PPerm< N, Scalar >

template<size_t N = 0, typename Scalar = std::conditional_t<N == 0, uint32_t, typename SmallestInteger<N>::type>>
class libsemigroups::PPerm< N, Scalar >

Defined in transf.hpp.

A partial permutation \(f\) is just an injective partial transformation, which is stored as a container of the images of \(\{0, 1, \ldots, n - 1\}\), i.e. \(((0)f, (1)f, \ldots, (n - 1)f)\) where the value UNDEFINED is used to indicate that \((i)f\) is undefined (i.e. not among the points where \(f\) is defined).

If N is 0 (the default), then the degree of a PPerm instance can be defined at runtime, and if N is not 0, then the degree is fixed at compile time.

If N is 0, then the default value of Scalar is uint32_t. If N is not 0, then the default value of Scalar is the smallest integer type able to hold N. See also SmallestInteger.

Template Parameters

N	the degree (default: 0).
Scalar	an unsigned integer type (the type of the image values) (default: uint32_t).

This class inherits from either StaticPTransf or DynamicPTransf, see the documentation of these classes for more details of the available member functions.

Public Types
using	container_type = typename base_type::container_type
	Type of the underlying container.
using	point_type = Scalar
	Type of the image values.

Public Member Functions
	PPerm (std::initializer_list< point_type > dom, std::initializer_list< point_type > img, size_t M)
	Construct from domain, range, and degree.
template<typename OtherScalar>
	PPerm (std::vector< OtherScalar > const &dom, std::vector< OtherScalar > const &img, size_t M)
	Construct from domain, range, and degree.
void	product_inplace (PPerm const &f, PPerm const &g)
	Multiply two partial perms and store the product in this.

Static Public Member Functions
static PPerm	one (size_t M)
	Returns the identity transformation on the given number of points.

Member Typedef Documentation

container_type

template<size_t N = 0, typename Scalar = std::conditional_t<N == 0, uint32_t, typename SmallestInteger<N>::type>>

using container_type = typename base_type::container_type

In this case, this is PTransf<N, Scalar>::container_type.

point_type

template<size_t N = 0, typename Scalar = std::conditional_t<N == 0, uint32_t, typename SmallestInteger<N>::type>>

using point_type = Scalar

Also the template parameter Scalar.

Constructor & Destructor Documentation

PPerm() [1/2]

template<size_t N = 0, typename Scalar = std::conditional_t<N == 0, uint32_t, typename SmallestInteger<N>::type>>

template<typename OtherScalar>

PPerm	(	std::vector< OtherScalar > const &	dom,
		std::vector< OtherScalar > const &	img,
		size_t	M )

Constructs a partial perm of degree M such that f[dom[i]] = img[i] for all i and which is UNDEFINED on every other value in the range \([0, M)\).

Template Parameters

OtherScalar

the type of the points in dom and img.

Parameters

dom	the domain.
img	the range.
M	the degree.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in the size of dom.

Warning

No checks whatsoever are performed on the validity of the arguments.

PPerm() [2/2]

template<size_t N = 0, typename Scalar = std::conditional_t<N == 0, uint32_t, typename SmallestInteger<N>::type>>

PPerm ( std::initializer_list< point_type > dom, std::initializer_list< point_type > img, size_t M )

inline

Constructs a partial perm of degree M such that f[dom[i]] = img[i] for all i and which is UNDEFINED on every other value in the range \([0, M)\).

Template Parameters

OtherScalar

the type of the points in dom and img.

Parameters

dom	the domain.
img	the range.
M	the degree.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in the size of dom.

Warning

No checks whatsoever are performed on the validity of the arguments.

Member Function Documentation

one()

template<size_t N = 0, typename Scalar = std::conditional_t<N == 0, uint32_t, typename SmallestInteger<N>::type>>

static PPerm one ( size_t M )

inlinestaticnodiscard

This function returns a newly constructed transformation with degree equal to M that fixes every value from 0 to M.

Parameters

M	the degree.

Returns

A value of type Transf.

Exceptions

LibsemigroupsException

if IsStatic<Transf> is true, and M is not the same as the template parameter N.

product_inplace()

template<size_t N = 0, typename Scalar = std::conditional_t<N == 0, uint32_t, typename SmallestInteger<N>::type>>

void product_inplace	(	PPerm< N, Scalar > const &	f,
		PPerm< N, Scalar > const &	g )

Replaces the contents of this by the product of f and g.

Parameters

f	a partial perm.
g	a partial perm.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in degree of f or g.

Warning

No checks are made on whether or not the parameters are compatible. If f and g have different degrees, then bad things will happen.

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

• /Users/jdm3/libsemigroups/include/libsemigroups/transf.hpp