A list of lists

[Hassediagram]

Dear members of python-forum,

I encounter a problem of list definition (i think). I would like to define def(S,T), where:
(i) S and T are two sets (lists in Python) and such that S is a subset of T.
(ii) def(S,T) gives the list of lists K such that S \subset K \subset T. (K is "between" S and T).

For example if S=[2] and T=[2,3,4], i want to get all the lists between [2] and [2,3,4], that is, L=[[2],[2,3],[2,4],[2,3,4]].

In the program below, i define subset(T,S) as being the elements in T which are not in S. In my example, setminus(T,S)=[3,4].


Notice that:
union(A,B) is the union of the lists A and B. (the union of sets).
interzz(A,B) is the intersection of lists A and B (the intersection of sets).
doublonsL removes the lists appearing several times in the list of lists.

The program works as follows: from the infimum S=[2] (for example) and the supremum T=[2,3,4], we compute the elements setminus(T,S) which are in T but not in S. We start from L=[[2]]. The elements 3 and 4 are in T but not in S. We take elements in L and we add lists with these elements setminus(T,S). For example:

[2]
[2],[2,3]
[2],[2,4],[2,3],[2,3,4].

My program, instead of giving what i want, gives Boolean([2],[2,3,4])=
[[2, 3, 4]]. That is, [2], [2,3] and [2,4] are missing.

I guess that my program is ugly but, actually, i just need something that works. Your suggestions would probably be helpful; thank you in advance.

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def doublons(LM):# This def is OK.     LP=[]     for k in LM:         if k not in LP:             LP.append(k)     return(LP)     def doublonsL(LM): # This def is OK.     LP=[]     for listtt in LM:         if listtt not in LP:             LP.append(listtt)     return(LP)   def union(A,B):# This def is OK.     uni=A     for k in B:         uni.append(k)     return doublons(sorted(uni))      def interzz(lst1, lst2): # This def is OK.     lst3 = [value for value in lst1 if value in lst2]     return doublons(sorted(lst3))     def setminus(S,T):# This def is OK.     for k in T:         S.remove(k)     return doublons(S)     def issubset(S,T):# This def is OK.     if interzz(S,T)==S:         return "true"     else:         return "false"     def Boolean(SQ,TQ): # The problem comes from this def.     if issubset(SQ,TQ)=="false": # We check that S is a subset of T.         print("error subset")     ZED=setminus(TQ,SQ) # All the elements of TQ which are not in SQ.     LILI=[SQ]     MOLI=LILI[:]     for k in ZED:         for PPP in MOLI:             LILI.append(union(PPP,[k]))         LILI=MOLI[:]         MOLI=LILI[:]     for kj in range(0,len(LILI)):         LILI[kj]=sorted(doublons(LILI[kj]))     return doublonsL(LILI)

Wishing you a nice week,
Hassediagram.

[Larz60+]

python has lists x = [1,2,3]
and sets x = {1,2,3}
plus all set operations see: https://docs.python.org/3.7/library/stdt...-frozenset

aslo see itertools for permutations, combinations and product

[ichabod801]

Also, Python has the boolean singletons True and False, so you don't need "true" and "false". If issubset returned those, you could just use if issubset(SQ, TQ):. Of course, since all issubset does is check interzz(), you could just replace that with if interzz(SQ, TQ) == SQ:.

[Hassediagram]

python has lists x = [1,2,3]
and sets x = {1,2,3}
plus all set operations see: https://docs.python.org/3.7/library/stdt...-frozenset

aslo see itertools for permutations, combinations and product

Thank you Larz60 for your answer; i meant sets in the mathematical sense, which i translate into lists in Python.

[ichabod801]

As Larz said, this functionality is all covered in Python. But if you need to recreate it for homework, to get the subsets, start with a list of the empty set. Loop through the items in the set, adding to the list of subsets every subset plus the item:

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>>> subsets = [[]] >>> fullset = [1, 2, 3] >>> for item in fullset: ...    subsets = subsets + [subset + [item] for subset in subsets] ... >>> subsets [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]

You should be able to modify that to get the list of subsets you want.

[Hassediagram]

As Larz said, this functionality is all covered in Python. But if you need to recreate it for homework, to get the subsets, start with a list of the empty set. Loop through the items in the set, adding to the list of subsets every subset plus the item:

1 2 3 4 5 6 7

>>> subsets = [[]] >>> fullset = [1, 2, 3] >>> for item in fullset: ...    subsets = subsets + [subset + [item] for subset in subsets] ... >>> subsets [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]

You should be able to modify that to get the list of subsets you want.

Thank you ichabod801, this works ! I will use your trick.
But why didn't it work in my program ?

Thank you also for your suggestion about the intersections.

[ichabod801]

But why didn't it work in my program ?

I don't know. Your code is really hard to read and very complicated, I just figured there must be a simpler solution. Always keep it simple when programming.

[Hassediagram]

But why didn't it work in my program ?

I don't know. Your code is really hard to read and very complicated, I just figured there must be a simpler solution. Always keep it simple when programming.

Yes that is true; ok i got my problem solved, thank you very much ichabod801 !