zzX_zero(3) == [[[]]]
assert zzX_const(1, 7) == [7]
assert zzX_const(3, 7) == [[[7]]]
assert zzX_const(0, 3) == 3
assert zzX_const(3, 0) == [[[]]]
assert zzX_zero_of(f_0, 1) == [[]]
assert zzX_zero_of(f_6, 1) == [[[]]]
assert zzX_const_of(f_0, 7, 1) == [[7]]
assert zzX_const_of(f_6, 7, 1) == [[[7]]]
assert zzX_value(3, 1) == [[[1]]]
assert zzX_value(0, [[1]]) == [[1]]
assert zzX_value(1, [[1]]) == [[[1]]]
assert zzX_value(2, [[1]]) == [[[[1]]]]
assert zzX_zeros_of([1,2,3], 4) == [0,0,0,0]
assert zzX_zeros_of(f_0, 0, 0) == []
assert zzX_zeros_of(f_0, 2, 0) == [[[[]]], [[[]]]]
assert zzX_zeros_of(f_0, 3, 1) == [[[]],[[]],[[]]]
assert zzX_consts_of([1,2,3], 7, 4) == [7,7,7,7]
assert zzX_consts_of(f_0, 7, 0, 0) == []
assert zzX_consts_of(f_0, 7, 2, 0) == [[[[7]]], [[[7]]]]
assert zzX_consts_of(f_0, 7, 3, 1) == [[[7]],[[7]],[[7]]]
assert zzX_lift(2, []) == [[[]]]
assert zzX_lift(2, [[1,2,3], [], [2,3]]) == \
[[[[1]],[[2]],[[3]]], [[[]]], [[[2]],[[3]]]]
assert zzX_zero_p([]) == True
assert zzX_zero_p([[]]) == True
assert zzX_zero_p([[[]]]) == True
assert zzX_zero_p([[[1]]]) == False
assert zzX_one_p([1]) == True
assert zzX_one_p([[1]]) == True
assert zzX_one_p([[[1]]]) == True
assert zzX_one_p([[[12]]]) == False
def test_zzX_values():
assert zzX_zero(0) == 0
assert zzX_zero(1) == []
assert zzX_zero(3) == [[[]]]
assert zzX_const(1, 7) == [7]
assert zzX_const(3, 7) == [[[7]]]
assert zzX_const(0, 3) == 3
assert zzX_const(3, 0) == [[[]]]
assert zzX_zero_of(f_0, 1) == [[]]
assert zzX_zero_of(f_6, 1) == [[[]]]
assert zzX_const_of(f_0, 7, 1) == [[7]]
assert zzX_const_of(f_6, 7, 1) == [[[7]]]
assert zzX_value(3, 1) == [[[1]]]
assert zzX_value(0, [[1]]) == [[1]]
assert zzX_value(1, [[1]]) == [[[1]]]
assert zzX_value(2, [[1]]) == [[[[1]]]]
assert zzX_zeros_of([1, 2, 3], 4) == [0, 0, 0, 0]
assert zzX_zeros_of(f_0, 0, 0) == []
assert zzX_zeros_of(f_0, 2, 0) == [[[[]]], [[[]]]]
assert zzX_zeros_of(f_0, 3, 1) == [[[]], [[]], [[]]]
assert zzX_consts_of([1, 2, 3], 7, 4) == [7, 7, 7, 7]
assert zzX_consts_of(f_0, 7, 0, 0) == []
assert zzX_consts_of(f_0, 7, 2, 0) == [[[[7]]], [[[7]]]]
assert zzX_consts_of(f_0, 7, 3, 1) == [[[7]], [[7]], [[7]]]
assert zzX_lift(2, []) == [[[]]]
assert zzX_lift(2, [[1,2,3], [], [2,3]]) == \
[[[[1]],[[2]],[[3]]], [[[]]], [[[2]],[[3]]]]
assert zzX_zero_p([]) == True
assert zzX_zero_p([[]]) == True
assert zzX_zero_p([[[]]]) == True
assert zzX_zero_p([[[1]]]) == False
assert zzX_one_p([1]) == True
assert zzX_one_p([[1]]) == True
assert zzX_one_p([[[1]]]) == True
assert zzX_one_p([[[12]]]) == False
def zzX_fateman_poly_F_1(n):
"""Fateman's GCD benchmark: trivial GCD """
u = [1, 0]
for i in xrange(1, n+1):
u = [zzX_const(i, 1), u]
v = [1, 0, 0]
for i in xrange(1, n+1):
v = [zzX_const(i, 1), zzX_zero(i), v]
U = zzX_add_term(u, zzX_const(n, 1))
V = zzX_add_term(u, zzX_const(n, 2))
W = zzX_add_term(v, zzX_const(n, 1))
Y = zzX_lift(n-1, [[-3, 0], [], [1, 0, -1]])
F = zzX_mul(U, V)
G = zzX_mul(W, Y)
H = zzX_const(n+1, 1)
return F, G, H
def zzX_fateman_poly_F_1(n):
"""Fateman's GCD benchmark: trivial GCD """
u = [1, 0]
for i in xrange(1, n + 1):
u = [zzX_const(i, 1), u]
v = [1, 0, 0]
for i in xrange(1, n + 1):
v = [zzX_const(i, 1), zzX_zero(i), v]
U = zzX_add_term(u, zzX_const(n, 1))
V = zzX_add_term(u, zzX_const(n, 2))
W = zzX_add_term(v, zzX_const(n, 1))
Y = zzX_lift(n - 1, [[-3, 0], [], [1, 0, -1]])
F = zzX_mul(U, V)
G = zzX_mul(W, Y)
H = zzX_const(n + 1, 1)
return F, G, H