def test_dup_isolate_real_roots_list():
assert dup_isolate_real_roots_list([[1, 1,0], [1,0]], ZZ) == \
[((-QQ(1), -QQ(1)), {0: 1}), ((QQ(0), QQ(0)), {0: 1, 1: 1})]
assert dup_isolate_real_roots_list([[1,-1,0], [1,0]], ZZ) == \
[((QQ(0), QQ(0)), {0: 1, 1: 1}), ((QQ(1), QQ(1)), {0: 1})]
f = dup_from_raw_dict({5: ZZ(1), 0: -ZZ(200)}, ZZ)
g = dup_from_raw_dict({5: ZZ(1), 0: -ZZ(201)}, ZZ)
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((QQ(75,26), QQ(101,35)), {0: 1}), ((QQ(283,98), QQ(26,9)), {1: 1})]
f = dup_from_raw_dict({5: -QQ(1,200), 0: QQ(1)}, QQ)
g = dup_from_raw_dict({5: -QQ(1,201), 0: QQ(1)}, QQ)
assert dup_isolate_real_roots_list([f, g], QQ) == \
[((QQ(75,26), QQ(101,35)), {0: 1}), ((QQ(283,98), QQ(26,9)), {1: 1})]
assert dup_isolate_real_roots_list([[1,1], [1,2], [1,-1], [1,1], [1,-1], [1,-1]], ZZ) == \
[((-QQ(2), -QQ(2)), {1: 1}), ((-QQ(1), -QQ(1)), {0: 1, 3: 1}), ((QQ(1), QQ(1)), {2: 1, 4: 1, 5: 1})]
assert dup_isolate_real_roots_list([[1,1], [1,2], [1,-1], [1,1], [1,-1], [1,2]], ZZ) == \
[((-QQ(2), -QQ(2)), {1: 1, 5: 1}), ((-QQ(1), -QQ(1)), {0: 1, 3: 1}), ((QQ(1), QQ(1)), {2: 1, 4: 1})]
f, g = [1, 0, -4, 0, 4], [1, -1]
assert dup_isolate_real_roots_list([f, g], ZZ, inf=QQ(7,4)) == []
assert dup_isolate_real_roots_list([f, g], ZZ, inf=QQ(7,5)) == [((QQ(7,5), QQ(3,2)), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, sup=QQ(7,5)) == [((-2, -1), {0: 2}), ((1, 1), {1: 1})]
assert dup_isolate_real_roots_list([f, g], ZZ, sup=QQ(7,4)) == [((-2, -1), {0: 2}), ((1, 1), {1: 1}), ((1, QQ(3,2)), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, sup=-QQ(7,4)) == []
assert dup_isolate_real_roots_list([f, g], ZZ, sup=-QQ(7,5)) == [((-QQ(3,2), -QQ(7,5)), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, inf=-QQ(7,5)) == [((1, 1), {1: 1}), ((1, 2), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, inf=-QQ(7,4)) == [((-QQ(3,2), -1), {0: 2}), ((1, 1), {1: 1}), ((1, 2), {0: 2})]
f, g = [2, 0, -1], [1, 0, -2]
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((-QQ(2), -QQ(1)), {1: 1}), ((-QQ(1), QQ(0)), {0: 1}), ((QQ(0), QQ(1)), {0: 1}), ((QQ(1), QQ(2)), {1: 1})]
assert dup_isolate_real_roots_list([f, g], ZZ, strict=True) == \
[((-QQ(3,2), -QQ(4,3)), {1: 1}), ((-QQ(1), -QQ(2,3)), {0: 1}), ((QQ(2,3), QQ(1)), {0: 1}), ((QQ(4,3), QQ(3,2)), {1: 1})]
f, g = [1, 0, -2], [1, -1, -2, 2]
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((-QQ(2), -QQ(1)), {1: 1, 0: 1}), ((QQ(1), QQ(1)), {1: 1}), ((QQ(1), QQ(2)), {1: 1, 0: 1})]
f, g = [1, 0, -2, 0], [1, -1, -2, 2, 0, 0]
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((-QQ(2), -QQ(1)), {1: 1, 0: 1}), ((QQ(0), QQ(0)), {0: 1, 1: 2}), ((QQ(1), QQ(1)), {1: 1}), ((QQ(1), QQ(2)), {1: 1, 0: 1})]
