def test_sring():
x, y, z, t = symbols("x,y,z,t")
R = PolyRing("x,y,z", ZZ, lex)
assert sring(x + 2 * y + 3 * z) == (R, R.x + 2 * R.y + 3 * R.z)
R = PolyRing("x,y,z", QQ, lex)
assert sring(x + 2 * y + z / 3) == (R, R.x + 2 * R.y + R.z / 3)
assert sring([x, 2 * y, z / 3]) == (R, [R.x, 2 * R.y, R.z / 3])
Rt = PolyRing("t", ZZ, lex)
R = PolyRing("x,y,z", Rt, lex)
assert sring(x + 2 * t * y + 3 * t**2 * z, x, y,
z) == (R, R.x + 2 * Rt.t * R.y + 3 * Rt.t**2 * R.z)
Rt = PolyRing("t", QQ, lex)
R = PolyRing("x,y,z", Rt, lex)
assert sring(x + t * y / 2 + t**2 * z / 3, x, y,
z) == (R, R.x + Rt.t * R.y / 2 + Rt.t**2 * R.z / 3)
Rt = FracField("t", ZZ, lex)
R = PolyRing("x,y,z", Rt, lex)
assert sring(x + 2 * y / t + t**2 * z / 3, x, y,
z) == (R, R.x + 2 * R.y / Rt.t + Rt.t**2 * R.z / 3)
r = sqrt(2) - sqrt(3)
R, a = sring(r, extension=True)
assert R.domain == QQ.algebraic_field(sqrt(2) + sqrt(3))
assert R.gens == ()
assert a == R.domain.from_sympy(r)
def test_pickling_polys_fields():
# NOTE: can't use protocols < 2 because we have to execute __new__ to
# make sure caching of fields works properly.
from sympy.polys.fields import FracField
field = FracField("x,y,z", ZZ, lex)
def test_sfield():
x = symbols("x")
F = FracField((E, exp(exp(x)), exp(x)), ZZ, lex)
e, exex, ex = F.gens
assert sfield(exp(x)*exp(exp(x) + 1 + log(exp(x) + 3)/2)**2/(exp(x) + 3)) \
== (F, e**2*exex**2*ex)
F = FracField((x, exp(1 / x), log(x), x**QQ(1, 3)), ZZ, lex)
_, ex, lg, x3 = F.gens
assert sfield(((x-3)*log(x)+4*x**2)*exp(1/x+log(x)/3)/x**2) == \
(F, (4*F.x**2*ex + F.x*ex*lg - 3*ex*lg)/x3**5)
F = FracField((x, log(x), sqrt(x + log(x))), ZZ, lex)
_, lg, srt = F.gens
assert sfield((x + 1) / (x * (x + log(x))**QQ(3, 2)) - 1/(x * log(x)**2)) \
== (F, (F.x*lg**2 - F.x*srt + lg**2 - lg*srt)/
(F.x**2*lg**2*srt + F.x*lg**3*srt))
def __init__(self, domain_or_field, symbols=None, order=None):
from sympy.polys.fields import FracField
if isinstance(domain_or_field, FracField) and symbols is None and order is None:
field = domain_or_field
else:
field = FracField(symbols, domain_or_field, order)
self.field = field
self.dtype = field.dtype
self.gens = field.gens
self.ngens = field.ngens
self.symbols = field.symbols
self.domain = field.domain
# TODO: remove this
self.dom = self.domain
def test_sring():
x, y, z, t = symbols("x,y,z,t")
R = PolyRing("x,y,z", ZZ, lex)
assert sring(x + 2*y + 3*z) == (R, R.x + 2*R.y + 3*R.z)
R = PolyRing("x,y,z", QQ, lex)
assert sring(x + 2*y + z/3) == (R, R.x + 2*R.y + R.z/3)
assert sring([x, 2*y, z/3]) == (R, [R.x, 2*R.y, R.z/3])
Rt = PolyRing("t", ZZ, lex)
R = PolyRing("x,y,z", Rt, lex)
assert sring(x + 2*t*y + 3*t**2*z, x, y, z) == (R, R.x + 2*Rt.t*R.y + 3*Rt.t**2*R.z)
Rt = PolyRing("t", QQ, lex)
R = PolyRing("x,y,z", Rt, lex)
assert sring(x + t*y/2 + t**2*z/3, x, y, z) == (R, R.x + Rt.t*R.y/2 + Rt.t**2*R.z/3)
Rt = FracField("t", ZZ, lex)
R = PolyRing("x,y,z", Rt, lex)
assert sring(x + 2*y/t + t**2*z/3, x, y, z) == (R, R.x + 2*R.y/Rt.t + Rt.t**2*R.z/3)
def to_field(self):
from sympy.polys.fields import FracField
return FracField(self.symbols, self.domain, self.order)
def frac_field(self, *symbols): # TODO:, order=lex):
"""Returns a fraction field, i.e. `K(X)`. """
from sympy.polys.fields import FracField
return FracField(symbols, self.field, order).to_domain()
