def test_dmp_from_to_dict():
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_dmp_from_to_dict():
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_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 to_sympy_dict(f, zero=False):
"""Convert `f` to a dict representation with SymPy coefficients. """
rep = dmp_to_dict(f.rep, f.lev, f.dom, zero=zero)
for k, v in rep.iteritems():
rep[k] = f.dom.to_sympy(v)
return rep
def to_sympy_dict(f, zero=False):
"""Convert `f` to a dict representation with SymPy coefficients. """
rep = dmp_to_dict(f.rep, f.lev, f.dom, zero=zero)
for k, v in rep.iteritems():
rep[k] = f.dom.to_sympy(v)
return rep
def to_sympy_dict(f):
"""Convert ``f`` to a dict representation with SymPy coefficients. """
rep = dmp_to_dict(f.rep, 0, f.dom)
for k, v in rep.iteritems():
rep[k] = f.dom.to_sympy(v)
return rep
def to_sympy_dict(f):
"""Convert ``f`` to a dict representation with SymPy coefficients. """
rep = dmp_to_dict(f.rep, 0, f.dom)
for k, v in rep.iteritems():
rep[k] = f.dom.to_sympy(v)
return rep
def dmp_lift(f, u, K):
"""
Convert algebraic coefficients to integers in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, QQ
>>> from sympy 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 K.is_GaussianField:
K1 = K.as_AlgebraicField()
f = dmp_convert(f, u, K, K1)
K = K1
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.dom)
def dmp_lift(f, u, K):
"""
Convert algebraic coefficients to integers in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, QQ
>>> from sympy 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.dom)
def dmp_lift(f, u, K):
"""
Convert algebraic coefficients to integers in ``K[X]``.
Examples
========
>>> from sympy import I
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.densetools import dmp_lift
>>> K = QQ.algebraic_field(I)
>>> f = [K(1), K([QQ(1), QQ(0)]), K([QQ(2), QQ(0)])]
>>> dmp_lift(f, 0, K)
[1/1, 0/1, 2/1, 0/1, 9/1, 0/1, -8/1, 0/1, 16/1]
"""
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.iteritems():
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.dom)
def dmp_lift(f, u, K):
"""
Convert algebraic coefficients to integers in ``K[X]``.
Examples
========
>>> from sympy import I
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.densetools import dmp_lift
>>> K = QQ.algebraic_field(I)
>>> f = [K(1), K([QQ(1), QQ(0)]), K([QQ(2), QQ(0)])]
>>> dmp_lift(f, 0, K)
[1/1, 0/1, 2/1, 0/1, 9/1, 0/1, -8/1, 0/1, 16/1]
"""
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.iteritems():
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.dom)
def is_quadratic(f):
"""Returns `True` if `f` is quadratic in all its variables. """
return all([ sum(monom) <= 2 for monom in dmp_to_dict(f.rep, f.lev, f.dom).keys() ])
def is_quadratic(f):
"""Returns `True` if `f` is quadratic in all its variables. """
return all([ sum(monom) <= 2 for monom in dmp_to_dict(f.rep, f.lev, f.dom).keys() ])
def is_linear(f):
"""Returns `True` if `f` is linear in all its variables. """
return all([ sum(monom) <= 1 for monom in dmp_to_dict(f.rep, f.lev, f.dom).keys() ])
def to_dict(f):
"""Convert `f` to a dict representation with native coefficients. """
return dmp_to_dict(f.rep, 0, f.dom)
def to_dict(f, zero=False):
"""Convert `f` to a dict representation with native coefficients. """
return dmp_to_dict(f.rep, f.lev, f.dom, zero=zero)
def to_dict(f):
"""Convert `f` to a dict representation with native coefficients. """
return dmp_to_dict(f.rep, 0, f.dom)
def to_dict(f, zero=False):
"""Convert `f` to a dict representation with native coefficients. """
return dmp_to_dict(f.rep, f.lev, f.dom, zero=zero)
def is_linear(f):
"""Returns `True` if `f` is linear in all its variables. """
return all([ sum(monom) <= 1 for monom in dmp_to_dict(f.rep, f.lev, f.dom).keys() ])