f, g = [1, -3, -1, 11, -8, -8, 12, -4, 0, 0], [1, -2, 3, -4, 2, 0]
assert dup_isolate_real_roots_list([f, g], ZZ, basis=False) == \
[((-2, -1), {0: 2}), ((0, 0), {0: 2, 1: 1}), ((1, 1), {0: 3, 1: 2}), ((1, 2), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, basis=True) == \
[((-2, -1), {0: 2}, [1, 0, -2]), ((0, 0), {0: 2, 1: 1}, [1, 0]), ((1, 1), {0: 3, 1: 2}, [1, -1]), ((1, 2), {0: 2}, [1, 0, -2])]
raises(DomainError, "dup_isolate_real_roots_list([[EX(1), EX(2)]], EX)")
def test_dup_isolate_real_roots_list():
assert dup_isolate_real_roots_list([[1, 1,0], [1,0]], ZZ) == \
[((-QQ(1), -QQ(1)), {0: 1}), ((QQ(0), QQ(0)), {0: 1, 1: 1})]
assert dup_isolate_real_roots_list([[1,-1,0], [1,0]], ZZ) == \
[((QQ(0), QQ(0)), {0: 1, 1: 1}), ((QQ(1), QQ(1)), {0: 1})]
f = dup_from_raw_dict({5: ZZ(1), 0: -ZZ(200)}, ZZ)
g = dup_from_raw_dict({5: ZZ(1), 0: -ZZ(201)}, ZZ)
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((QQ(75,26), QQ(101,35)), {0: 1}), ((QQ(283,98), QQ(26,9)), {1: 1})]
f = dup_from_raw_dict({5: -QQ(1,200), 0: QQ(1)}, QQ)
g = dup_from_raw_dict({5: -QQ(1,201), 0: QQ(1)}, QQ)
assert dup_isolate_real_roots_list([f, g], QQ) == \
[((QQ(75,26), QQ(101,35)), {0: 1}), ((QQ(283,98), QQ(26,9)), {1: 1})]
assert dup_isolate_real_roots_list([[1,1], [1,2], [1,-1], [1,1], [1,-1], [1,-1]], ZZ) == \
[((-QQ(2), -QQ(2)), {1: 1}), ((-QQ(1), -QQ(1)), {0: 1, 3: 1}), ((QQ(1), QQ(1)), {2: 1, 4: 1, 5: 1})]
assert dup_isolate_real_roots_list([[1,1], [1,2], [1,-1], [1,1], [1,-1], [1,2]], ZZ) == \
[((-QQ(2), -QQ(2)), {1: 1, 5: 1}), ((-QQ(1), -QQ(1)), {0: 1, 3: 1}), ((QQ(1), QQ(1)), {2: 1, 4: 1})]
f, g = [1, 0, -4, 0, 4], [1, -1]
assert dup_isolate_real_roots_list([f, g], ZZ, inf=QQ(7,4)) == []
assert dup_isolate_real_roots_list([f, g], ZZ, inf=QQ(7,5)) == [((QQ(7,5), QQ(3,2)), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, sup=QQ(7,5)) == [((-2, -1), {0: 2}), ((1, 1), {1: 1})]
assert dup_isolate_real_roots_list([f, g], ZZ, sup=QQ(7,4)) == [((-2, -1), {0: 2}), ((1, 1), {1: 1}), ((1, QQ(3,2)), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, sup=-QQ(7,4)) == []
assert dup_isolate_real_roots_list([f, g], ZZ, sup=-QQ(7,5)) == [((-QQ(3,2), -QQ(7,5)), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, inf=-QQ(7,5)) == [((1, 1), {1: 1}), ((1, 2), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, inf=-QQ(7,4)) == [((-QQ(3,2), -1), {0: 2}), ((1, 1), {1: 1}), ((1, 2), {0: 2})]
f, g = [2, 0, -1], [1, 0, -2]
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((-QQ(2), -QQ(1)), {1: 1}), ((-QQ(1), QQ(0)), {0: 1}), ((QQ(0), QQ(1)), {0: 1}), ((QQ(1), QQ(2)), {1: 1})]
assert dup_isolate_real_roots_list([f, g], ZZ, strict=True) == \
