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 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_content():
f, g, F = [3, 2, 1], [1], []
for i in xrange(0, 5):
g = zzX_mul(g, f)
F.insert(0, g)
assert zzX_content(F) == f
assert zzX_one_p(zzX_content(f_4))
assert zzX_one_p(zzX_content(f_5))
assert zzX_one_p(zzX_content(f_6))
def test_zzX_content():
f, g, F = [3,2,1], [1], []
for i in xrange(0, 5):
g = zzX_mul(g, f)
F.insert(0, g)
assert zzX_content(F) == f
assert zzX_one_p(zzX_content(f_4))
assert zzX_one_p(zzX_content(f_5))
assert zzX_one_p(zzX_content(f_6))
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
def test_zzX_primitive():
f, g, F = [3, 2, 1], [1], []
for i in xrange(0, 5):
g = zzX_mul(g, f)
F.insert(0, g)
assert zzX_primitive(F) == (f, [zzX_quo(cf, f) for cf in F])
cont, f = zzX_primitive(f_4)
assert zzX_one_p(cont) and f == f_4
cont, f = zzX_primitive(f_5)
assert zzX_one_p(cont) and f == f_5
cont, f = zzX_primitive(f_6)
assert zzX_one_p(cont) and f == f_6
def test_zzX_primitive():
f, g, F = [3,2,1], [1], []
for i in xrange(0, 5):
g = zzX_mul(g, f)
F.insert(0, g)
assert zzX_primitive(F) == (f,
[ zzX_quo(cf, f) for cf in F ])
cont, f = zzX_primitive(f_4)
assert zzX_one_p(cont) and f == f_4
cont, f = zzX_primitive(f_5)
assert zzX_one_p(cont) and f == f_5
cont, f = zzX_primitive(f_6)
assert zzX_one_p(cont) and f == f_6
def test_zzX_expand():
zzX_expand(f_0, f_1, f_2) == zzX_mul(f_0, zzX_mul(f_1, f_2))
def test_zzX_mul():
assert zzX_mul([[[]]], [[[]]]) == [[[]]]
assert zzX_mul([[[1]]], [[[]]]) == [[[]]]
assert zzX_mul([[[]]], [[[1]]]) == [[[]]]
assert zzX_mul([[[2]]], [[[1]]]) == [[[2]]]
assert zzX_mul([[[1]]], [[[2]]]) == [[[2]]]
def test_zzX_expand():
zzX_expand(f_0, f_1, f_2) == zzX_mul(f_0, zzX_mul(f_1, f_2))
def test_zzx_gcd():
assert zzx_heu_gcd([], []) == ([], [], [])
assert zzx_mod_gcd([], []) == ([], [], [])
assert zzx_heu_gcd([2], []) == ([2], [1], [])
assert zzx_mod_gcd([2], []) == ([2], [1], [])
assert zzx_heu_gcd([], [2, 4]) == ([2, 4], [], [1])
assert zzx_mod_gcd([], [2, 4]) == ([2, 4], [], [1])
assert zzx_heu_gcd([2, 4], []) == ([2, 4], [1], [])
assert zzx_mod_gcd([2, 4], []) == ([2, 4], [1], [])
assert zzx_heu_gcd([2], [2]) == ([2], [1], [1])
assert zzx_mod_gcd([2], [2]) == ([2], [1], [1])
assert zzx_heu_gcd([1, 2, 1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_mod_gcd([1, 2, 1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_heu_gcd([1, 2, 1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_mod_gcd([1, 2, 1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_heu_gcd([2, 4, 2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_mod_gcd([2, 4, 2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_heu_gcd([2], [2, 4, 2]) == ([2], [1], [1, 2, 1])
assert zzx_mod_gcd([2], [2, 4, 2]) == ([2], [1], [1, 2, 1])
assert zzx_heu_gcd([2, 4, 2], [1, 1]) == ([1, 1], [2, 2], [1])
assert zzx_mod_gcd([2, 4, 2], [1, 1]) == ([1, 1], [2, 2], [1])
assert zzx_heu_gcd([1, 1], [2, 4, 2]) == ([1, 1], [1], [2, 2])
assert zzx_mod_gcd([1, 1], [2, 4, 2]) == ([1, 1], [1], [2, 2])
f, g = [1, -31], [1, 0]
assert zzx_heu_gcd(f, g) == ([1], f, g)
assert zzx_mod_gcd(f, g) == ([1], f, g)
f = [1, 8, 21, 22, 8]
g = [1, 6, 11, 6]
h = [1, 3, 2]
cff = [1, 5, 4]
cfg = [1, 3]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
f = [1, 0, 0, 0, -4]
g = [1, 0, 4, 0, 4]
h = [1, 0, 2]
cff = [1, 0, -2]
