Exemple #1
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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
Exemple #2
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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
Exemple #3
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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 AorB.subset(A) and AorB.subset(B)
    assert A.subset(AandB)
    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)

    # Ensure a variety of types can exist in a FiniteSet
    S = FiniteSet((1, 2), Float, A, -5, x, 'eggs', x**2, Interval)
Exemple #4
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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 AorB.subset(A) and AorB.subset(B)
    assert A.subset(AandB)
    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)

    # Ensure a variety of types can exist in a FiniteSet
    S = FiniteSet((1,2), Float, A, -5, x, 'eggs', x**2, Interval)
Exemple #5
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# 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)
print(A - B)

# Calculando el producto cartesiano. Con el conjunto por
# defecto de python no podemos hacer esto con el operador *
print('-' * 30)
A = FiniteSet(1, 2)
B = FiniteSet(3, 4)
P = A * B
print(P)

for elem in P:
    print(elem)
# Union
s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)
s.union(t)              # {1, 2, 3, 4, 6,}

# Union of three Sets
s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)
u = FiniteSet(3, 5, 7)
s.union(t).union(u)     # {1, 2, 3, 4, 5, 6, 7}

# Intersection
s = FiniteSet(1, 2)
t = FiniteSet(2, 3)
s.intersect(t)          # 2

# Intersection of three Sets
s.intersect(t).interset(u)      # EmpySet()

# Cartesian Product
s = FiniteSet(1, 2)
t = FiniteSet(3, 4)
p = s*t
p                       # {1, 2} x {3, 4}
for elem in p:
    print(elem)         # (1, 3), (1,4), (2, 3), (2, 4)

# Cardinality of the Cartesian Product
len(p) == len(s)*len(t)     # True
Exemple #7
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	event = FiniteSet( *primes )

	p = probability( space, event )
	
	print( 'Sample Space: {0}'.format( space ) )
	print( 'Event: {0}'.format( event ) )
	print( 'Probability of rolling a prime: {0:.5f}'.format( p ) )


# P( A | B )

s = FiniteSet( 1, 2, 3, 4, 5, 6 )
a = FiniteSet( 2, 3, 5 )
b = FiniteSet( 1, 3, 5 )

e = a.union( b )

probability( s, e )

# P( A & B )

s = FiniteSet( 1, 2, 3, 4, 5, 6 )
a = FiniteSet( 2, 3, 5 )
b = FiniteSet( 1, 3, 5 )

e = a.intersect( b )

probability( s, e )

from sympy import FiniteSet

six_sided = FiniteSet(1, 2, 3, 4, 5, 6)
roll_one = FiniteSet(2, 3, 5)
roll_two = FiniteSet(1, 3, 5)

event = roll_one.intersect(roll_two)
prob = len(event) / len(six_sided)
print(prob)
s = FiniteSet(1, 15
iFraction(1, 5)
for member in s:
    print(member)
t = FiniteSet(Fraction(1, 5), 1.5, 1, 1)
if s == t:
    print("True")
s.intersect(t)
s.unson(t)
p = s ** 2
p1 = s ** 3
A = FiniteSet(1, 10, 20)
B = FiniteSet(5, 8)
if A == B:
    var = A.intersect(B).union
A ** 2,


list1 = [1, 4, 7, 84, 3, 62, 23]
myd = dict()
# myd1={}
myd = {1: 'bir', 2: 2, '3': 'three'}
print(myd)
for key in myd.keys():
    print(key, myd[key])
var = 1 in myd
if -41 not in myd:
    myd[-40] = 50
print(myd)
from sympy import FiniteSet

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

t == s  #burası biraz saçma
t.union(s)  #t kümesi ile s kümesini birleştirir. (t U s)
t.intersect(s)  #t kümesi ile s kümesini ayirir t kesişim s demek

t**2  #burası biraz saçma


def probability(space, event):
    return len(event) / len(space)


def check_prime(number):  #asal sayilari bulur
    if number != 1:
        for factor in range(2, number):
            if number % factor == 0:
                return False
    else:
        return False
    return True


space = FiniteSet(*range(1, 21))
primes = []
for num in space:
    if check_prime(num):
        primes.append(num)
Exemple #11
0
True
>>> t.is_proper_superset(s)
True