[((-QQ(3,2), -QQ(4,3)), {1: 1}), ((-QQ(1), -QQ(2,3)), {0: 1}), ((QQ(2,3), QQ(1)), {0: 1}), ((QQ(4,3), QQ(3,2)), {1: 1})]
f, g = [1, 0, -2], [1, -1, -2, 2]
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((-QQ(2), -QQ(1)), {1: 1, 0: 1}), ((QQ(1), QQ(1)), {1: 1}), ((QQ(1), QQ(2)), {1: 1, 0: 1})]
f, g = [1, 0, -2, 0], [1, -1, -2, 2, 0, 0]
assert dup_isolate_real_roots_list([f, g], ZZ) == \
[((-QQ(2), -QQ(1)), {1: 1, 0: 1}), ((QQ(0), QQ(0)), {0: 1, 1: 2}), ((QQ(1), QQ(1)), {1: 1}), ((QQ(1), QQ(2)), {1: 1, 0: 1})]
f, g = [1, -3, -1, 11, -8, -8, 12, -4, 0, 0], [1, -2, 3, -4, 2, 0]
assert dup_isolate_real_roots_list([f, g], ZZ, basis=False) == \
[((-2, -1), {0: 2}), ((0, 0), {0: 2, 1: 1}), ((1, 1), {0: 3, 1: 2}), ((1, 2), {0: 2})]
assert dup_isolate_real_roots_list([f, g], ZZ, basis=True) == \
[((-2, -1), {0: 2}, [1, 0, -2]), ((0, 0), {0: 2, 1: 1}, [1, 0]), ((1, 1), {0: 3, 1: 2}, [1, -1]), ((1, 2), {0: 2}, [1, 0, -2])]
raises(DomainError, lambda: dup_isolate_real_roots_list([[EX(1), EX(2)]], EX))
def test_dup_from_to_dict():
assert dup_from_raw_dict({}, ZZ) == []
assert dup_from_dict({}, ZZ) == []
assert dup_to_raw_dict([]) == {}
assert dup_to_dict([]) == {}
assert dup_to_raw_dict([], ZZ, zero=True) == {0: ZZ(0)}
assert dup_to_dict([], ZZ, zero=True) == {(0,): ZZ(0)}
f = [3,0,0,2,0,0,0,0,8]
g = {8: 3, 5: 2, 0: 8}
h = {(8,): 3, (5,): 2, (0,): 8}
assert dup_from_raw_dict(g, ZZ) == f
assert dup_from_dict(h, ZZ) == f
assert dup_to_raw_dict(f) == g
assert dup_to_dict(f) == h
K = ZZ['x','y']
f = [K([[3]]),K([[]]),K([[2]]),K([[]]),K([[]]),K([[8]])]
g = {5: K([[3]]), 3: K([[2]]), 0: K([[8]])}
h = {(5,): K([[3]]), (3,): K([[2]]), (0,): K([[8]])}
assert dup_from_raw_dict(g, K) == f
assert dup_from_dict(h, K) == f
assert dup_to_raw_dict(f) == g
assert dup_to_dict(f) == h
def test_dup_from_to_dict():
assert dup_from_raw_dict({}, ZZ) == []
assert dup_from_dict({}, ZZ) == []
assert dup_to_raw_dict([]) == {}
assert dup_to_dict([]) == {}
assert dup_to_raw_dict([], ZZ, zero=True) == {0: ZZ(0)}
assert dup_to_dict([], ZZ, zero=True) == {(0,): ZZ(0)}
f = [3, 0, 0, 2, 0, 0, 0, 0, 8]
g = {8: 3, 5: 2, 0: 8}
h = {(8,): 3, (5,): 2, (0,): 8}
assert dup_from_raw_dict(g, ZZ) == f
assert dup_from_dict(h, ZZ) == f
assert dup_to_raw_dict(f) == g
assert dup_to_dict(f) == h
R, x,y = ring("x,y", ZZ)
K = R.to_domain()
f = [R(3), R(0), R(2), R(0), R(0), R(8)]
g = {5: R(3), 3: R(2), 0: R(8)}
h = {(5,): R(3), (3,): R(2), (0,): R(8)}
assert dup_from_raw_dict(g, K) == f
assert dup_from_dict(h, K) == f
assert dup_to_raw_dict(f) == g
assert dup_to_dict(f) == h
def test_dup_from_to_dict():
assert dup_from_raw_dict({}, ZZ) == []
assert dup_from_dict({}, ZZ) == []
assert dup_to_raw_dict([]) == {}
assert dup_to_dict([]) == {}
assert dup_to_raw_dict([], ZZ, zero=True) == {0: ZZ(0)}
