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