Datatypes for finite words#

class sage.combinat.words.word_datatypes.WordDatatype#

Bases: object

The generic WordDatatype class.

Any word datatype must contain two attributes (at least):

- _parent
- _hash

They are automatically defined here and it’s not necessary (and forbidden) to define them anywhere else.

class sage.combinat.words.word_datatypes.WordDatatype_list#

Bases: WordDatatype

Datatype class for words defined by lists.

length()#

Return the length of the word.

EXAMPLES:

sage: w = Word([0,1,1,0])
sage: w.length()
4

number_of_letter_occurrences(a)#

Returns the number of occurrences of the letter a in the word self.

INPUT:

a - a letter

OUTPUT:

integer

EXAMPLES:

sage: w = Word([0,1,1,0,1])
sage: w.number_of_letter_occurrences(0)
2
sage: w.number_of_letter_occurrences(1)
3
sage: w.number_of_letter_occurrences(2)
0

class sage.combinat.words.word_datatypes.WordDatatype_str#

Bases: WordDatatype

Datatype for words defined by strings.

find(sub, start=0, end=None)#

Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.

INPUT:

sub - string or word to search for.
start - non negative integer (default: 0) specifying the position from which to start the search.
end - non negative integer (default: None) specifying the position at which the search must stop. If None, then the search is performed up to the end of the string.

OUTPUT:

non negative integer or -1

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: w.find("a")
0
sage: w.find("a", 4)
5
sage: w.find("a", 4, 5)
-1

has_prefix(other)#

Test whether self has other as a prefix.

INPUT:

other - a word (an instance of Word_class) or a str.

OUTPUT:

boolean

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: u = Word("abbab")
sage: w.has_prefix(u)
True
sage: u.has_prefix(w)
False
sage: u.has_prefix("abbab")
True

has_suffix(other)#

Test whether self has other as a suffix.

INPUT:

other - a word (an instance of Word_class) or a str.

OUTPUT:

boolean

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: u = Word("ababa")
sage: w.has_suffix(u)
True
sage: u.has_suffix(w)
False
sage: u.has_suffix("ababa")
True

is_prefix(other)#

Test whether self is a prefix of other.

INPUT:

other - a word (an instance of Word_class) or a str.

OUTPUT:

boolean

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: u = Word("abbab")
sage: w.is_prefix(u)
False
sage: u.is_prefix(w)
True
sage: u.is_prefix("abbabaabababa")
True

is_suffix(other)#

Test whether self is a suffix of other.

INPUT:

other - a word (an instance of Word_class) or a str.

OUTPUT:

boolean

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: u = Word("ababa")
sage: w.is_suffix(u)
False
sage: u.is_suffix(w)
True
sage: u.is_suffix("abbabaabababa")
True

length()#

Return the length of the word.

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: w.length()
13

number_of_letter_occurrences(letter)#

Count the number of occurrences of letter.

INPUT:

letter - a letter

OUTPUT:

integer

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: w.number_of_letter_occurrences('a')
7
sage: w.number_of_letter_occurrences('b')
6
sage: w.number_of_letter_occurrences('c')
0

sage: w.number_of_letter_occurrences('abb')
0

See also the split method.

Note

This just wraps Python’s builtin str::partition() for str.

INPUT:

sep - string or word

EXAMPLES:

sage: w = Word("MyTailorIsPoor")
sage: w.partition("Tailor")
[word: My, word: Tailor, word: IsPoor]

sage: w = Word("3230301030323212323032321210121232121010")
sage: l = w.partition("323")
sage: print(l)
[word: , word: 323, word: 0301030323212323032321210121232121010]
sage: sum(l, Word('')) == w
True

If the separator is not a string an error is raised:

sage: w = Word("le papa du papa du papa etait un petit pioupiou")
sage: w.partition(Word(['p','a','p','a']))
Traceback (most recent call last):
...
ValueError: the separator must be a string

rfind(sub, start=0, end=None)#

Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.

INPUT:

sub - string or word to search for.
start - non negative integer (default: 0) specifying the position at which the search must stop.
end - non negative integer (default: None) specifying the position from which to start the search. If None, then the search is performed up to the end of the string.

OUTPUT:

non negative integer or -1

EXAMPLES:

sage: w = Word("abbabaabababa")
sage: w.rfind("a")
12
sage: w.rfind("a", 4, 8)
6
sage: w.rfind("a", 4, 5)
-1

split(sep=None, maxsplit=None)#

Returns a list of words, using sep as a delimiter string. If maxsplit is given, at most maxsplit splits are done.

See also the partition method.

Note

This just wraps Python’s builtin str::split() for str.

INPUT:

sep - string or word (optional, default: None)
maxsplit - positive integer (optional, default: None)

OUTPUT:

a list of words

EXAMPLES:

You can split along white space to find words in a sentence:

sage: w = Word("My tailor is poor")
sage: w.split(" ")
[word: My, word: tailor, word: is, word: poor]

The python behavior is kept when no argument is given:

sage: w.split()
[word: My, word: tailor, word: is, word: poor]

You can split in two words letters to get the length of blocks in the other letter:

sage: w = Word("ababbabaaba")
sage: w.split('a')
[word: , word: b, word: bb, word: b, word: , word: b, word: ]
sage: w.split('b')
[word: a, word: a, word: , word: a, word: aa, word: a]

You can split along words:

sage: w = Word("3230301030323212323032321")
sage: w.split("32")
[word: , word: 30301030, word: , word: 12, word: 30, word: , word: 1]

If the separator is not a string a ValueError is raised:

sage: w = Word("le papa du papa du papa etait un petit pioupiou")
sage: w.split(Word(['p','a','p','a']))
Traceback (most recent call last):
...
ValueError: the separator must be a string

class sage.combinat.words.word_datatypes.WordDatatype_tuple#

Bases: WordDatatype

Datatype class for words defined by tuples.

length()#

Return the length of the word.

EXAMPLES:

sage: w = Word((0,1,1,0))
sage: w.length()
4