assert dup_to_dict([], ZZ, zero=True) == {(0, ): ZZ(0)}
f = [3, 0, 0, 2, 0, 0, 0, 0, 8]
g = {8: 3, 5: 2, 0: 8}
h = {(8, ): 3, (5, ): 2, (0, ): 8}
assert dup_from_raw_dict(g, ZZ) == f
assert dup_from_dict(h, ZZ) == f
assert dup_to_raw_dict(f) == g
assert dup_to_dict(f) == h
R, x, y = ring("x,y", ZZ)
K = R.to_domain()
f = [R(3), R(0), R(2), R(0), R(0), R(8)]
g = {5: R(3), 3: R(2), 0: R(8)}
h = {(5, ): R(3), (3, ): R(2), (0, ): R(8)}
assert dup_from_raw_dict(g, K) == f
assert dup_from_dict(h, K) == f
assert dup_to_raw_dict(f) == g
assert dup_to_dict(f) == h
def test_dup_zz_hensel_lift():
f = dup_from_raw_dict({4:1, 0:-1}, ZZ)
f1 = dup_from_raw_dict({1:1, 0:-1}, ZZ)
f2 = dup_from_raw_dict({1:1, 0:-2}, ZZ)
f3 = dup_from_raw_dict({1:1, 0: 2}, ZZ)
f4 = dup_from_raw_dict({1:1, 0: 1}, ZZ)
ff_list = dup_zz_hensel_lift(5, f, [f1, f2, f3, f4], 4, ZZ)
assert dup_to_raw_dict(ff_list[0]) == {0: -1, 1: 1}
assert dup_to_raw_dict(ff_list[1]) == {0: -182, 1: 1}
assert dup_to_raw_dict(ff_list[2]) == {0: 182, 1: 1}
assert dup_to_raw_dict(ff_list[3]) == {0: 1, 1: 1}
def test_dup_zz_hensel_lift():
f = dup_from_raw_dict({4: 1, 0: -1}, ZZ)
f1 = dup_from_raw_dict({1: 1, 0: -1}, ZZ)
f2 = dup_from_raw_dict({1: 1, 0: -2}, ZZ)
f3 = dup_from_raw_dict({1: 1, 0: 2}, ZZ)
f4 = dup_from_raw_dict({1: 1, 0: 1}, ZZ)
ff_list = dup_zz_hensel_lift(5, f, [f1, f2, f3, f4], 4, ZZ)
assert dup_to_raw_dict(ff_list[0]) == {0: -1, 1: 1}
assert dup_to_raw_dict(ff_list[1]) == {0: -182, 1: 1}
assert dup_to_raw_dict(ff_list[2]) == {0: 182, 1: 1}
assert dup_to_raw_dict(ff_list[3]) == {0: 1, 1: 1}
def _dup_right_decompose(f, s, K):
"""Helper function for :func:`_dup_decompose`."""
n = len(f) - 1
lc = dup_LC(f, K)
f = dup_to_raw_dict(f)
g = {s: K.one}
r = n // s
for i in range(1, s):
coeff = K.zero
for j in range(0, i):
if not n + j - i in f:
continue
if not s - j in g:
continue
fc, gc = f[n + j - i], g[s - j]
coeff += (i - r * j) * fc * gc
g[s - i] = K.quo(coeff, i * r * lc)
return dup_from_raw_dict(g, K)
def _dup_right_decompose(f, s, K):
"""Helper function for :func:`_dup_decompose`."""
n = len(f) - 1
lc = dup_LC(f, K)
f = dup_to_raw_dict(f)
g = { s: K.one }
r = n // s
for i in range(1, s):
coeff = K.zero
for j in range(0, i):
if not n + j - i in f:
continue
if not s - j in g:
continue
fc, gc = f[n + j - i], g[s - j]
coeff += (i - r*j)*fc*gc
g[s - i] = K.quo(coeff, i*r*lc)
return dup_from_raw_dict(g, K)
def test_dup_integrate():
assert dup_integrate([], 1, QQ) == []
assert dup_integrate([], 2, QQ) == []
assert dup_integrate([QQ(1)], 1, QQ) == [QQ(1), QQ(0)]
