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rl/Lib/site-packages/sympy/polys/domains/tests/test_polynomialring.py

@@ -0,0 +1,93 @@
+"""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 * (Y**2 + 1) == R.convert(x * (y**2 + 1))
+    assert X + 1 == R.convert(x + 1)
+    raises(ExactQuotientFailed, lambda: X/Y)
+    raises(TypeError, lambda: x/Y)
+    raises(TypeError, 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*(Y**2 + 1)/(1 + X) == R.convert(x*(y**2 + 1)/(1 + x))
+    raises(TypeError, lambda: x/Y)
+    raises(TypeError, lambda: 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: R.exquo(X, Y))
+    raises(NotReversible, lambda: R.revert(X))
+
+    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))

rl/Lib/site-packages/sympy/polys/domains/tests/test_quotientring.py

@@ -0,0 +1,52 @@
+"""Tests for quotient rings."""
+
+from sympy.polys.domains.integerring import ZZ
+from sympy.polys.domains.rationalfield import QQ
+from sympy.abc import x, y
+
+from sympy.polys.polyerrors import NotReversible
+
+from sympy.testing.pytest import raises
+
+
+def test_QuotientRingElement():
+    R = QQ.old_poly_ring(x)/[x**10]
+    X = R.convert(x)
+
+    assert X*(X + 1) == R.convert(x**2 + x)
+    assert X*x == R.convert(x**2)
+    assert x*X == R.convert(x**2)
+    assert X + x == R.convert(2*x)
+    assert x + X == 2*X
+    assert X**2 == R.convert(x**2)
+    assert 1/(1 - X) == R.convert(sum(x**i for i in range(10)))
+    assert X**10 == R.zero
+    assert X != x
+
+    raises(NotReversible, lambda: 1/X)
+
+
+def test_QuotientRing():
+    I = QQ.old_poly_ring(x).ideal(x**2 + 1)
+    R = QQ.old_poly_ring(x)/I
+
+    assert R == QQ.old_poly_ring(x)/[x**2 + 1]
+    assert R == QQ.old_poly_ring(x)/QQ.old_poly_ring(x).ideal(x**2 + 1)
+    assert R != QQ.old_poly_ring(x)
+
+    assert R.convert(1)/x == -x + I
+    assert -1 + I == x**2 + I
+    assert R.convert(ZZ(1), ZZ) == 1 + I
+    assert R.convert(R.convert(x), R) == R.convert(x)
+
+    X = R.convert(x)
+    Y = QQ.old_poly_ring(x).convert(x)
+    assert -1 + I == X**2 + I
+    assert -1 + I == Y**2 + I
+    assert R.to_sympy(X) == x
+
+    raises(ValueError, lambda: QQ.old_poly_ring(x)/QQ.old_poly_ring(x, y).ideal(x))
+
+    R = QQ.old_poly_ring(x, order="ilex")
+    I = R.ideal(x)
+    assert R.convert(1) + I == (R/I).convert(1)