def test_finiteset_rewrite_powerset():
assert FiniteSet(S.EmptySet).rewrite(PowerSet) == PowerSet(S.EmptySet)
assert FiniteSet(
S.EmptySet, FiniteSet(1),
FiniteSet(2), FiniteSet(1, 2)).rewrite(PowerSet) == \
PowerSet(FiniteSet(1, 2))
assert FiniteSet(1, 2, 3).rewrite(PowerSet) == FiniteSet(1, 2, 3)
def test_is_subset():
# covers line 101-102
# initalize powerset(1), which is a subset of powerset(1,2)
subset = PowerSet(FiniteSet(1))
pset = PowerSet(FiniteSet(1, 2))
# assert "subset" is subset of pset == True
assert subset.is_subset(pset)
def test_powerset__contains__():
subset_series = [
S.EmptySet,
FiniteSet(1, 2),
S.Naturals,
S.Naturals0,
S.Integers,
S.Rationals,
S.Reals,
S.Complexes]
l = len(subset_series)
for i in range(l):
for j in range(l):
try:
if i <= j:
assert subset_series[i] in \
PowerSet(subset_series[j], evaluate=False)
else:
assert subset_series[i] not in \
PowerSet(subset_series[j], evaluate=False)
except:
raise AssertionError(
'Powerset membership test failed between '
'{} and {}.'.format(subset_series[i], subset_series[j]))
def test_powerset__len__():
A = PowerSet(S.EmptySet, evaluate=False)
assert len(A) == 1
A = PowerSet(A, evaluate=False)
assert len(A) == 2
A = PowerSet(A, evaluate=False)
assert len(A) == 4
A = PowerSet(A, evaluate=False)
assert len(A) == 16
def test_powerset__iter__():
a = PowerSet(FiniteSet(1, 2)).__iter__()
assert next(a) == S.EmptySet
assert next(a) == FiniteSet(1)
assert next(a) == FiniteSet(2)
assert next(a) == FiniteSet(1, 2)
a = PowerSet(S.Naturals).__iter__()
assert next(a) == S.EmptySet
assert next(a) == FiniteSet(1)
assert next(a) == FiniteSet(2)
assert next(a) == FiniteSet(1, 2)
assert next(a) == FiniteSet(3)
assert next(a) == FiniteSet(1, 3)
assert next(a) == FiniteSet(2, 3)
assert next(a) == FiniteSet(1, 2, 3)
def test_powerset__contains__():
subset_series = [
S.EmptySet,
FiniteSet(1, 2), S.Naturals, S.Naturals0, S.Integers, S.Rationals,
S.Reals, S.Complexes
]
l = len(subset_series)
for i in range(l):
for j in range(l):
if i <= j:
assert subset_series[i] in \
PowerSet(subset_series[j], evaluate=False)
else:
assert subset_series[i] not in \
PowerSet(subset_series[j], evaluate=False)
def test_powerset_contains():
A = PowerSet(FiniteSet(1), evaluate=False)
assert A.contains(2) == Contains(2, A)
x = Symbol('x')
A = PowerSet(FiniteSet(x), evaluate=False)
assert A.contains(FiniteSet(1)) == Contains(FiniteSet(1), A)
def test_powerset_method():
# EmptySet
A = FiniteSet()
pset = A.powerset()
assert len(pset) == 1
assert pset == FiniteSet(S.EmptySet)
# FiniteSets
A = FiniteSet(1, 2)
pset = A.powerset()
assert len(pset) == 2**len(A)
assert pset == FiniteSet(FiniteSet(), FiniteSet(1), FiniteSet(2), A)
# Not finite sets
A = Interval(0, 1)
assert A.powerset() == PowerSet(A)
def test_failing_powerset__contains__():
# XXX These are failing when evaluate=True,
# but using unevaluated PowerSet works fine.
assert FiniteSet(1, 2) not in PowerSet(S.EmptySet).rewrite(FiniteSet)
assert S.Naturals not in PowerSet(S.EmptySet).rewrite(FiniteSet)
assert S.Naturals not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet)
assert S.Naturals0 not in PowerSet(S.EmptySet).rewrite(FiniteSet)
assert S.Naturals0 not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet)
assert S.Integers not in PowerSet(S.EmptySet).rewrite(FiniteSet)
assert S.Integers not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet)
assert S.Rationals not in PowerSet(S.EmptySet).rewrite(FiniteSet)
assert S.Rationals not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet)
assert S.Reals not in PowerSet(S.EmptySet).rewrite(FiniteSet)
assert S.Reals not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet)
assert S.Complexes not in PowerSet(S.EmptySet).rewrite(FiniteSet)
assert S.Complexes not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet)
def test_powerset_rewrite_FiniteSet():
assert PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) == \
FiniteSet(S.EmptySet, FiniteSet(1), FiniteSet(2), FiniteSet(1, 2))
assert PowerSet(S.EmptySet).rewrite(FiniteSet) == FiniteSet(S.EmptySet)
assert PowerSet(S.Naturals).rewrite(FiniteSet) == PowerSet(S.Naturals)
def test_powerset_creation():
assert unchanged(PowerSet, FiniteSet(1, 2))
assert unchanged(PowerSet, S.EmptySet)
raises(ValueError, lambda: PowerSet(123))
assert unchanged(PowerSet, S.Reals)
assert unchanged(PowerSet, S.Integers)
Run this cell before any other Declare any other sets here if you'd like """ from sympy import FiniteSet, ProductSet from sympy.sets.powerset import PowerSet """Finite Sets: represents a finite set of discrete numbers""" A = FiniteSet(1, 2, 3, 4, 5) B = FiniteSet(5, 6, 7, 8, 9) C = FiniteSet(9, 10, 11, 12) #%% """Powersets: all possible sets in a set""" E = A.powerset() # Returns a new finite set with a finite set F = PowerSet(A).rewrite(FiniteSet) # Returns a setwith many finite sets print(F) #%% """Cartesian product: """ cp_m1 = ProductSet(A, B) # Uses sympy function cp_m2 = A*B # Sympy syntax for finite sets print()
