def test_sets():
x = Integer(2)
y = Integer(3)
x1 = sympy.Integer(2)
y1 = sympy.Integer(3)
assert Interval(x, y) == Interval(x1, y1)
assert Interval(x1, y) == Interval(x1, y1)
assert Interval(x, y)._sympy_() == sympy.Interval(x1, y1)
assert sympify(sympy.Interval(x1, y1)) == Interval(x, y)
assert sympify(sympy.EmptySet()) == EmptySet()
assert sympy.EmptySet() == EmptySet()._sympy_()
assert FiniteSet(x, y) == FiniteSet(x1, y1)
assert FiniteSet(x1, y) == FiniteSet(x1, y1)
assert FiniteSet(x, y)._sympy_() == sympy.FiniteSet(x1, y1)
assert sympify(sympy.FiniteSet(x1, y1)) == FiniteSet(x, y)
x = Interval(1, 2)
y = Interval(2, 3)
x1 = sympy.Interval(1, 2)
y1 = sympy.Interval(2, 3)
assert Union(x, y) == Union(x1, y1)
assert Union(x1, y) == Union(x1, y1)
assert Union(x, y)._sympy_() == sympy.Union(x1, y1)
assert sympify(sympy.Union(x1, y1)) == Union(x, y)
assert Complement(x, y) == Complement(x1, y1)
assert Complement(x1, y) == Complement(x1, y1)
assert Complement(x, y)._sympy_() == sympy.Complement(x1, y1)
assert sympify(sympy.Complement(x1, y1)) == Complement(x, y)
def test_FiniteSet():
x = Symbol("x")
A = FiniteSet(1, 2, 3)
B = FiniteSet(3, 4, 5)
AorB = Union(A, B)
AandB = A.intersection(B)
assert AandB == FiniteSet(3)
assert FiniteSet(EmptySet()) != EmptySet()
assert FiniteSet(FiniteSet(1, 2, 3)) != FiniteSet(1, 2, 3)
def test_solve():
x = Symbol("x")
reals = Interval(-oo, oo)
assert solve(1, x, reals) == EmptySet()
assert solve(0, x, reals) == reals
assert solve(x + 3, x, reals) == FiniteSet(-3)
assert solve(x + 3, x, Interval(0, oo)) == EmptySet()
assert solve(x, x, reals) == FiniteSet(0)
assert solve(x**2 + 1, x) == FiniteSet(-I, I)
assert solve(x**2 - 2*x + 1, x) == FiniteSet(1)
assert solve(Eq(x**3 + 3*x**2 + 3*x, -1), x, reals) == FiniteSet(-1)
assert solve(x**3 - x, x) == FiniteSet(0, 1, -1)
def test_ConditionSet():
x = Symbol("x")
i1 = Interval(-oo, oo)
f1 = FiniteSet(0, 1, 2, 4)
cond1 = Ge(x**2, 9)
assert ConditionSet(x, And(Eq(0, 1), i1.contains(x))) == EmptySet()
assert ConditionSet(x, And(Gt(1, 0), i1.contains(x))) == i1
assert ConditionSet(x, And(cond1, f1.contains(x))) == FiniteSet(4)
def test_sets():
x = Integer(2)
y = Integer(3)
x1 = sympy.Integer(2)
y1 = sympy.Integer(3)
assert Interval(x, y) == Interval(x1, y1)
assert Interval(x1, y) == Interval(x1, y1)
assert Interval(x, y)._sympy_() == sympy.Interval(x1, y1)
assert sympify(sympy.Interval(x1, y1)) == Interval(x, y)
assert sympify(sympy.S.EmptySet) == EmptySet()
assert sympy.S.EmptySet == EmptySet()._sympy_()
assert sympify(sympy.S.UniversalSet) == UniversalSet()
assert sympy.S.UniversalSet == UniversalSet()._sympy_()
assert sympify(sympy.S.Reals) == Reals()
assert sympy.S.Reals == Reals()._sympy_()
assert sympify(sympy.S.Rationals) == Rationals()
assert sympy.S.Rationals == Rationals()._sympy_()
assert sympify(sympy.S.Integers) == Integers()
assert sympy.S.Integers == Integers()._sympy_()
assert FiniteSet(x, y) == FiniteSet(x1, y1)
assert FiniteSet(x1, y) == FiniteSet(x1, y1)
assert FiniteSet(x, y)._sympy_() == sympy.FiniteSet(x1, y1)
assert sympify(sympy.FiniteSet(x1, y1)) == FiniteSet(x, y)
x = Interval(1, 2)
y = Interval(2, 3)
