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