# Why is the Subwords class separated from FiniteWord?

Subwords could be a method of FiniteWord as factors is already one. Is there a reason why this is not the case?

Why is the Subwords class separated from FiniteWord?

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2

The module `subword.py`

was created in 2007 during the translation by Mike Hansen of 30k lines of code from Mupad-Combinat to sage. Around the same time, in 2008, the module `sage/combinat/words`

was created and nothing has ever been done to merge the two.

Notice that the code in `subword.py`

is based on `itertools.combinations`

and no wiser algorithm is coded to enumerate *distinct* subwords.

```
sage: s = Subwords('aaaaa', 3)
sage: s.__iter__??
...
iterator = itertools.combinations(self._w, self._k)
...
sage: list(s)
['aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa']
```

If you know the existence of a better algorithm, you are welcome to add it to the `finite_word.py`

file which contains already 3 methods related to subwords:

```
sage: w = Word('abc')
sage: w.*subword*?
w.is_subword_of
w.longest_common_subword
w.nb_subword_occurrences_in
```

1

Here is a function that compute the set of subwords (no repetition)

```
def subwords(w, W=None):
r"""
Return the subwords of ``w`` without repetition.
INPUT:
- ``w`` - a finite word (or string or list)
- ``W`` - an optional parent
EXAMPLES::
sage: subwords('aab')
['', 'a', 'aa', 'b', 'ab', 'aab']
sage: subwords('aba')
['', 'a', 'b', 'ab', 'ba', 'aa', 'aba']
sage: subwords('aaa')
['', 'a', 'aa', 'aaa']
sage: subwords(Word('abc'))
[word: , word: a, word: b, word: ab, word: c, word: bc, word: ac, word: abc]
"""
if W is None:
try:
W = w.parent()
except AttributeError:
W = type(w)
T = {}
L = [W()]
for a in w:
todo = [(W(),T)]
while todo:
cw, t = todo.pop()
todo.extend((cw+W(b),tt) for b,tt in t.items())
if a not in t:
t[a] = {}
L.append(cw + W(a))
return L
```

Asked: **
2018-07-10 21:40:01 -0600
**

Seen: **40 times**

Last updated: **Jul 11 '18**

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