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- """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)
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