assert dup_integrate([QQ(1)], 2, QQ) == [QQ(1, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 0, QQ) == [QQ(1), QQ(2), QQ(3)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 1, QQ) == [QQ(1, 3), QQ(1), QQ(3), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 2, QQ) == [QQ(1, 12), QQ(1, 3), QQ(3, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 3, QQ) == [QQ(1, 60), QQ(1, 12), QQ(1, 2), QQ(0), QQ(0), QQ(0)]
assert dup_integrate(dup_from_raw_dict({29: QQ(17)}, QQ), 3, QQ) == dup_from_raw_dict({32: QQ(17, 29760)}, QQ)
assert dup_integrate(dup_from_raw_dict({29: QQ(17), 5: QQ(1, 2)}, QQ), 3, QQ) == dup_from_raw_dict(
{32: QQ(17, 29760), 8: QQ(1, 672)}, QQ
)
def test_dup_zz_hensel_step():
f = dup_from_raw_dict({4: 1, 0: -1}, ZZ)
g = dup_from_raw_dict({3: 1, 2: 2, 1: -1, 0: -2}, ZZ)
h = dup_from_raw_dict({1: 1, 0: -2}, ZZ)
s = dup_from_raw_dict({0: -2}, ZZ)
t = dup_from_raw_dict({2: 2, 1: -2, 0: -1}, ZZ)
G, H, S, T = dup_zz_hensel_step(5, f, g, h, s, t, ZZ)
assert G == dup_from_raw_dict({3: 1, 2: 7, 1: -1, 0: -7}, ZZ)
assert H == dup_from_raw_dict({1: 1, 0: -7}, ZZ)
assert S == dup_from_raw_dict({0: 8}, ZZ)
assert T == dup_from_raw_dict({2: -8, 1: -12, 0: -1}, ZZ)
def test_dup_zz_hensel_step():
f = dup_from_raw_dict({4:1, 0:-1}, ZZ)
g = dup_from_raw_dict({3:1, 2:2, 1:-1, 0:-2}, ZZ)
h = dup_from_raw_dict({1:1, 0:-2}, ZZ)
s = dup_from_raw_dict({0:-2}, ZZ)
t = dup_from_raw_dict({2:2, 1:-2, 0:-1}, ZZ)
G, H, S, T = dup_zz_hensel_step(5, f, g, h, s, t, ZZ)
assert G == dup_from_raw_dict({3:1, 2:7, 1:-1, 0:-7}, ZZ)
assert H == dup_from_raw_dict({1:1, 0:-7}, ZZ)
assert S == dup_from_raw_dict({0:8}, ZZ)
assert T == dup_from_raw_dict({2:-8, 1:-12, 0:-1}, ZZ)
def test_dup_integrate():
assert dup_integrate([], 1, QQ) == []
assert dup_integrate([], 2, QQ) == []
assert dup_integrate([QQ(1)], 1, QQ) == [QQ(1), QQ(0)]
assert dup_integrate([QQ(1)], 2, QQ) == [QQ(1, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 0, QQ) == \
[QQ(1), QQ(2), QQ(3)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 1, QQ) == \
[QQ(1, 3), QQ(1), QQ(3), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 2, QQ) == \
[QQ(1, 12), QQ(1, 3), QQ(3, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 3, QQ) == \
[QQ(1, 60), QQ(1, 12), QQ(1, 2), QQ(0), QQ(0), QQ(0)]
assert dup_integrate(dup_from_raw_dict({29: QQ(17)}, QQ), 3, QQ) == \
dup_from_raw_dict({32: QQ(17, 29760)}, QQ)
assert dup_integrate(dup_from_raw_dict({29: QQ(17), 5: QQ(1, 2)}, QQ), 3, QQ) == \
dup_from_raw_dict({32: QQ(17, 29760), 8: QQ(1, 672)}, QQ)
def _dup_left_decompose(f, h, K):
"""Helper function for :func:`_dup_decompose`."""
g, i = {}, 0
while f:
q, r = dup_div(f, h, K)
if dup_degree(r) > 0:
return None
else:
g[i] = dup_LC(r, K)
f, i = q, i + 1
return dup_from_raw_dict(g, K)
def _dup_left_decompose(f, h, K):
"""Helper function for :func:`_dup_decompose`."""