cfg = [1, 0, 2]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
assert zzx_gcd(f, g) == h
assert zzx_cofactors(f, g) == (h, cff, cfg)
f, g, h = zzX_fateman_poly_F_3(4)
H, cff, cfg = zzX_cofactors(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
def test_zzX_heu_gcd():
f,g,h = zzX_fateman_poly_F_1(2)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f,g,h = zzX_fateman_poly_F_1(4)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f,g,h = zzX_fateman_poly_F_1(6)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f,g,h = zzX_fateman_poly_F_2(2)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f,g,h = zzX_fateman_poly_F_3(2)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f,g,h = zzX_fateman_poly_F_1(8)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
def test_zzx_gcd():
assert zzx_heu_gcd([], []) == ([], [], [])
assert zzx_mod_gcd([], []) == ([], [], [])
assert zzx_heu_gcd([2], []) == ([2], [1], [])
assert zzx_mod_gcd([2], []) == ([2], [1], [])
assert zzx_heu_gcd([], [2,4]) == ([2,4], [], [1])
assert zzx_mod_gcd([], [2,4]) == ([2,4], [], [1])
assert zzx_heu_gcd([2,4], []) == ([2,4], [1], [])
assert zzx_mod_gcd([2,4], []) == ([2,4], [1], [])
assert zzx_heu_gcd([2], [2]) == ([2], [1], [1])
assert zzx_mod_gcd([2], [2]) == ([2], [1], [1])
assert zzx_heu_gcd([1,2,1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_mod_gcd([1,2,1], [1]) == ([1], [1, 2, 1], [1])
assert zzx_heu_gcd([1,2,1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_mod_gcd([1,2,1], [2]) == ([1], [1, 2, 1], [2])
assert zzx_heu_gcd([2,4,2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_mod_gcd([2,4,2], [2]) == ([2], [1, 2, 1], [1])
assert zzx_heu_gcd([2], [2,4,2]) == ([2], [1], [1, 2, 1])
assert zzx_mod_gcd([2], [2,4,2]) == ([2], [1], [1, 2, 1])
assert zzx_heu_gcd([2,4,2], [1,1]) == ([1, 1], [2, 2], [1])
assert zzx_mod_gcd([2,4,2], [1,1]) == ([1, 1], [2, 2], [1])
assert zzx_heu_gcd([1,1], [2,4,2]) == ([1, 1], [1], [2, 2])
assert zzx_mod_gcd([1,1], [2,4,2]) == ([1, 1], [1], [2, 2])
f, g = [1, -31], [1, 0]
assert zzx_heu_gcd(f, g) == ([1], f, g)
assert zzx_mod_gcd(f, g) == ([1], f, g)
f = [1,8,21,22,8]
g = [1,6,11,6]
h = [1,3,2]
cff = [1,5,4]
cfg = [1,3]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
f = [1,0,0,0,-4]
g = [1,0,4,0, 4]
h = [1,0,2]
cff = [1,0,-2]
cfg = [1,0, 2]
assert zzx_heu_gcd(f, g) == (h, cff, cfg)
assert zzx_mod_gcd(f, g) == (h, cff, cfg)
assert zzx_gcd(f, g) == h
assert zzx_cofactors(f, g) == (h, cff, cfg)
f,g,h = zzX_fateman_poly_F_3(4)
H, cff, cfg = zzX_cofactors(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
def test_zzX_mul():
assert zzX_mul([[[]]], [[[]]]) == [[[]]]
assert zzX_mul([[[1]]], [[[]]]) == [[[]]]
assert zzX_mul([[[]]], [[[1]]]) == [[[]]]
assert zzX_mul([[[2]]], [[[1]]]) == [[[2]]]
assert zzX_mul([[[1]]], [[[2]]]) == [[[2]]]
def test_zzX_heu_gcd():
f, g, h = zzX_fateman_poly_F_1(2)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f, g, h = zzX_fateman_poly_F_1(4)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f, g, h = zzX_fateman_poly_F_1(6)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f, g, h = zzX_fateman_poly_F_2(2)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f, g, h = zzX_fateman_poly_F_3(2)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
f, g, h = zzX_fateman_poly_F_1(8)
H, cff, cfg = zzX_heu_gcd(f, g)
assert H == h and zzX_mul(H, cff) == f \
and zzX_mul(H, cfg) == g
