Correct or incorrect?

Surprisingly, the answer is actually correct. As often, it is a matter of definition!

Let us walk through this.

What does count count?

Define a random word and give it a name:

sage: w = Words('ab', 20).random_element()
sage: w
baabaaaaaaabbabbbbba

Count for 'aa' in w:

sage: w.count('aa')
0

Since we may be surprised, let us read the documentation for the count method:

sage: w.count?

or its source code:

sage: w.count??

Oh, so count counts the occurrences of letters.

Here, w is a word on the alphabet {'a', 'b'}, and 'aa' is not a letter in that alphabet.

So the count of how many times 'aa' appears in w as a letter must be zero.

Compare:

sage: w = Words(['a', 'b', 'aa'], 10).random_element()
sage: w
word: aa,aa,a,aa,a,a,a,b,a,aa
sage: w.count('aa')
4

Factors and subwords

So how do we count factors? or subwords?

Get hold of the set of words.

sage: W = w.parent()
sage: W
Finite words over {'a', 'b'}

Define the factor we are looking for:

sage: f = W('aa')

Count its occurrences as a factor or a subword in w.

sage: f.nb_factor_occurrences_in(w)
7
sage: f.nb_subword_occurrences_in(w)
55

Improve the documentation?

The question raises a valid point! The documentation for count should at least point to the nb_factor_occurrences, maybe with an example such as the one here.

This is now tracked at

• Sage Trac ticket 30143