         #Set Operations

               #Union and intersection

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

>>> s=FiniteSet(1,2)
>>> t=FiniteSet(2,3)
>>> s.intersect(t)
{2}

                    #We can make an union and intersection of more than 2 sets

>>> s=FiniteSet(1,2,3)
>>> t=FiniteSet(2,4,6)
>>> u=FiniteSet(3,5,7)
>>> s.union(t).union(u)
{1, 2, 3, 4, 5, 6, 7}

>>> s.intersect(t).intersect(u)
EmptySet()


          #Cartesian product
#        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)
t = FiniteSet(3, 4, 5)
u = FiniteSet(3, 6)

# 和集合を求める。
print(s.union(t))

# unionはメソッドチェーンして使用可能。
# 後述するintersectについても同様。
print(s.union(t).union(u))

# 積集合を求める。
print(s.intersect(t).intersect(u))

# 直積を求める。
# ※直積:それぞれの集合から要素を一つづつ選んでできる、全ての集合。
p = s * t * u

# そのままの状態では、各集合を表示できない(ProductSetオブジェクトが返る)。
print(p)
print(type(p))

# forで列挙すると、各集合を表示できる。
for elem in p:
    print(elem)
print(len(p))
Exemple #13
0
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)
t = FiniteSet(2, 4, 6)
u = FiniteSet(3, 5, 7)

s.union(t).union(u)

s.intersect(t).intersect(u)

s = FiniteSet(1, 2)
t = FiniteSet(3, 4)

p = s * t
p
Exemple #14
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event = primes(20)

len(event)/len(range(1,21))

import matplotlib.pyplot as plt
plt.plot(range(1,len(prime1)+1), prime1)


from sympy import FiniteSet
s = FiniteSet()
for i in range(1,7):
    s1 = FiniteSet(i)
    s = s.union(s1)
a = FiniteSet(2,3,5)
b = FiniteSet(1,3,5)
PrimeOrOdd = a.union(b)
PrimeAndOdd = a.intersect(b)
ProbPrimeOrOdd = len(PrimeOrOdd)/len(s)
ProbPrimeAndOdd = len(PrimeAndOdd)/len(s)


import random
random.randint(1,6)







Exemple #15
0
from sympy import FiniteSet
s = FiniteSet(1, 1.5, Fraction(1, 5))
for member in s:
    print(member)
t = FiniteSet(Fraction(1, 5), 1.5, 1, 1)
if s == t:
    print("True")
s.intersect(t)
s.uninon(t)

p = s**2
p1 = s**3
from sympy import FiniteSet
from fractions import Fraction

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

s = FiniteSet(1, 2)
t = FiniteSet(2, 3)
print("intersect  ", s.intersect(t))

s = FiniteSet(1, 2)
t = FiniteSet(2, 3)
u = FiniteSet(3, 5, 7)
print("Union ", s.union(t).union(u))

s = FiniteSet(1, 2)
t = FiniteSet(2, 3)
p = s * t
print("Cartesian ", p)

for elem in p:
    print("Cartesian ", elem)

s = FiniteSet(1, 2)
p = s**3
print("carteisna ** ", p)

for elem in p:
    print("Cartesian ", elem)
#ElifCelik Programlama Lab 3. Hafta Cuma
#Zar için olasilik hesabi
from sympy import FiniteSet

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

t == s
t.union(s)
t.intersect(s)

t**2


#probability calculation
def probability(space, event):
    return len(event) / len(space)


#is it prime number
def check_prime(number):
    if number != 1:
        for factor in range(2, number):
            if number % factor == 0:
                return False
    else:
        return False
    return True


space = FiniteSet(*range(1, 21))
Exemple #18
0
from sympy import FiniteSet, pi
# Unions & Intersections
s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)

union = s.union(t)
print(union)

intersection = s.intersect(t)
print(intersection)

