libsemigroups::words Namespace Reference

Defined in word-range.hpp.

This namespace contains some functions for creating word_type objects in a compact form.

Example

using namespace words;
pow("a", 5)            // same as "aaaaa"
01_w + 2               // same as 012_w
01_w + 01_w            // same as 0101_w
prod(0123_w, 0, 16, 3) // same as 032103_w

Functions
letter_type	human_readable_index (char c)
	Returns the index of a character in human readable order.
template<typename Word = std::string>
Word::value_type	human_readable_letter (size_t i)
	Returns a character by index in human readable order.
word_type	operator+ (letter_type w, word_type const &u)
	Concatenate a letter and a word.
word_type	operator+ (word_type const &u, letter_type w)
	Concatenate a word and a letter.
word_type	operator+ (word_type const &u, word_type const &w)
	Concatenate two words.
void	operator+= (letter_type a, word_type &u)
	Concatenate a letter and a word in-place.
void	operator+= (word_type &u, letter_type a)
	Concatenate a word and a letter in-place.
static void	operator+= (word_type &u, word_type const &v)
	Concatenate a word with another word in-place.
word_type	pow (std::initializer_list< letter_type > ilist, size_t n)
	Returns the power of a word.
std::string	pow (std::string_view w, size_t n)
	Returns the power of a string.
template<typename Word>
Word	pow (Word const &x, size_t n)
	Returns the power of a word.
template<typename Word>
void	pow_inplace (Word &w, size_t n)
	Power a word in-place.
template<typename Container, typename Word = Container>
Word	prod (Container const &elts, int first, int last, int step=1)
	Returns a product of letters or words.
template<typename Container, typename Word = Container>
Word	prod (Container const &elts, size_t last)
	Returns a product of letters or words.
static word_type	prod (std::initializer_list< letter_type > const &elts, size_t last)
	Returns a product of letters.
static word_type	prod (std::initializer_list< letter_type > ilist, int first, int last, int step=1)
	Returns a product of letters.
static std::string	prod (std::initializer_list< std::string_view > const &elts, size_t last)
	Returns a product of words.
static std::string	prod (std::initializer_list< std::string_view > const &sv, int first, int last, int step=1)
	Returns a product of strings.
static word_type	prod (std::initializer_list< word_type > const &elts, int first, int last, int step=1)
	Returns a product of words.
static word_type	prod (std::initializer_list< word_type > const &elts, size_t last)
	Returns a product of words.
static std::string	prod (std::string_view elts, size_t last)
	Returns a product of letters.
static std::string	prod (std::string_view sv, int first, int last, int step=1)
	Returns a product of letters.

Function Documentation

human_readable_index()

letter_type human_readable_index ( char c )

nodiscard

Defined in word-range.hpp.

This function is the inverse of human_readable_letter, see the documentation of that function for more details.

Parameters

c	character whose index is sought.

Returns

A value of type letter_type.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

See also

human_readable_letter

human_readable_letter()

template<typename Word = std::string>

Word::value_type human_readable_letter

(

size_t

i

)

This function exists to map the numbers 0 to 255 to the possible values of a char, in such a way that the first characters are a-zA-Z0-9. The ascii ranges for these characters are: \([97, 123)\), \([65, 91)\), \([48, 58)\) so the remaining range of chars that are appended to the end after these chars are \([0,48)\), \([58, 65)\), \([91, 97)\), \([123, 255]\).

This function is the inverse of human_readable_index.

Parameters

i	the index of the character.

Returns

A value of type char.

Exceptions

LibsemigroupsException

if i exceeds the number of characters.

operator+() [1/3]

word_type operator+	(	letter_type	w,
		word_type const &	u )

See operator+.

operator+() [2/3]

word_type operator+	(	word_type const &	u,
		letter_type	w )

See operator+.

operator+() [3/3]

word_type operator+	(	word_type const &	u,
		word_type const &	w )

Returns the concatenation of u and w.

Parameters

u	a word.
w	a word.

Returns

A word_type.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

operator+=() [1/3]

void operator+= ( letter_type a, word_type & u )

inline

See operator+=.

operator+=() [2/3]

void operator+= ( word_type & u, letter_type a )

inline

See operator+=.

operator+=() [3/3]

static void operator+= ( word_type & u, word_type const & v )

inlinestatic

Changes u to u + v in-place. See operator+.