g, i = {}, 0
while f:
q, r = dup_div(f, h, K)
if dup_degree(r) > 0:
return None
else:
g[i] = dup_LC(r, K)
f, i = q, i + 1
return dup_from_raw_dict(g, K)
def test_dup_deflate():
assert dup_deflate([], ZZ) == (1, [])
assert dup_deflate([2], ZZ) == (1, [2])
assert dup_deflate([1, 2, 3], ZZ) == (1, [1, 2, 3])
assert dup_deflate([1, 0, 2, 0, 3], ZZ) == (2, [1, 2, 3])
assert dup_deflate(dup_from_raw_dict({7: 1, 1: 1}, ZZ), ZZ) == (1, [1, 0, 0, 0, 0, 0, 1, 0])
assert dup_deflate(dup_from_raw_dict({7: 1, 0: 1}, ZZ), ZZ) == (7, [1, 1])
assert dup_deflate(dup_from_raw_dict({7: 1, 3: 1}, ZZ), ZZ) == (1, [1, 0, 0, 0, 1, 0, 0, 0])
assert dup_deflate(dup_from_raw_dict({7: 1, 4: 1}, ZZ), ZZ) == (1, [1, 0, 0, 1, 0, 0, 0, 0])
assert dup_deflate(dup_from_raw_dict({8: 1, 4: 1}, ZZ), ZZ) == (4, [1, 1, 0])
assert dup_deflate(dup_from_raw_dict({8: 1}, ZZ), ZZ) == (8, [1, 0])
assert dup_deflate(dup_from_raw_dict({7: 1}, ZZ), ZZ) == (7, [1, 0])
assert dup_deflate(dup_from_raw_dict({1: 1}, ZZ), ZZ) == (1, [1, 0])
def test_dup_zz_cyclotomic_factor():
assert dup_zz_cyclotomic_factor([], ZZ) is None
assert dup_zz_cyclotomic_factor([1], ZZ) is None
f = dup_from_raw_dict({10: 2, 0: -1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) is None
f = dup_from_raw_dict({10: 1, 0: -3}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) is None
f = dup_from_raw_dict({10: 1, 5: 1, 0: -1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) is None
f = dup_from_raw_dict({1: 1, 0: 1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, 1]]
f = dup_from_raw_dict({1: 1, 0: -1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, -1]]
f = dup_from_raw_dict({2: 1, 0: 1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, 0, 1]]
f = dup_from_raw_dict({2: 1, 0: -1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1,-1],
[1, 1]]
f = dup_from_raw_dict({27: 1, 0: 1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, 1],
[1, -1, 1],
[1, 0, 0, -1, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
f = dup_from_raw_dict({27: 1, 0: -1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, -1],
[1, 1, 1],
[1, 0, 0, 1, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
def test_dup_zz_cyclotomic_factor():
assert dup_zz_cyclotomic_factor([], ZZ) is None
assert dup_zz_cyclotomic_factor([1], ZZ) is None
f = dup_from_raw_dict({10:2, 0:-1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) is None
f = dup_from_raw_dict({10:1, 0:-3}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) is None
f = dup_from_raw_dict({10:1, 5:1, 0:-1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) is None
f = dup_from_raw_dict({1:1,0:1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, 1]]
f = dup_from_raw_dict({1:1,0:-1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, -1]]
f = dup_from_raw_dict({2:1,0:1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, 0, 1]]
f = dup_from_raw_dict({2:1,0:-1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1,-1],
[1, 1]]
f = dup_from_raw_dict({27:1,0:1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, 1],
[1, -1, 1],
[1, 0, 0, -1, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
f = dup_from_raw_dict({27:1,0:-1}, ZZ)
assert dup_zz_cyclotomic_factor(f, ZZ) == \
[[1, -1],
[1, 1, 1],
[1, 0, 0, 1, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