### Cartesian Products
cartesianProduct = s * t
print(cartesianProduct)

for elem in cartesianProduct:
    print(elem)

# Raise set to the power (calculate triplets)
cartesianProductCubed = s**3
for elem in cartesianProductCubed:
    print(elem)


def time_period(length, g):
    T = 2 * pi * (length / g)**0.5
    return T


L = FiniteSet(15, 18, 21, 22.5, 25)
g_values = FiniteSet(9.8, 9.78, 9.83)
from sympy import FiniteSet, pi
# Unions & Intersections
s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)

union = s.union(t)
print(union)

intersection = s.intersect(t)
print(intersection)

### Cartesian Products
cartesianProduct = s * t
print(cartesianProduct)

for elem in cartesianProduct:
    print(elem)

# Raise set to the power (calculate triplets)
cartesianProductCubed = s ** 3
for elem in cartesianProductCubed:
    print(elem)




def time_period(length, g):
    T = 2*pi*(length/g)**0.5
    return T

L = FiniteSet(15, 18, 21, 22.5, 25)
Exemple #20
0
from sympy import FiniteSet
from fractions import Fraction

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

if t == s:
    print("True")
else:
    print("False")

print(t.union(s))
print(t.intersect(s))
print(t**2)


def probability(space, event):
    return len(event) / len(space)


def check_prime(number):
    if number != 1:
        for factor in range(2, number):
            if number % factor == 0:
                return False
    else:
        return False
    return True


space = FiniteSet(* range(1, 21))
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()
#The cartesian product creates a set that consists of all possible pairs made by taking an element from each set.
print(tenthset*eleventhset) #print {1, 2, 3} x {2, 4, 6}
tentheleventh = tenthset*eleventhset
for eachtentheleventh in tentheleventh:
	print(eachtentheleventh)
'''
(1, 2)
(1, 4)
(1, 6)
# Set Operations  such as Union, Intresection and the cartesian product allow you to
# combine sets in certain methodical ways. These set operations are extremely useful in real world
# Problem solving situations when we have to consider multiple sets together.

from sympy import FiniteSet
s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)
#The result is the third set with all the distinct  members of the two sets
print(s.union(t))

# The intersection of two sets creates a new set from the elelments common to both sets
# For Example, the intersection of the sets {1,2} and {2,3} will result in a new set with the only common element 2.
s = FiniteSet(1, 2)
t = FiniteSet(2, 3)
print(s.intersect(t))

# Whereas the union operation finds memebers that are in one set or another,
# the intersection operation finds elements that are present in both.Both of these operations
# can also be applied to more than two sets. For Example- here's how you'd find the union of three sets

s = FiniteSet(1, 2, 3)
t = FiniteSet(2, 4, 6)
u = FiniteSet(3, 5, 7)

print(s.union(t).union(u))

# CARTESIAN PRODUCT
# The cartesian product of two sets creates a set that consist all the possible pairs made by taking
# an element from each set. For examples cartesian product of the sets {1,2} and {3,4} is {(1,3),(1,4),(2,3),(2,4)}
# In SymPy you can find the cartesian product of two sets by simply using the multiplication operator
p = s * t
# Subconjunto y subconjunto propio
A = FiniteSet(1,2,3)
B = FiniteSet(1,2,3,4,5)
A.subset(B)

# Union de dos conjuntos
A = FiniteSet(1, 2, 3)
B = FiniteSet(2, 4, 6)
A.union(B)


# Interseccion de dos conjuntos
A = FiniteSet(1, 2) 
B = FiniteSet(2, 3) 
A.intersect(B)


# Diferencia entre conjuntos
print A - B


# Calculando el producto cartesiano. 
A = FiniteSet(1, 2)
B = FiniteSet(3, 4)
P = A * B
for elem in P:
    print(elem)
    
    
# Calcula el n producto cartesiano del mismo conjunto.