def test_finite_basic():
x = Symbol('x')
A = FiniteSet(1, 2, 3)
B = FiniteSet(3, 4, 5)
AorB = Union(A, B)
AandB = A.intersect(B)
assert A.is_subset(AorB) and B.is_subset(AorB)
assert AandB.is_subset(A)
assert AandB == FiniteSet(3)
assert A.inf == 1 and A.sup == 3
assert AorB.inf == 1 and AorB.sup == 5
assert FiniteSet(x, 1, 5).sup == Max(x, 5)
assert FiniteSet(x, 1, 5).inf == Min(x, 1)
# issue 7335
assert FiniteSet(S.EmptySet) != S.EmptySet
assert FiniteSet(FiniteSet(1, 2, 3)) != FiniteSet(1, 2, 3)
assert FiniteSet((1, 2, 3)) != FiniteSet(1, 2, 3)
# Ensure a variety of types can exist in a FiniteSet
s = FiniteSet((1, 2), Float, A, -5, x, 'eggs', x**2, Interval)
assert (A > B) is False
assert (A >= B) is False
assert (A < B) is False
assert (A <= B) is False
assert AorB > A and AorB > B
assert AorB >= A and AorB >= B
assert A >= A and A <= A
assert A >= AandB and B >= AandB
assert A > AandB and B > AandB
def test_real():
x = Symbol('x', real=True, finite=True)
I = Interval(0, 5)
J = Interval(10, 20)
A = FiniteSet(1, 2, 30, x, S.Pi)
B = FiniteSet(-4, 0)
C = FiniteSet(100)
D = FiniteSet('Ham', 'Eggs')
assert all(s.is_subset(S.Reals) for s in [I, J, A, B, C])
assert not D.is_subset(S.Reals)
assert all((a + b).is_subset(S.Reals) for a in [I, J, A, B, C] for b in [I, J, A, B, C])
assert not any((a + D).is_subset(S.Reals) for a in [I, J, A, B, C, D])
assert not (I + A + D).is_subset(S.Reals)
from sympy import FiniteSet
from fractions import Fraction
s = FiniteSet(1)
t = FiniteSet(1, 2)
print("Is s is subset of t ", s.is_subset(t))
print("Is t is subset of s ", t.is_subset(s))
s = FiniteSet(1, 2, 3)
ps = s.powerset()
print("Power set ", ps)
s = FiniteSet(1, 2, 3)
t = FiniteSet(1, 2, 3)
print("Is s is proper subset ", s.is_proper_subset(t))
print("Is t is proper subset ", t.is_proper_subset(s))
s = FiniteSet(1, 2, 3)
t = FiniteSet(1, 2, 3, 4)
print("Is s is proper subset ", s.is_proper_subset(t))
print("Is t is proper subset ", t.is_proper_subset(s))
# Igualdad
print('-' * 30)
A = FiniteSet(1, 2, 3)
B = FiniteSet(1, 3, 2)
print(A == B)
A = FiniteSet(1, 2, 3)
B = FiniteSet(1, 3, 4)
print(A == B)
# Subconjunto y subconjunto propio
print('-' * 30)
A = FiniteSet(1, 2, 3)
B = FiniteSet(1, 2, 3, 4, 5)
print(A.is_subset(B))
# A == B. El test de subconjunto propio da falso
print('-' * 30)
B = FiniteSet(2, 1, 3)
print(A.is_proper_subset(B))
# Union de dos conjuntos
print('-' * 30)
A = FiniteSet(1, 2, 3)
B = FiniteSet(2, 4, 6)
print(A.union(B))
# Interseccion de dos conjuntos
print('-' * 30)
A = FiniteSet(1, 2)
numberslist = [1, 99, 840]
fifthset = FiniteSet(*numberslist)
print(fifthset) #print {1, 99, 840}
print(set(numberslist)) #print {840, 1, 99}
#sets ignore repeats of a member and don't keep track of the order
numberslist2 = [1, 99, 7392, 99]
sixthset = FiniteSet(*numberslist2)
print(sixthset) #print {1, 99, 7392}
for eachsixthset in sixthset:
print(eachsixthset) #print 1\n 99\n 7392
#A set is a subset of another set if all the members are also members of the other set. Remember, all.