def dmp_fateman_poly_F_3(n, K):
"""Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """
u = dup_from_raw_dict({n+1: K.one}, K)
for i in xrange(0, n-1):
u = dmp_add_term([u], dmp_one(i, K), n+1, i+1, K)
v = dmp_add_term(u, dmp_ground(K(2), n-2), 0, n, K)
f = dmp_sqr(dmp_add_term([dmp_neg(v, n-1, K)], dmp_one(n-1, K), n+1, n, K), n, K)
g = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
v = dmp_add_term(u, dmp_one(n-2, K), 0, n-1, K)
h = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
return dmp_mul(f, h, n, K), dmp_mul(g, h, n, K), h
def dmp_fateman_poly_F_3(n, K):
"""Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """
u = dup_from_raw_dict({n+1: K.one}, K)
for i in xrange(0, n-1):
u = dmp_add_term([u], dmp_one(i, K), n+1, i+1, K)
v = dmp_add_term(u, dmp_ground(K(2), n-2), 0, n, K)
f = dmp_sqr(dmp_add_term([dmp_neg(v, n-1, K)], dmp_one(n-1, K), n+1, n, K), n, K)
g = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
v = dmp_add_term(u, dmp_one(n-2, K), 0, n-1, K)
h = dmp_sqr(dmp_add_term([v], dmp_one(n-1, K), n+1, n, K), n, K)
return dmp_mul(f, h, n, K), dmp_mul(g, h, n, K), h
def test_dup_deflate():
assert dup_deflate([], ZZ) == (1, [])
assert dup_deflate([2], ZZ) == (1, [2])
assert dup_deflate([1, 2, 3], ZZ) == (1, [1, 2, 3])
assert dup_deflate([1, 0, 2, 0, 3], ZZ) == (2, [1, 2, 3])
assert dup_deflate(dup_from_raw_dict({
7: 1,
1: 1
}, ZZ), ZZ) == (
1,
[1, 0, 0, 0, 0, 0, 1, 0],
)
assert dup_deflate(dup_from_raw_dict({7: 1, 0: 1}, ZZ), ZZ) == (7, [1, 1])
assert dup_deflate(dup_from_raw_dict({
7: 1,
3: 1
}, ZZ), ZZ) == (
1,
[1, 0, 0, 0, 1, 0, 0, 0],
)
assert dup_deflate(dup_from_raw_dict({
7: 1,
4: 1
}, ZZ), ZZ) == (
1,
[1, 0, 0, 1, 0, 0, 0, 0],
)
assert dup_deflate(dup_from_raw_dict({
8: 1,
4: 1
}, ZZ), ZZ) == (4, [1, 1, 0])
assert dup_deflate(dup_from_raw_dict({8: 1}, ZZ), ZZ) == (8, [1, 0])
assert dup_deflate(dup_from_raw_dict({7: 1}, ZZ), ZZ) == (7, [1, 0])
assert dup_deflate(dup_from_raw_dict({1: 1}, ZZ), ZZ) == (1, [1, 0])
def test_dup_zz_factor():
assert dup_zz_factor([], ZZ) == (0, [])
assert dup_zz_factor([7], ZZ) == (7, [])
assert dup_zz_factor([-7], ZZ) == (-7, [])
assert dup_zz_factor_sqf([], ZZ) == (0, [])
assert dup_zz_factor_sqf([7], ZZ) == (7, [])
assert dup_zz_factor_sqf([-7], ZZ) == (-7, [])
assert dup_zz_factor([2,4], ZZ) == \
(2, [([1, 2], 1)])
assert dup_zz_factor_sqf([2,4], ZZ) == \
(2, [([1, 2], 1)])
f = [1, 0, 0, 1, 1]
for i in xrange(0, 20):
assert dup_zz_factor(f, ZZ) == (1, [(f, 1)])
assert dup_zz_factor([1,2,2], ZZ) == \
(1, [([1,2,2], 1)])
assert dup_zz_factor([18,12,2], ZZ) == \
(2, [([3, 1], 2)])
assert dup_zz_factor([-9,0,1], ZZ) == \
(-1, [([3,-1], 1),
([3, 1], 1)])
assert dup_zz_factor_sqf([-9,0,1], ZZ) == \
(-1, [[3,-1],
[3, 1]])
assert dup_zz_factor([1,-6,11,-6], ZZ) == \
(1, [([1,-3], 1),
([1,-2], 1),
([1,-1], 1)])
assert dup_zz_factor_sqf([1,-6,11,-6], ZZ) == \
(1, [[1,-3],
[1,-2],
[1,-1]])
assert dup_zz_factor([3,10,13,10], ZZ) == \
(1, [([1,2], 1),
([3,4,5], 1)])
assert dup_zz_factor_sqf([3,10,13,10], ZZ) == \
(1, [[1,2],
[3,4,5]])
assert dup_zz_factor([-1,0,0,0,1,0,0], ZZ) == \
(-1, [([1,-1], 1),
([1, 1], 1),
([1, 0], 2),
([1, 0, 1], 1)])
f = [1080, 5184, 2099, 744, 2736, -648, 129, 0, -324]
assert dup_zz_factor(f, ZZ) == \
(1, [([5, 24, 9, 0, 12], 1),
