68 lines
2.6 KiB
Python
68 lines
2.6 KiB
Python
from sympy.sets.ordinals import Ordinal, OmegaPower, ord0, omega
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from sympy.testing.pytest import raises
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def test_string_ordinals():
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assert str(omega) == 'w'
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assert str(Ordinal(OmegaPower(5, 3), OmegaPower(3, 2))) == 'w**5*3 + w**3*2'
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assert str(Ordinal(OmegaPower(5, 3), OmegaPower(0, 5))) == 'w**5*3 + 5'
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assert str(Ordinal(OmegaPower(1, 3), OmegaPower(0, 5))) == 'w*3 + 5'
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assert str(Ordinal(OmegaPower(omega + 1, 1), OmegaPower(3, 2))) == 'w**(w + 1) + w**3*2'
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def test_addition_with_integers():
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assert 3 + Ordinal(OmegaPower(5, 3)) == Ordinal(OmegaPower(5, 3))
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assert Ordinal(OmegaPower(5, 3))+3 == Ordinal(OmegaPower(5, 3), OmegaPower(0, 3))
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assert Ordinal(OmegaPower(5, 3), OmegaPower(0, 2))+3 == \
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Ordinal(OmegaPower(5, 3), OmegaPower(0, 5))
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def test_addition_with_ordinals():
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assert Ordinal(OmegaPower(5, 3), OmegaPower(3, 2)) + Ordinal(OmegaPower(3, 3)) == \
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Ordinal(OmegaPower(5, 3), OmegaPower(3, 5))
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assert Ordinal(OmegaPower(5, 3), OmegaPower(3, 2)) + Ordinal(OmegaPower(4, 2)) == \
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Ordinal(OmegaPower(5, 3), OmegaPower(4, 2))
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assert Ordinal(OmegaPower(omega, 2), OmegaPower(3, 2)) + Ordinal(OmegaPower(4, 2)) == \
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Ordinal(OmegaPower(omega, 2), OmegaPower(4, 2))
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def test_comparison():
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assert Ordinal(OmegaPower(5, 3)) > Ordinal(OmegaPower(4, 3), OmegaPower(2, 1))
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assert Ordinal(OmegaPower(5, 3), OmegaPower(3, 2)) < Ordinal(OmegaPower(5, 4))
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assert Ordinal(OmegaPower(5, 4)) < Ordinal(OmegaPower(5, 5), OmegaPower(4, 1))
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assert Ordinal(OmegaPower(5, 3), OmegaPower(3, 2)) == \
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Ordinal(OmegaPower(5, 3), OmegaPower(3, 2))
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assert not Ordinal(OmegaPower(5, 3), OmegaPower(3, 2)) == Ordinal(OmegaPower(5, 3))
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assert Ordinal(OmegaPower(omega, 3)) > Ordinal(OmegaPower(5, 3))
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def test_multiplication_with_integers():
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w = omega
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assert 3*w == w
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assert w*9 == Ordinal(OmegaPower(1, 9))
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def test_multiplication():
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w = omega
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assert w*(w + 1) == w*w + w
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assert (w + 1)*(w + 1) == w*w + w + 1
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assert w*1 == w
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assert 1*w == w
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assert w*ord0 == ord0
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assert ord0*w == ord0
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assert w**w == w * w**w
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assert (w**w)*w*w == w**(w + 2)
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def test_exponentiation():
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w = omega
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assert w**2 == w*w
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assert w**3 == w*w*w
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assert w**(w + 1) == Ordinal(OmegaPower(omega + 1, 1))
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assert (w**w)*(w**w) == w**(w*2)
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def test_comapre_not_instance():
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w = OmegaPower(omega + 1, 1)
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assert(not (w == None))
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assert(not (w < 5))
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raises(TypeError, lambda: w < 6.66)
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def test_is_successort():
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w = Ordinal(OmegaPower(5, 1))
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assert not w.is_successor_ordinal
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