seventhset = FiniteSet(999, 439, 20984)
eigthset = FiniteSet(999, 69, 48)
ninthset = FiniteSet(999, 69)
print(seventhset.is_subset(eigthset)) #print False
print(eigthset.is_subset(seventhset)) #print False
print(ninthset.is_subset(eigthset)) #print True
#A set is a superset if the set contains all of the members. Remember, contains.
print(ninthset.is_superset(eigthset)) #print False
print(eigthset.is_superset(ninthset)) #print True
#The power set is the set of all possible subsets
tenthset = FiniteSet(20, 55, 41, 98)
print(tenthset.powerset()) #print {EmptySet(), {20}, {41}, ..., {20, 55, 98}, {41, 55, 98}, {20, 41, 55, 98}}
seventhset = FiniteSet(999, 439, 20984)
eigthset = FiniteSet(999, 69, 48)
ninthset = FiniteSet(999, 69)
print(seventhset.is_proper_subset(eigthset)) #print False
print(eigthset.is_proper_subset(seventhset)) #print False
# 集合オブジェクトの特徴 # 集合オブジェクトは重複を許さない s1 = FiniteSet(1, 3, 3, 5) print(s1) # 集合オブジェクトの順序は不定で、全ての要素が等しければ等価なオブジェクトである。 s2 = FiniteSet(5, 1, 3) print(s1 == s2) # 以下、集合に対する概念(若干マイナーな概念も含むかも...)。 sub = FiniteSet(1, 2) super = FiniteSet(1, 2, 3) # AはBの部分集合か? print(sub.is_subset(super)) # AはBの上位集合か? print(super.is_superset(sub)) # AはBの真部分集合か? # ※真部分集合:Bが、Aにない要素を一つ以上含んでいる場合、BをAの真部分集合と呼ぶ。 print(sub.is_proper_subset(super)) # AはBの真上位集合か? print(super.is_proper_superset(sub)) # 通常の上位集合と、真上位集合の違い。 print(FiniteSet(3, 1, 2).is_superset(super)) print(FiniteSet(3, 1, 2).is_proper_superset(super))
s
a = FiniteSet(1, 2, 3)
for member in a:
print(member)
a = FiniteSet(3, 4, 5)
t = FiniteSet(5, 4, 3)
s == t
a = FiniteSet(1)
t = FiniteSet(1, 2)
s.is_subset(t)
t.is_subset(t)
s = FiniteSet(1, 2, 3)
ps = s.powerset()
ps
len(ps)
s = FiniteSet(1, 2, 3)
t = FiniteSet(1, 2, 3)
s.is_proper_subset(t)
t = FiniteSet(1, 2, 3, 4)
#Two sets are said to be equal when they have the same mebers, irrelevant of their order
>>> s=FiniteSet(3,4,5)
>>> t=FiniteSet(5,4,3)
>>> s==t
True
#Subsets,Supersets and Power Sets
#A set s is a subset of another set t if all the members of s are also members of t
>>> s=FiniteSet(1)
>>> t=FiniteSet(1,2)
>>> s.is_subset(t)
True
>>> t.is_subset(s)
False
#An empty set is also a susbset of every set.
#Also, any set is a subset of itself
>>> e=FiniteSet()
>>> e.is_subset(t)
True
>>> e.is_subset(s)
True
>>> s.is_subset(s)
True
# Check whether a number is in the set
4 in s # False
# Empty Set
s = FiniteSet() # EmptySet()
# Set Repetition and Order
members = [1, 2, 3, 2]
FiniteSet(*members) # {1, 2, 3}
for member in s:
print(member) # 1, 2, 3
# Subsets -> if all the members of s are also a member of t
s = FiniteSet(1)
t = FiniteSet(1,2)
s.is_subset(t) # True
t.is_subset(s) # False
# Supersets -> if t contains all of the members contained in s
s.is_superset(t) # True
t.is_superset(s) # True
# Powerset -> is the set of all possible subsets of s
s = FiniteSet(1, 2, 3)
ps = s.powerset()
ps # {{1}, {1, 2}, {1, 3}, {1, 2, 3}, {2}, {2, 3}, {3}, EmptySet()}
len(ps) # 8
# Proper subset -> if all the members of s are also in t and t has at least one member that is not in s
s = FiniteSet(1, 2, 3)