([216, 0, 31, 0, -27], 1)])
f = [
-29802322387695312500000000000000000000, 0, 0, 0, 0,
2980232238769531250000000000000000, 0, 0, 0, 0,
1743435859680175781250000000000, 0, 0, 0, 0,
114142894744873046875000000, 0, 0, 0, 0, -210106372833251953125, 0, 0,
0, 0, 95367431640625
]
assert dup_zz_factor(f, ZZ) == \
(-95367431640625, [([5, -1], 1),
([100, 10, -1], 2),
([625, 125, 25, 5, 1], 1),
([10000, -3000, 400, -20, 1], 2),
([10000, 2000, 400, 30, 1], 2)])
f = dup_from_raw_dict({10: 1, 0: -1}, ZZ)
F_0 = dup_zz_factor(f, ZZ, cyclotomic=True)
F_1 = dup_zz_factor(f, ZZ, cyclotomic=False)
assert F_0 == F_1 == \
(1, [([1,-1], 1),
([1, 1], 1),
([1,-1, 1,-1, 1], 1),
([1, 1, 1, 1, 1], 1)])
f = dup_from_raw_dict({10: 1, 0: 1}, ZZ)
F_0 = dup_zz_factor(f, ZZ, cyclotomic=True)
F_1 = dup_zz_factor(f, ZZ, cyclotomic=False)
assert F_0 == F_1 == \
(1, [([1, 0, 1], 1),
([1, 0, -1, 0, 1, 0, -1, 0, 1], 1)])
def test_dup_zz_factor():
assert dup_zz_factor([], ZZ) == (0, [])
assert dup_zz_factor([7], ZZ) == (7, [])
assert dup_zz_factor([-7], ZZ) == (-7, [])
assert dup_zz_factor_sqf([], ZZ) == (0, [])
assert dup_zz_factor_sqf([7], ZZ) == (7, [])
assert dup_zz_factor_sqf([-7], ZZ) == (-7, [])
assert dup_zz_factor([2,4], ZZ) == \
(2, [([1, 2], 1)])
assert dup_zz_factor_sqf([2,4], ZZ) == \
(2, [([1, 2], 1)])
f = [1,0,0,1,1]
for i in xrange(0, 20):
assert dup_zz_factor(f, ZZ) == (1, [(f, 1)])
assert dup_zz_factor([1,2,2], ZZ) == \
(1, [([1,2,2], 1)])
assert dup_zz_factor([18,12,2], ZZ) == \
(2, [([3, 1], 2)])
assert dup_zz_factor([-9,0,1], ZZ) == \
(-1, [([3,-1], 1),
([3, 1], 1)])
assert dup_zz_factor_sqf([-9,0,1], ZZ) == \
(-1, [[3,-1],
[3, 1]])
assert dup_zz_factor([1,-6,11,-6], ZZ) == \
(1, [([1,-3], 1),
([1,-2], 1),
([1,-1], 1)])
assert dup_zz_factor_sqf([1,-6,11,-6], ZZ) == \
(1, [[1,-3],
[1,-2],
[1,-1]])
assert dup_zz_factor([3,10,13,10], ZZ) == \
(1, [([1,2], 1),
([3,4,5], 1)])
assert dup_zz_factor_sqf([3,10,13,10], ZZ) == \
(1, [[1,2],
[3,4,5]])
assert dup_zz_factor([-1,0,0,0,1,0,0], ZZ) == \
(-1, [([1,-1], 1),
([1, 1], 1),
([1, 0], 2),
([1, 0, 1], 1)])
f = [1080, 5184, 2099, 744, 2736, -648, 129, 0, -324]
assert dup_zz_factor(f, ZZ) == \
(1, [([5, 24, 9, 0, 12], 1),
([216, 0, 31, 0, -27], 1)])
f = [-29802322387695312500000000000000000000,
0, 0, 0, 0,
2980232238769531250000000000000000,
0, 0, 0, 0,
1743435859680175781250000000000,
0, 0, 0, 0,
114142894744873046875000000,
0, 0, 0, 0,
-210106372833251953125,
0, 0, 0, 0,
95367431640625]
assert dup_zz_factor(f, ZZ) == \
(-95367431640625, [([5, -1], 1),
([100, 10, -1], 2),
([625, 125, 25, 5, 1], 1),
([10000, -3000, 400, -20, 1], 2),
([10000, 2000, 400, 30, 1], 2)])
f = dup_from_raw_dict({10:1, 0:-1}, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', True)
F_0 = dup_zz_factor(f, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', False)
F_1 = dup_zz_factor(f, ZZ)
assert F_0 == F_1 == \
(1, [([1,-1], 1),
([1, 1], 1),
([1,-1, 1,-1, 1], 1),
([1, 1, 1, 1, 1], 1)])
config.setup('USE_CYCLOTOMIC_FACTOR')
f = dup_from_raw_dict({10:1, 0:1}, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', True)
F_0 = dup_zz_factor(f, ZZ)
config.setup('USE_CYCLOTOMIC_FACTOR', False)
F_1 = dup_zz_factor(f, ZZ)
assert F_0 == F_1 == \
(1, [([1, 0, 1], 1),
([1, 0, -1, 0, 1, 0, -1, 0, 1], 1)])
config.setup('USE_CYCLOTOMIC_FACTOR')