Exemplo n.º 1
0
from sympy import FiniteSet

set_one = FiniteSet(1, 2, 3)
set_two = FiniteSet(1, 2, 3)

subset = set_one.is_proper_subset(set_two)
print("Set one proper subset set two:")
print(subset)

print()

subset = set_two.is_proper_subset(set_one)
print("Set two proper subset set one:")
print(subset)

print()

set_three = FiniteSet(1, 2, 3, 4)

subset = set_one.is_proper_subset(set_three)
print("Set one proper subset set three:")
print(subset)

print()

subset = set_three.is_proper_subset(set_one)
print("Set three proper subset set one:")
print(subset)
Exemplo n.º 2
0
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))
Exemplo n.º 3
0
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)
B = FiniteSet(2, 3)
print(A.intersect(B))

# Diferencia entre conjuntos
print('-' * 30)
Exemplo n.º 4
0
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
print(ninthset.is_proper_subset(eigthset)) #print True
print(ninthset.is_proper_superset(eigthset)) #print False
print(eigthset.is_proper_superset(ninthset)) #print True

tenthset = FiniteSet(1, 2, 3)
eleventhset = FiniteSet(2, 4, 6)
print(tenthset.union(eleventhset)) #print {1, 2, 3, 4, 6}
print(tenthset.intersect(eleventhset)) #print {2}
#we can apply union and intersect to more than two sets.
tenthset = FiniteSet(1, 2, 3)
eleventhset = FiniteSet(2, 4, 6)
twelthset = FiniteSet(3, 5, 7)
print(tenthset.union(eleventhset).union(twelthset)) #print {1, 2, 3, 4, 5, 6, 7}
print(tenthset.intersect(eleventhset).intersect(twelthset)) #print EmptySet()
Exemplo n.º 5
0
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))

# 冪集合を求める例。
# ※冪集合:ある集合の、全ての部分集合を列挙した集合。
#        ある集合の濃度をsとすれば、部分集合の個数は、2^sとなることが知られている。
print(FiniteSet(3, 1, 2).powerset())

# 集合の和集合や積集合を求める。
s = FiniteSet(1, 2, 3)
Exemplo n.º 6
0
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)

t.is_proper_subset(s)
s.is_proper_subset(t)

s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)
s.union(t)

s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)
s.intersect(t)

s = FiniteSet(1, 2, 3)
Exemplo n.º 7
0

>>> s=FiniteSet(1,2,3)
>>> ps=s.powerset()
>>> ps
{EmptySet(), {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
>>> len(ps)
8


               #A set s is a proper subset of t iff t contains all the members of s and at least one more member.
               #A set t is a proper superset of s iff t contains all the members of s and at least one more member.

>>> s=FiniteSet(1,2,3)
>>> t=FiniteSet(1,2,3)
>>> s.is_proper_subset(t)
False
>>> t.is_proper_superset(s)
False

>>> t=FiniteSet(1,2,3,4)
>>> s.is_proper_subset(t)
True
>>> t.is_proper_superset(s)
True

         #Set Operations

               #Union and intersection

>>> s=FiniteSet(1,2,3)
Exemplo n.º 8
0
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)
t = FiniteSet(1, 2, 3)
s.is_proper_subset(t)       # False
t.is_proper_subset(s)       # False

t = FiniteSet(1, 2, 3, 4)
s.is_proper_subset(t)       # True
t.is_proper_subset(s)       # True