def test_dmp_from_to_dict():
assert dmp_from_dict({}, 1, ZZ) == [[]]
assert dmp_to_dict([[]], 1) == {}
assert dmp_to_dict([], 0, ZZ, zero=True) == {(0,): ZZ(0)}
assert dmp_to_dict([[]], 1, ZZ, zero=True) == {(0, 0): ZZ(0)}
f = [[3], [], [], [2], [], [], [], [], [8]]
g = {(8, 0): 3, (5, 0): 2, (0, 0): 8}
assert dmp_from_dict(g, 1, ZZ) == f
assert dmp_to_dict(f, 1) == g
def test_dmp_from_to_dict():
assert dmp_from_dict({}, 0, ZZ) == []
assert dmp_to_dict([], 0) == {}
f = [3, 0, 0, 2, 0, 0, 0, 0, 8]
h = {(8, ): 3, (5, ): 2, (0, ): 8}
assert dmp_from_dict(h, 0, ZZ) == f
assert dmp_to_dict(f, 0) == h
R, x, y = ring("x,y", ZZ)
f = [R(3), R(0), R(2), R(0), R(0), R(8)]
h = {(5, ): R(3), (3, ): R(2), (0, ): R(8)}
assert dmp_from_dict(h, 0, R) == f
assert dmp_to_dict(f, 0) == h
assert dmp_to_dict([1, 0, 5, 0, 7], 0) == {(0, ): 7, (2, ): 5, (4, ): 1}
assert dmp_from_dict({}, 1, ZZ) == [[]]
assert dmp_to_dict([[]], 1) == {}
f = [[3], [], [], [2], [], [], [], [], [8]]
g = {(8, 0): 3, (5, 0): 2, (0, 0): 8}
assert dmp_from_dict(g, 1, ZZ) == f
assert dmp_to_dict(f, 1) == g
def test_dup_from_to_dict():
assert dup_from_dict({}, ZZ) == []
assert dmp_to_dict([], 0) == {}
assert dmp_to_dict([], 0, ZZ, zero=True) == {(0, ): ZZ(0)}
f = [3, 0, 0, 2, 0, 0, 0, 0, 8]
h = {(8, ): 3, (5, ): 2, (0, ): 8}
assert dup_from_dict(h, ZZ) == f
assert dmp_to_dict(f, 0) == h
R, x, y = ring("x,y", ZZ)
f = [R(3), R(0), R(2), R(0), R(0), R(8)]
h = {(5, ): R(3), (3, ): R(2), (0, ): R(8)}
assert dup_from_dict(h, R) == f
assert dmp_to_dict(f, 0) == h
assert dmp_to_dict([1, 0, 5, 0, 7], 0) == {(0, ): 7, (2, ): 5, (4, ): 1}
def dmp_lift(f, u, K):
"""
Convert algebraic coefficients to integers in ``K[X]``.
Examples
========
>>> from diofant.polys import ring, QQ
>>> from diofant import I
>>> K = QQ.algebraic_field(I)
>>> R, x = ring("x", K)
>>> f = x**2 + K([QQ(1), QQ(0)])*x + K([QQ(2), QQ(0)])
>>> R.dmp_lift(f)
x**8 + 2*x**6 + 9*x**4 - 8*x**2 + 16
"""
if not K.is_Algebraic:
raise DomainError(
'computation can be done only in an algebraic domain')
F, monoms, polys = dmp_to_dict(f, u), [], []
for monom, coeff in F.items():
if not coeff.is_ground:
monoms.append(monom)
perms = variations([-1, 1], len(monoms), repetition=True)
for perm in perms:
G = dict(F)
for sign, monom in zip(perm, monoms):
if sign == -1:
G[monom] = -G[monom]
polys.append(dmp_from_dict(G, u, K))
return dmp_convert(dmp_expand(polys, u, K), u, K, K.domain)