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 dup_real_imag(f, K):
"""
Return bivariate polynomials ``f1`` and ``f2``, such that ``f = f1 + f2*I``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dup_real_imag(x**3 + x**2 + x + 1)
(x**3 + x**2 - 3*x*y**2 + x - y**2 + 1, 3*x**2*y + 2*x*y - y**3 + y)
"""
if not K.is_ZZ and not K.is_QQ:
raise DomainError(
"computing real and imaginary parts is not supported over %s" % K)
f1 = dmp_zero(1)
f2 = dmp_zero(1)
if not f:
return f1, f2
g = [[[K.one, K.zero]], [[K.one], []]]
h = dmp_ground(f[0], 2)
for c in f[1:]:
h = dmp_mul(h, g, 2, K)
h = dmp_add_term(h, dmp_ground(c, 1), 0, 2, K)
H = dup_to_raw_dict(h)
for k, h in H.items():
m = k % 4
if not m:
f1 = dmp_add(f1, h, 1, K)
elif m == 1:
f2 = dmp_add(f2, h, 1, K)
elif m == 2:
f1 = dmp_sub(f1, h, 1, K)
else:
f2 = dmp_sub(f2, h, 1, K)
return f1, f2
def dup_real_imag(f, K):
"""
Return bivariate polynomials ``f1`` and ``f2``, such that ``f = f1 + f2*I``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densetools import dup_real_imag
>>> dup_real_imag([ZZ(1), ZZ(1), ZZ(1), ZZ(1)], ZZ)
([[1], [1], [-3, 0, 1], [-1, 0, 1]], [[3, 0], [2, 0], [-1, 0, 1, 0]])
"""
if not K.is_ZZ and not K.is_QQ:
raise DomainError(
"computing real and imaginary parts is not supported over %s" % K)
f1 = dmp_zero(1)
f2 = dmp_zero(1)
if not f:
return f1, f2
g = [[[K.one, K.zero]], [[K.one], []]]
h = dmp_ground(f[0], 2)
for c in f[1:]:
h = dmp_mul(h, g, 2, K)
h = dmp_add_term(h, dmp_ground(c, 1), 0, 2, K)
H = dup_to_raw_dict(h)
for k, h in H.iteritems():
m = k % 4
if not m:
f1 = dmp_add(f1, h, 1, K)
elif m == 1:
f2 = dmp_add(f2, h, 1, K)
elif m == 2:
f1 = dmp_sub(f1, h, 1, K)
else:
f2 = dmp_sub(f2, h, 1, K)
return f1, f2
def dup_real_imag(f, K):
"""
Return bivariate polynomials ``f1`` and ``f2``, such that ``f = f1 + f2*I``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densetools import dup_real_imag
>>> dup_real_imag([ZZ(1), ZZ(1), ZZ(1), ZZ(1)], ZZ)
([[1], [1], [-3, 0, 1], [-1, 0, 1]], [[3, 0], [2, 0], [-1, 0, 1, 0]])
"""
if not K.is_ZZ and not K.is_QQ:
raise DomainError(
"computing real and imaginary parts is not supported over %s" % K)
f1 = dmp_zero(1)
f2 = dmp_zero(1)
if not f:
return f1, f2
g = [[[K.one, K.zero]], [[K.one], []]]
h = dmp_ground(f[0], 2)
for c in f[1:]:
h = dmp_mul(h, g, 2, K)
h = dmp_add_term(h, dmp_ground(c, 1), 0, 2, K)
H = dup_to_raw_dict(h)
for k, h in H.iteritems():
m = k % 4
if not m:
f1 = dmp_add(f1, h, 1, K)
elif m == 1:
f2 = dmp_add(f2, h, 1, K)
elif m == 2:
f1 = dmp_sub(f1, h, 1, K)
else:
f2 = dmp_sub(f2, h, 1, K)
return f1, f2
def dup_real_imag(f, K):
"""
Return bivariate polynomials ``f1`` and ``f2``, such that ``f = f1 + f2*I``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dup_real_imag(x**3 + x**2 + x + 1)
(x**3 + x**2 - 3*x*y**2 + x - y**2 + 1, 3*x**2*y + 2*x*y - y**3 + y)
"""
if not K.is_ZZ and not K.is_QQ:
raise DomainError("computing real and imaginary parts is not supported over %s" % K)
f1 = dmp_zero(1)
f2 = dmp_zero(1)
if not f:
return f1, f2
g = [[[K.one, K.zero]], [[K.one], []]]
h = dmp_ground(f[0], 2)
for c in f[1:]:
h = dmp_mul(h, g, 2, K)
h = dmp_add_term(h, dmp_ground(c, 1), 0, 2, K)
H = dup_to_raw_dict(h)
for k, h in H.items():
m = k % 4
if not m:
f1 = dmp_add(f1, h, 1, K)
elif m == 1:
f2 = dmp_add(f2, h, 1, K)
elif m == 2:
f1 = dmp_sub(f1, h, 1, K)
else:
f2 = dmp_sub(f2, h, 1, K)
return f1, f2
