Initialization¶

This page contains information about initialising the FpSemigroupInterface class.

inline void libsemigroups::FpSemigroupInterface::add_rule(relation_type rel)¶

Add a rule using a relation_type.

Complexity: Constant.

Parameters

rel – the rule being added.

Throws

LibsemigroupsException – if any of the following apply:

started() returns true; or
rel.first or rel.second contains a letter that is out of bounds.

Returns

(None)

inline void libsemigroups::FpSemigroupInterface::add_rule(rule_type rel)¶

Add a rule using a rule_type.

Complexity: Constant.

Parameters

rel – the rule being added.

Throws

LibsemigroupsException – if any of the following apply:

started() returns true; or
rel.first or rel.second contains a letter that is out of bounds.

Returns

(None)

inline void libsemigroups::FpSemigroupInterface::add_rule(std::initializer_list<size_t> u, std::initializer_list<size_t> v)¶

Add a rule using two word_type const references.

Complexity: Constant.

Parameters

u – the left-hand side of the rule being added.
v – the right-hand side of the rule being added.

Throws

LibsemigroupsException – if any of the following apply:

started() returns true; or
u or v contains a letter that is out of bounds.

Returns

(None)

inline void libsemigroups::FpSemigroupInterface::add_rule(std::string const &u, std::string const &v)¶

Add a rule using two std::string const references.

Complexity: Constant.

Parameters

u – the left-hand side of the rule being added.
v – the right-hand side of the rule being added.

Throws

LibsemigroupsException – if any of the following apply:

started() returns true; or
u or v contains a letter that does not belong to alphabet().

Returns

(None)

inline void libsemigroups::FpSemigroupInterface::add_rule(word_type const &u, word_type const &v)¶

Add a rule using two word_type const references.

Complexity: Constant.

Parameters

u – the left-hand side of the rule being added.
v – the right-hand side of the rule being added.

Throws

LibsemigroupsException – if any of the following apply:

started() returns true; or
u or v contains a letter that is out of bounds.

Returns

(None)

void libsemigroups::FpSemigroupInterface::add_rules(FroidurePinBase &S)¶

Add rules from a FroidurePin instance.

Complexity: At most \(O(|S||A|)\) where \(A\) is a generating set for S.

Parameters

S – a FroidurePin object representing a semigroup.

Throws

LibsemigroupsException – if any of the following apply:

alphabet() is empty;
the number of generators of S is not equal to alphabet().size(); or
started() returns true;

Returns

(None)

inline void libsemigroups::FpSemigroupInterface::add_rules(std::vector<rule_type> const &rels)¶

Add rules in a vector.

Complexity: \(O(n)\) where \(n\) is the size of rels.

Parameters: rels – a vector of rule_type.
Throws: LibsemigroupsException – if add_rule() with argument any item in rels throws.
Returns: (None)

inline std::string const &libsemigroups::FpSemigroupInterface::alphabet() const noexcept¶

Returns a const reference to the alphabet.

Complexity: Constant.
Parameters: (None)

Throws: (None) – This function is noexcept and is guaranteed never to throw.
Returns: A const reference to the alphabet, a value of type std::string.

inline std::string libsemigroups::FpSemigroupInterface::alphabet(size_t i) const¶

Returns the ith letter of the alphabet.

Complexity: Constant.

Parameters: i – the index of the letter.
Throws: std::range_error – if the index i is out of range.
Returns: A std::string by value.

inline bool libsemigroups::FpSemigroupInterface::has_identity() const noexcept¶

Check if an identity has been set.

This function returns true if an identity has been set and false if it has not.

Complexity: Constant.
Parameters: (None)

Throws: (None) – This function is noexcept and is guaranteed never to throw.
Returns: A value of type bool.

std::string const &libsemigroups::FpSemigroupInterface::identity() const¶

Returns the identity (if any).

Complexity: Constant.
Parameters: (None)

Throws: LibsemigroupsException – if no identity has been defined.
Returns: A const reference to the identity, a value of type std::string.

std::string const &libsemigroups::FpSemigroupInterface::inverses() const¶

Returns the inverses (if any).

See also

set_inverses() for the meaning of the return value of this function.

Complexity: Constant.
Parameters: (None)

Throws: LibsemigroupsException – if no identity has been defined.
Returns: A const reference to the inverses, a value of type std::string.

inline size_t libsemigroups::FpSemigroupInterface::number_of_rules() const noexcept¶

Returns the number of rules.

Complexity: Constant.
Parameters: (None)

Throws: (None) – This function is noexcept and is guaranteed never to throw.
Returns: A value of type size_t.

void libsemigroups::FpSemigroupInterface::set_alphabet(size_t n)¶

Set the size of the alphabet.

Use this to specify the alphabet of a finitely presented semigroup if you intend to use indices rather than the actual letters in the alphabet in subsequent calculations.

Complexity: Constant.

Parameters: n – the number of letters.
Throws: LibsemigroupsException – If the size of the of alphabet has already been set to another value, or the parameter n is 0.
Returns: (None)

void libsemigroups::FpSemigroupInterface::set_alphabet(std::string const &a)¶

Set the alphabet of the finitely presented semigroup.

See also

alphabet() and set_alphabet(size_t).

Complexity: Constant.

Parameters: a – the alphabet.
Throws: LibsemigroupsException – If the alphabet has already been set to another value, the parameter a is empty, or there are repeated characters in a.
Returns: (None)

inline void libsemigroups::FpSemigroupInterface::set_identity(letter_type id)¶

Set a character in alphabet() to be the identity using its index.

This function adds rules to this so that id is the identity. This function can be called repeatedly.

See also

set_identity(std::string const&).

Complexity: \(O(n)\) where \(n\) is alphabet().size().

Parameters: id – the index of the character to be the identity.
Throws: LibsemigroupsException – If id is out of bounds.
Returns: (None)

void libsemigroups::FpSemigroupInterface::set_identity(std::string const &id)¶

Set a character in alphabet() to be the identity.

This function adds rules to this so that id is the identity. This function can be called repeatedly.

See also

set_identity(letter_type).

Complexity: \(O(n)\) where \(n\) is alphabet().size().

Parameters: id – a string containing the character to be the identity.
Throws: LibsemigroupsException – If id has length greater than 1, or id contains a character that is not in alphabet().
Returns: (None)

void libsemigroups::FpSemigroupInterface::set_inverses(std::string const &a)¶

Set the inverses of letters in alphabet().

The letter in a with index i is the inverse of the letter in alphabet() with index i.

See also

set_identity(std::string const&).

Complexity: \(O(n)\) where \(n\) is alphabet().size().

Parameters

a – a string of length alphabet().size().

Throws

LibsemigroupsException – if any of the following apply:

a is empty;
alphabet() is empty;
no identity has been defined using set_identity();
the length of a is not equal to alphabet().size();
the letters in a are not exactly those in alphabet() (perhaps in a different order).

Returns

(None)