132 lines
3.7 KiB
Python
132 lines
3.7 KiB
Python
"""Test ideals.py code."""
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from sympy.polys import QQ, ilex
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from sympy.abc import x, y, z
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from sympy.testing.pytest import raises
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def test_ideal_operations():
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R = QQ.old_poly_ring(x, y)
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I = R.ideal(x)
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J = R.ideal(y)
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S = R.ideal(x*y)
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T = R.ideal(x, y)
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assert not (I == J)
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assert I == I
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assert I.union(J) == T
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assert I + J == T
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assert I + T == T
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assert not I.subset(T)
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assert T.subset(I)
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assert I.product(J) == S
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assert I*J == S
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assert x*J == S
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assert I*y == S
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assert R.convert(x)*J == S
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assert I*R.convert(y) == S
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assert not I.is_zero()
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assert not J.is_whole_ring()
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assert R.ideal(x**2 + 1, x).is_whole_ring()
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assert R.ideal() == R.ideal(0)
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assert R.ideal().is_zero()
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assert T.contains(x*y)
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assert T.subset([x, y])
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assert T.in_terms_of_generators(x) == [R(1), R(0)]
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assert T**0 == R.ideal(1)
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assert T**1 == T
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assert T**2 == R.ideal(x**2, y**2, x*y)
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assert I**5 == R.ideal(x**5)
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def test_exceptions():
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I = QQ.old_poly_ring(x).ideal(x)
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J = QQ.old_poly_ring(y).ideal(1)
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raises(ValueError, lambda: I.union(x))
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raises(ValueError, lambda: I + J)
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raises(ValueError, lambda: I * J)
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raises(ValueError, lambda: I.union(J))
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assert (I == J) is False
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assert I != J
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def test_nontriv_global():
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R = QQ.old_poly_ring(x, y, z)
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def contains(I, f):
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return R.ideal(*I).contains(f)
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assert contains([x, y], x)
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assert contains([x, y], x + y)
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assert not contains([x, y], 1)
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assert not contains([x, y], z)
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assert contains([x**2 + y, x**2 + x], x - y)
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assert not contains([x + y + z, x*y + x*z + y*z, x*y*z], x**2)
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assert contains([x + y + z, x*y + x*z + y*z, x*y*z], x**3)
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assert contains([x + y + z, x*y + x*z + y*z, x*y*z], x**4)
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assert not contains([x + y + z, x*y + x*z + y*z, x*y*z], x*y**2)
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assert contains([x + y + z, x*y + x*z + y*z, x*y*z], x**4 + y**3 + 2*z*y*x)
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assert contains([x + y + z, x*y + x*z + y*z, x*y*z], x*y*z)
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assert contains([x, 1 + x + y, 5 - 7*y], 1)
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assert contains(
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[x**3 + y**3, y**3 + z**3, z**3 + x**3, x**2*y + x**2*z + y**2*z],
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x**3)
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assert not contains(
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[x**3 + y**3, y**3 + z**3, z**3 + x**3, x**2*y + x**2*z + y**2*z],
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x**2 + y**2)
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# compare local order
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assert not contains([x*(1 + x + y), y*(1 + z)], x)
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assert not contains([x*(1 + x + y), y*(1 + z)], x + y)
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def test_nontriv_local():
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R = QQ.old_poly_ring(x, y, z, order=ilex)
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def contains(I, f):
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return R.ideal(*I).contains(f)
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assert contains([x, y], x)
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assert contains([x, y], x + y)
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assert not contains([x, y], 1)
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assert not contains([x, y], z)
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assert contains([x**2 + y, x**2 + x], x - y)
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assert not contains([x + y + z, x*y + x*z + y*z, x*y*z], x**2)
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assert contains([x*(1 + x + y), y*(1 + z)], x)
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assert contains([x*(1 + x + y), y*(1 + z)], x + y)
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def test_intersection():
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R = QQ.old_poly_ring(x, y, z)
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# SCA, example 1.8.11
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assert R.ideal(x, y).intersect(R.ideal(y**2, z)) == R.ideal(y**2, y*z, x*z)
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assert R.ideal(x, y).intersect(R.ideal()).is_zero()
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R = QQ.old_poly_ring(x, y, z, order="ilex")
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assert R.ideal(x, y).intersect(R.ideal(y**2 + y**2*z, z + z*x**3*y)) == \
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R.ideal(y**2, y*z, x*z)
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def test_quotient():
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# SCA, example 1.8.13
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R = QQ.old_poly_ring(x, y, z)
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assert R.ideal(x, y).quotient(R.ideal(y**2, z)) == R.ideal(x, y)
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def test_reduction():
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from sympy.polys.distributedmodules import sdm_nf_buchberger_reduced
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R = QQ.old_poly_ring(x, y)
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I = R.ideal(x**5, y)
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e = R.convert(x**3 + y**2)
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assert I.reduce_element(e) == e
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assert I.reduce_element(e, NF=sdm_nf_buchberger_reduced) == R.convert(x**3)
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