103 lines
3.2 KiB
Python
103 lines
3.2 KiB
Python
|
"""Tests for the PolynomialRing classes. """
|
||
|
|
|
||
|
|
from sympy.polys.domains import QQ, ZZ
|
||
|
|
from sympy.polys.polyerrors import ExactQuotientFailed, CoercionFailed, NotReversible
|
||
|
|
|
||
|
|
from sympy.abc import x, y
|
||
|
|
|
||
|
|
from sympy.testing.pytest import raises
|
||
|
|
|
||
|
|
|
||
|
|
def test_build_order():
|
||
|
|
R = QQ.old_poly_ring(x, y, order=(("lex", x), ("ilex", y)))
|
||
|
|
assert R.order((1, 5)) == ((1,), (-5,))
|
||
|
|
|
||
|
|
|
||
|
|
def test_globalring():
|
||
|
|
Qxy = QQ.old_frac_field(x, y)
|
||
|
|
R = QQ.old_poly_ring(x, y)
|
||
|
|
X = R.convert(x)
|
||
|
|
Y = R.convert(y)
|
||
|
|
|
||
|
|
assert x in R
|
||
|
|
assert 1/x not in R
|
||
|
|
assert 1/(1 + x) not in R
|
||
|
|
assert Y in R
|
||
|
|
assert X.ring == R
|
||
|
|
assert X * (Y**2 + 1) == R.convert(x * (y**2 + 1))
|
||
|
|
assert X * y == X * Y == R.convert(x * y) == x * Y
|
||
|
|
assert X + y == X + Y == R.convert(x + y) == x + Y
|
||
|
|
assert X - y == X - Y == R.convert(x - y) == x - Y
|
||
|
|
assert X + 1 == R.convert(x + 1)
|
||
|
|
raises(ExactQuotientFailed, lambda: X/Y)
|
||
|
|
raises(ExactQuotientFailed, lambda: x/Y)
|
||
|
|
raises(ExactQuotientFailed, lambda: X/y)
|
||
|
|
assert X**2 / X == X
|
||
|
|
|
||
|
|
assert R.from_GlobalPolynomialRing(ZZ.old_poly_ring(x, y).convert(x), ZZ.old_poly_ring(x, y)) == X
|
||
|
|
assert R.from_FractionField(Qxy.convert(x), Qxy) == X
|
||
|
|
assert R.from_FractionField(Qxy.convert(x)/y, Qxy) is None
|
||
|
|
|
||
|
|
assert R._sdm_to_vector(R._vector_to_sdm([X, Y], R.order), 2) == [X, Y]
|
||
|
|
|
||
|
|
|
||
|
|
def test_localring():
|
||
|
|
Qxy = QQ.old_frac_field(x, y)
|
||
|
|
R = QQ.old_poly_ring(x, y, order="ilex")
|
||
|
|
X = R.convert(x)
|
||
|
|
Y = R.convert(y)
|
||
|
|
|
||
|
|
assert x in R
|
||
|
|
assert 1/x not in R
|
||
|
|
assert 1/(1 + x) in R
|
||
|
|
assert Y in R
|
||
|
|
assert X.ring == R
|
||
|
|
assert X*(Y**2 + 1)/(1 + X) == R.convert(x*(y**2 + 1)/(1 + x))
|
||
|
|
assert X*y == X*Y
|
||
|
|
raises(ExactQuotientFailed, lambda: X/Y)
|
||
|
|
raises(ExactQuotientFailed, lambda: x/Y)
|
||
|
|
raises(ExactQuotientFailed, lambda: X/y)
|
||
|
|
assert X + y == X + Y == R.convert(x + y) == x + Y
|
||
|
|
assert X - y == X - Y == R.convert(x - y) == x - Y
|
||
|
|
assert X + 1 == R.convert(x + 1)
|
||
|
|
assert X**2 / X == X
|
||
|
|
|
||
|
|
assert R.from_GlobalPolynomialRing(ZZ.old_poly_ring(x, y).convert(x), ZZ.old_poly_ring(x, y)) == X
|
||
|
|
assert R.from_FractionField(Qxy.convert(x), Qxy) == X
|
||
|
|
raises(CoercionFailed, lambda: R.from_FractionField(Qxy.convert(x)/y, Qxy))
|
||
|
|
raises(ExactQuotientFailed, lambda: X/Y)
|
||
|
|
raises(NotReversible, lambda: X.invert())
|
||
|
|
|
||
|
|
assert R._sdm_to_vector(
|
||
|
|
R._vector_to_sdm([X/(X + 1), Y/(1 + X*Y)], R.order), 2) == \
|
||
|
|
[X*(1 + X*Y), Y*(1 + X)]
|
||
|
|
|
||
|
|
|
||
|
|
def test_conversion():
|
||
|
|
L = QQ.old_poly_ring(x, y, order="ilex")
|
||
|
|
G = QQ.old_poly_ring(x, y)
|
||
|
|
|
||
|
|
assert L.convert(x) == L.convert(G.convert(x), G)
|
||
|
|
assert G.convert(x) == G.convert(L.convert(x), L)
|
||
|
|
raises(CoercionFailed, lambda: G.convert(L.convert(1/(1 + x)), L))
|
||
|
|
|
||
|
|
|
||
|
|
def test_units():
|
||
|
|
R = QQ.old_poly_ring(x)
|
||
|
|
assert R.is_unit(R.convert(1))
|
||
|
|
assert R.is_unit(R.convert(2))
|
||
|
|
assert not R.is_unit(R.convert(x))
|
||
|
|
assert not R.is_unit(R.convert(1 + x))
|
||
|
|
|
||
|
|
R = QQ.old_poly_ring(x, order='ilex')
|
||
|
|
assert R.is_unit(R.convert(1))
|
||
|
|
assert R.is_unit(R.convert(2))
|
||
|
|
assert not R.is_unit(R.convert(x))
|
||
|
|
assert R.is_unit(R.convert(1 + x))
|
||
|
|
|
||
|
|
R = ZZ.old_poly_ring(x)
|
||
|
|
assert R.is_unit(R.convert(1))
|
||
|
|
assert not R.is_unit(R.convert(2))
|
||
|
|
assert not R.is_unit(R.convert(x))
|
||
|
|
assert not R.is_unit(R.convert(1 + x))
|