NTPSemiring< Scalar >

template<typename Scalar = size_t>
class libsemigroups::NTPSemiring< Scalar >

Defined in matrix.hpp.

This class represents the ntp semiring consists of the integers \(\{0, 1, ..., t, t + 1, ..., t + p - 1\}\) for some \(t\) and \(p\) (called the threshold and period). Instances of this class can be used to define the value of the threshold \(t\) and period \(p\) at run time.

Template Parameters

Scalar

the type of the elements of the semiring.

Public Member Functions
	NTPSemiring ()=delete
	Deleted default constructor.
	NTPSemiring (NTPSemiring &&)=default
	Default move constructor.
	NTPSemiring (NTPSemiring const &)=default
	Default copy constructor.
	NTPSemiring (Scalar t, Scalar p)
	Construct from threshold and period.
NTPSemiring &	operator= (NTPSemiring &&)=default
	Default move assignment operator.
NTPSemiring &	operator= (NTPSemiring const &)=default
	Default copy assignment operator.
Scalar	period () const noexcept
	Get the period.
Scalar	plus_no_checks (Scalar x, Scalar y) const noexcept
	Addition in an ntp semiring.
Scalar	product_no_checks (Scalar x, Scalar y) const noexcept
	Multiplication in an ntp semiring.
Scalar	threshold () const noexcept
	Get the threshold.

Static Public Member Functions
static constexpr Scalar	scalar_one () noexcept
	Get the multiplicative identity.
static constexpr Scalar	scalar_zero () noexcept
	Get the additive identity.

Constructor & Destructor Documentation

NTPSemiring() [1/4]

template<typename Scalar = size_t>

NTPSemiring ( )

delete

Deleted default constructor.

NTPSemiring() [2/4]

template<typename Scalar = size_t>

NTPSemiring ( NTPSemiring< Scalar > const & )

default

Default copy constructor.

NTPSemiring() [3/4]

template<typename Scalar = size_t>

NTPSemiring ( NTPSemiring< Scalar > && )

default

Default move constructor.

NTPSemiring() [4/4]

template<typename Scalar = size_t>

NTPSemiring ( Scalar t, Scalar p )

inline

Construct from threshold and period.

Parameters

t	the threshold ( \(t \geq 0\)).
p	the period ( \(p > 0\)).

Exceptions

LibsemigroupsException	if t is less than zero.
LibsemigroupsException	if p is less than or equal to zero.

Complexity

Constant.

Member Function Documentation

operator=() [1/2]

template<typename Scalar = size_t>

NTPSemiring & operator= ( NTPSemiring< Scalar > && )

default

Default move assignment operator.

operator=() [2/2]

template<typename Scalar = size_t>

NTPSemiring & operator= ( NTPSemiring< Scalar > const & )

default

Default copy assignment operator.

period()

template<typename Scalar = size_t>

Scalar period ( ) const

inlinenoexcept

Returns the period value used to construct NTPSemiring instance.

Returns

A value of type Scalar.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

plus_no_checks()

template<typename Scalar = size_t>

Scalar plus_no_checks ( Scalar x, Scalar y ) const

inlinenoexcept

This function returns \(x \oplus y\) which is defined by

\[ x\oplus y = \begin{cases} x + y & \text{if } x + y \leq t \\ \mbox{} t + ((x + y - t) \pmod{p}) & \text{if } x + y > t \end{cases} \]

where \(t\) is the threshold and \(p\) is the period; representing multiplication in the quotient of the semiring of natural numbers.

Parameters

x	scalar ( \(0\leq x < t + p\)).
y	scalar ( \(0\leq y < t + p\)).

Returns

A value of type Scalar.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

product_no_checks()

template<typename Scalar = size_t>

Scalar product_no_checks ( Scalar x, Scalar y ) const

inlinenoexcept

This function returns \(x \otimes y\) which is defined by

\[ x\otimes y = \begin{cases} xy & \text{if } xy \leq t \\ \mbox{} t + ((xy - t)\pmod{p}) & \text{if } xy > t \end{cases} \]

where \(t\) is the threshold and \(p\) is the period; representing multiplication in the quotient of the semiring of natural numbers.

Parameters

x	scalar (0 <= x < threshold() + period()).
y	scalar (0 <= y < threshold() + period()).

Returns

A value of type Scalar.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

scalar_one()

template<typename Scalar = size_t>

static constexpr Scalar scalar_one ( )

inlinestaticconstexprnoexcept

This function returns \(1\); representing the multiplicative identity of the quotient of the semiring of natural numbers.

Returns

The multiplicative identity in an ntp semiring (the value 0).

Exceptions

This function is noexcept and is guaranteed never to throw.

scalar_zero()

template<typename Scalar = size_t>

static constexpr Scalar scalar_zero ( )

inlinestaticconstexprnoexcept

This function returns \(0\) representing the additive identity of the quotient of the semiring of natural numbers.

Returns

A value of type Scalar.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

threshold()

template<typename Scalar = size_t>

Scalar threshold ( ) const

inlinenoexcept

Returns the threshold value used to construct NTPSemiring instance.

Returns

A value of type Scalar.

Exceptions

This function is noexcept and is guaranteed never to throw.

Complexity

Constant.

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The documentation for this class was generated from the following file:

• /Users/jdm/libsemigroups/include/libsemigroups/matrix.hpp