Parameters

u	a word.
v	a word.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

See also

operator+

pow() [1/3]

word_type pow	(	std::initializer_list< letter_type >	ilist,
		size_t	n )

See pow(Word const&, size_t) for details.

pow() [2/3]

std::string pow	(	std::string_view	w,
		size_t	n )

See pow(Word const&, size_t) for details.

pow() [3/3]

template<typename Word>

Word pow	(	Word const &	x,
		size_t	n )

Returns the Word w to the power n.

Template Parameters

Word	the type of the first parameter.

Parameters

x	the word to power.
n	the power.

Returns

A Word.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

pow_inplace()

template<typename Word>

void pow_inplace	(	Word &	w,
		size_t	n )

Modify the Word w to contains its nth power.

Template Parameters

Word	the type of the first parameter.

Parameters

w	the word.
n	the power.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

prod() [1/10]

template<typename Container, typename Word = Container>

Word prod	(	Container const &	elts,
		int	first,
		int	last,
		int	step = 1 )

Let elts correspond to the ordered set \(a_0, a_1, \ldots, a_{n - 1}\), first to \(f\), last to \(l\), and step to \(s\). If \(f \leq l\), let \(k\) be the greatest positive integer such that \(f + ks < l\). Then the function prod returns the word corresponding to \(a_f a_{f + s} a_{f + 2s} \cdots a_{f + ks}\). All subscripts are taken modulo \(n\).

If there is no such \(k\) (i.e. \(s < 0\), or \(f = l\)), then the empty word is returned. Where \(f > l\), the function works analogously, where \(k\) is the greatest positive integer such that \(f + k s > l\).

Template Parameters

Container	the type of the 1st argument elts.
Word	the return type (defaults to Container).

Parameters

elts	the ordered set.
first	the first index.
last	the last index.
step	the step.

Returns

A Word.

Exceptions

LibsemigroupsException	if step = 0
LibsemigroupsException	if elts is empty, but the specified range is not

Examples

using namespace words;
word_type w = 012345_w
prod(w, 0, 5, 2)              // {0, 2, 4}
prod(w, 1, 9, 2)              // {1, 3, 5, 1}
prod("abcde", 4, 1, -1)       // "edc"
prod({"aba", "xyz"}, 0, 4, 1) // "abaxyzabaxyz"

prod() [2/10]

template<typename Container, typename Word = Container>

Word prod	(	Container const &	elts,
		size_t	last )

Returns the same as prod(elts, 0, last, 1).

See prod(Container const&, int, int, int).

prod() [3/10]

static word_type prod ( std::initializer_list< letter_type > const & elts, size_t last )

inlinestatic

Returns the same as prod(elts, 0, last, 1).

See prod(Container const&, int, int, int).

prod() [4/10]

static word_type prod ( std::initializer_list< letter_type > ilist, int first, int last, int step = 1 )

inlinestatic

See prod(Container const&, int, int, int).

prod() [5/10]

static std::string prod ( std::initializer_list< std::string_view > const & elts, size_t last )

inlinestatic

Returns the same as prod(elts, 0, last, 1).

See prod(Container const&, int, int, int).

prod() [6/10]

static std::string prod ( std::initializer_list< std::string_view > const & sv, int first, int last, int step = 1 )

inlinestatic

See prod(Container const&, int, int, int).

prod() [7/10]

static word_type prod ( std::initializer_list< word_type > const & elts, int first, int last, int step = 1 )

inlinestatic

See prod(Container const&, int, int, int).

prod() [8/10]

static word_type prod ( std::initializer_list< word_type > const & elts, size_t last )

inlinestatic

Returns the same as prod(elts, 0, last, 1).

See prod(Container const&, int, int, int).

prod() [9/10]

static std::string prod ( std::string_view elts, size_t last )

inlinestatic

Returns the same as prod(elts, 0, last, 1).

See prod(Container const&, int, int, int).

prod() [10/10]

static std::string prod ( std::string_view sv, int first, int last, int step = 1 )

inlinestatic

See prod(Container const&, int, int, int).