The WordRange class

Class for generating words in a given range and in a particular order.

The WordRange class is a class for generating words (i.e. lists of int values) in a given range and in a particular order.

The order and range of the words in a WordRange instance can be set using the member functions:

WordRange.order
WordRange.alphabet_size
WordRange.min
WordRange.max
WordRange.first
WordRange.last

See also

StringRange

Example

>>> from libsemigroups_pybind11 import WordRange, Order
>>> words = WordRange();
>>> words.order(Order.shortlex) \
...      .alphabet_size(2) \
...      .min(1) \
...      .max(5)
<WordRange of length 30 with letters in [0, 2) in shortlex order>
>>> words.order()
<Order.shortlex: 1>

>>> from libsemigroups_pybind11 import ToString
>>> words.alphabet_size(1).min(0).max(10)
<WordRange of length 10 with letters in [0, 1) in shortlex order>

>>> strings = words | ToString("a")
>>> list(strings)
['', 'a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa']

Contents

`WordRange`	Class for generating words in a given range and in a particular order.
`WordRange.alphabet_size`(…)	Overloaded function.
`WordRange.at_end`(…)	Check if the range object is exhausted.
`WordRange.copy`(…)	Copy a `WordRange` object.
`WordRange.count`(…)	The actual size of the range.
`WordRange.first`(…)	Overloaded function.
`WordRange.get`(…)	Get the current value.
`WordRange.init`(…)	Initialize an existing `WordRange` object.
`WordRange.last`(…)	Overloaded function.
`WordRange.max`(…)	Set one past the last word in the range by length.
`WordRange.min`(…)	Set the first word in the range by length.
`WordRange.next`(…)	Advance to the next value.
`WordRange.order`(…)	Overloaded function.
`WordRange.size_hint`(…)	The possible size of the range.
`WordRange.upper_bound`(…)	Overloaded function.
`WordRange.valid`(…)	Returns whether or not the settings have been changed since the last time either next or get has been called.

Full API

class WordRange

__init__(self: WordRange) → None

Default constructor.

Constructs an empty range with:

WordRange.min() equal to 0 ;
WordRange.max() equal to 0 ;
WordRange.order() equal to Order.shortlex ;
WordRange.first() equal to the empty word;
WordRange.last() equal to the empty word;
WordRange.upper_bound() equal to 0 ;
WordRange.alphabet_size() equal to 0.

alphabet_size(self: WordRange, n: int) → WordRange

Overloaded function.

alphabet_size(self: WordRange) → int

The current number of letters in the alphabet.

Returns the current number of letters in a WordRange object.

Returns:: The current number of letters.
Return type:: int

alphabet_size(self: WordRange, n: int) → WordRange

Set the number of letters in the alphabet.

Sets the number of letters in a WordRange object to n.

Parameters:: n (int) – the number of letters.
Returns:: self.
Return type:: WordRange

at_end(self: WordRange) → bool

Check if the range object is exhausted.

Returns True if a WordRange object is exhausted, and False if not.

Returns:: Whether the range object is exhausted.
Return type:: bool

copy(self: WordRange) → WordRange

Copy a WordRange object.

Returns:: A copy.
Return type:: WordRange

count(self: WordRange) → int

The actual size of the range.

Returns the number of words in a WordRange object. If WordRange.order() is Order.shortlex , then WordRange.size_hint() is used. If WordRange.order() is not Order.shortlex, then a copy of the range may have to be looped over in order to find the return value of this function.

Returns:: The size of the range.
Return type:: int

first(self: WordRange, frst: list[int]) → WordRange

Overloaded function.

first(self: WordRange) → list[int]

The current first word in the range.

Returns the first word in a WordRange object.

Returns:: The first word in the range.
Return type:: list[int]

See also

WordRange.min

first(self: WordRange, frst: list[int]) → WordRange

Set the first word in the range.

