Transf< N, Scalar >

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

Defined in transf.hpp.

A transformation \(f\) is just a function defined on the whole of \(\{0, 1, \ldots, n - 1\}\) for some integer \(n\) called the degree of \(f\). A transformation is stored as a container of the images of \(\{0, 1, \ldots, n - 1\}\), i.e. \(((0)f, (1)f, \ldots, (n - 1)f)\).

If N is 0 (the default), then the degree of a Transf 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).

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

Inheritance diagram for Transf< N, Scalar >:

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
void	product_inplace (Transf const &f, Transf const &g)
	Multiply two transformations and store the product in this.

Static Public Member Functions
static Transf	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.

Member Function Documentation

one()

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

static Transf 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	(	Transf< N, Scalar > const &	f,
		Transf< N, Scalar > const &	g )

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

Parameters

f	a transformation.
g	a transformation.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

Linear in the degree of the transformation.

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.

See also

degree

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

• /home/joseph/Dev/Comp_Maths/testing/libsemigroups/include/libsemigroups/transf.hpp