Python 与元组集的关系 [英] Python Relations with Sets of Tuples

问题描述

我正在尝试确定元组集是否具有某种类型的关系.我试图找出传递关系和复合关系.

对于传递关系:

 # 关系Relation"在以下情况下被称为可传递的:# ∀ (a, b) ∈ Relation, (b, c) ∈ Relation ==>(a, c) ∈ 关系

例如:

<预><代码>>>>{(1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1), (4,4)} #应该是假的>>>{(1,1), (2,1), (3,1), (3,2), (4,1), (4,2), (4,3)} # 应该为真

对于复合关系:

#关系'R1'和'R2'的复合是组成的关系# 元组 (a,c)，使得 (a,b) ∈ R1 和 (b,c) ∈ R2

例如:

{(1,0), (1,1), (2,1), (2,2), (3,0), (3,1)} == R1={(1),1), (1,4), (2,3), (3,1), (3,4)}, R2={(1,0), (2,0), (3,1),(3,2), (4,1)}# 应该返回真

我不确定如何开始编写这些函数.任何让我开始的帮助将不胜感激.谢谢！

以下是我能够成功编码的其他一些关系:

# 自反关系# 集合 'Set' 上的关系 'Relation' 在以下情况下称为自反:# ∀ a ∈ 集合，(a,a) ∈ 关系def is_reflexive(Set, Relation):newSet = {(a, b) for a in Set for b in Set if a == b}如果关系 >= newSet:返回真返回错误# 对称关系# 关系Relation"在以下情况下称为对称关系:# ∀ (a, b) ∈ Relation, (b, a) ∈ Relation定义是_对称(关系):if all(tup[::-1] in Relation for tup in Relation):返回真返回错误

解决方案

对于传递测试，只需转换 Python 中的数学定义:

def is_transitive(relation):对于 a,b 的关系:对于 c,d 的关系:如果 b == c 和((a，d)不相关):# 打印 (a,b),(c,d) # 取消注释测试...返回错误返回真

I'm trying to determine whether or not sets of tuples have a certain type of relation. I'm trying to figure out the transitive relation, and the composite relation.

For the transitive relation:

 # A relation 'Relation' is called transitive when:
 # ∀ (a, b) ∈ Relation, (b, c) ∈ Relation ==> (a, c) ∈ Relation

For example:

>>> {(1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1), (4,4)} # Should be False
>>> {(1,1), (2,1), (3,1), (3,2), (4,1), (4,2), (4,3)} # Should be True

For the composite relation:

# The composite of relations 'R1' and 'R2' is the relation consisting
# of tuples (a,c), such that (a,b) ∈ R1 and (b,c) ∈ R2

For example:

{(1,0), (1,1), (2,1), (2,2), (3,0), (3,1)} == R1={(1,1), (1,4), (2,3), (3,1), (3,4)}, R2={(1,0), (2,0), (3,1), (3,2), (4,1)}
# Should return True

I am uncertain on how to start coding these functions. Any help to get me started would be greatly appreciated. Thank you!

EDIT: Here are some other relations I was able to successfully code:

# Reflexive Relation
# A relation 'Relation' on a set 'Set' is called reflexive when:
# ∀ a ∈ Set, (a,a) ∈ Relation
def is_reflexive(Set, Relation):
    newSet = {(a, b) for a in Set for b in Set if a == b}
    if Relation >= newSet:
        return True

    return False

# Symmetric Relation
# A relation 'Relation' is called symmetric when:
#  ∀ (a, b) ∈ Relation, (b, a) ∈ Relation
def is_symmetric(Relation):
    if all(tup[::-1] in Relation for tup in Relation):
        return True


    return False

解决方案

For the transitive test, just convert the math definition in Python:

def is_transitive(relation):
    for a,b in relation:
        for c,d in relation:
            if b == c and ((a,d) not in relation):
                    # print (a,b),(c,d) # uncomment for tests...
                    return False
    return True

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