Sets the first word in a WordRange object to be frst. This function performs no checks on its arguments. If frst contains letters greater than WordRange.alphabet_size(), then the WordRange object will be empty. Similarly, if WordRange.first() is greater than WordRange.last() with respect to WordRange.order(), then the object will be empty.

Parameters:: frst (list[int]) – the first word.
Returns:: self.
Return type:: WordRange

See also

WordRange.min

get(self: WordRange) → list[int]

Get the current value.

Returns the current word in a WordRange object.

Returns:: The current word.
Return type:: list[int]

init(self: WordRange) → WordRange

Initialize an existing WordRange object.

This function puts a WordRange object back into the same state as if it had been newly default constructed, and returns that object.

Returns:: self.
Return type:: WordRange

last(self: WordRange, lst: list[int]) → WordRange

Overloaded function.

last(self: WordRange) → list[int]

Returns the one past the last word in a WordRange object.

Returns:: One past the last word.
Return type:: list[int]

See also

WordRange.max

last(self: WordRange, lst: list[int]) → WordRange

Set one past the last word in the range.

Sets one past the last word in a WordRange object to be lst. This function performs no checks on its arguments. If lst contains letters greater than WordRange.alphabet_size(), then the WordRange object will be empty.

Parameters:: lst (list[int]) – one past the last word.
Returns:: self.
Return type:: WordRange

See also

WordRange.max

max(self: WordRange, val: int) → WordRange

Set one past the last word in the range by length.

Sets one past the last word in a WordRange object to be words.pow(0_w, val) (the word consisting of val letters equal to 0 ).

Parameters:: val (int) – the exponent.
Returns:: self.
Return type:: WordRange

min(self: WordRange, val: int) → WordRange

Set the first word in the range by length.

Sets the first word in a WordRange object to be pow(0_w, val) (the word consisting of val letters equal to 0 ).

Parameters:: val (int) – the exponent.
Returns:: self.
Return type:: WordRange

next(self: WordRange) → None

Advance to the next value.

Advances a WordRange object to the next value (if any).

See also

WordRange.at_end

order(*args, **kwargs)

Overloaded function.

order(self: WordRange) → Order

The current order of the words in the range.

Returns the current order of the words in a WordRange object.

Returns:: The current order.
Return type:: Order

order(self: WordRange, val: Order) → WordRange

Set the order of the words in the range.

Sets the order of the words in a WordRange object to val.

Parameters:: val (Order) – the order.
Returns:: self.
Return type:: WordRange
Raises:: LibsemigroupsError – if val is not Order.shortlex or Order.lex.

size_hint(self: WordRange) → int

The possible size of the range.

Returns the number of words in a WordRange object if WordRange.order() is Order.shortlex. If WordRange.order() is not Order.shortlex, then the return value of this function is meaningless.

Returns:: A value of type int.
Return type:: int

upper_bound(self: WordRange, n: int) → WordRange

Overloaded function.

upper_bound(self: WordRange) → int

The current upper bound on the length of a word in the range.

Returns the current upper bound on the length of a word in a WordRange object. This setting is only used if WordRange.order() is Order.lex.

Returns:: A value of type int.
Return type:: int

upper_bound(self: WordRange, n: int) → WordRange

Set an upper bound for the length of a word in the range.

Sets an upper bound for the length of a word in a WordRange object. This setting is only used if WordRange.order() is Order.lex.

Parameters:: n (int) – the upper bound.
Returns:: self.
Return type:: WordRange

valid(self: WordRange) → bool

Returns whether or not the settings have been changed since the last time either next or get has been called.

Other than by calling WordRange.next() , the value returned by WordRange.get() may be altered by a call to one of the following:

order(Order)
alphabet_size(int)
min(int)
max(int)
first(list[int])
last(list[int])
upper_bound(int)

This function returns True if none of the above settings have been changed since the last time WordRange.next() or WordRange.get() is called, and False otherwise.

Returns:: Whether or not the settings have been changed.
Return type:: bool