x1 = sympy.Interval(1, 2)
y1 = sympy.Interval(2, 3)
assert Union(x, y) == Union(x1, y1)
assert Union(x1, y) == Union(x1, y1)
assert Union(x, y)._sympy_() == sympy.Union(x1, y1)
assert sympify(sympy.Union(x1, y1)) == Union(x, y)
assert Complement(x, y) == Complement(x1, y1)
assert Complement(x1, y) == Complement(x1, y1)
assert Complement(x, y)._sympy_() == sympy.Complement(x1, y1)
assert sympify(sympy.Complement(x1, y1)) == Complement(x, y)
def test_Union():
assert Union(Interval(1, 2), Interval(2, 3)) == Interval(1, 3)
assert Union(Interval(1, 2), Interval(2, 3, True)) == Interval(1, 3)
assert Union(Interval(1, 3), Interval(2, 4)) == Interval(1, 4)
assert Union(Interval(1, 2), Interval(1, 3)) == Interval(1, 3)
assert Union(Interval(1, 3), Interval(1, 2)) == Interval(1, 3)
assert Union(Interval(1, 3, False, True), Interval(1, 2)) == \
Interval(1, 3, False, True)
assert Union(Interval(1, 3), Interval(1, 2, False, True)) == Interval(1, 3)
assert Union(Interval(1, 2, True), Interval(1, 3)) == Interval(1, 3)
assert Union(Interval(1, 2, True), Interval(1, 3, True)) == \
Interval(1, 3, True)
assert Union(Interval(1, 2, True), Interval(1, 3, True, True)) == \
Interval(1, 3, True, True)
assert Union(Interval(1, 2, True, True), Interval(1, 3, True)) == \
Interval(1, 3, True)
assert Union(Interval(1, 3), Interval(2, 3)) == Interval(1, 3)
assert Union(Interval(1, 3, False, True), Interval(2, 3)) == \
Interval(1, 3)
assert Union(Interval(1, 2, False, True), Interval(2, 3, True)) != \
Interval(1, 3)
assert Union(Interval(1, 2), EmptySet()) == Interval(1, 2)
assert Union(EmptySet()) == EmptySet()
def test_Interval():
assert Interval(0, oo) == Interval(0, oo, False, True)
assert Interval(-oo, 0) == Interval(-oo, 0, True, False)
assert Interval(oo, -oo) == EmptySet()
assert Interval(oo, oo) == EmptySet()
assert Interval(-oo, -oo) == EmptySet()
assert isinstance(Interval(1, 1), FiniteSet)
assert Interval(1, 0) == EmptySet()
assert Interval(1, 1, False, True) == EmptySet()
assert Interval(1, 1, True, False) == EmptySet()
assert Interval(1, 1, True, True) == EmptySet()
assert Interval(1, 2).union(Interval(2, 3)) == Interval(1, 3)
def test_Interval():
assert Interval(0, oo) == Interval(0, oo, False, True)
assert Interval(0, oo) == Interval(0, oo, left_open=False, right_open=True)
assert Interval(-oo, 0) == Interval(-oo, 0, True, False)
assert Interval(-oo, 0) == Interval(-oo,
0,
left_open=True,
right_open=False)
assert Interval(oo, -oo) == EmptySet()
assert Interval(oo, oo) == EmptySet()
assert Interval(-oo, -oo) == EmptySet()
assert isinstance(Interval(1, 1), FiniteSet)
assert Interval(1, 0) == EmptySet()
assert Interval(1, 1, False, True) == EmptySet()
assert Interval(1, 1, True, False) == EmptySet()
assert Interval(1, 1, True, True) == EmptySet()
assert Interval(1, 2).union(Interval(2, 3)) == Interval(1, 3)
assert Interval(-oo, 0).start == -oo
assert Interval(-oo, 0).end == 0
def test_ImageSet():
x = Symbol("x")
i1 = Interval(0, 1)
assert ImageSet(x, x**2, EmptySet()) == EmptySet()
assert ImageSet(x, 1, i1) == FiniteSet(1)
assert ImageSet(x, x, i1) == i1
def test_EmptySet():
E = EmptySet()
assert E.intersection(UniversalSet()) == E