Permutation

Permutations of indices or lattice sites. Basic building block of a PermutationGroup. Permutations can be multiplied, inverted and raised to a power.

Sources
permutation.hpp
permutation.cpp
permutation.jl

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Constructors

From an array

Creates an Permutation out of an array of integers, e.g. {0, 2, 1, 3}. If the input array is of size N then every number between 0 and N-1 must occur exactly once, otherwise the Permutation is invalid.

1-indexing in Julia / 0-indexing in C++

To enumerate the sites of a Permutation, we start counting at 1 in Julia and 0 in C++.

C++Julia

Permutation(std::initializer_list<int64_t> list);
Permutation(std::vector<int32_t> const &array);
Permutation(std::vector<int64_t> const &array);

Permutation(array::Vector{Int64})

Name	Description
array	array of integers, e.g.
list	initializer list of the permutation
ptr	pointer to memory as an array
size	size of the array

For identity

Constructs an identity permutation of a given size, e.g. {0, 1, 2, 3}.

C++Julia

Permutation(int64_t size);

Permutation(size::Int64)

Name	Description
size	size of the identity permutation

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Methods

inv

Computes the inverse permutation.

C++Julia

Permutation inv(Permutation const &p);

inv(perm::Permutation)::Permutation

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* operator

Concatenates two permutations by overloading the * operator.

C++Julia

Permutation operator*(Permutation const &p1, Permutation const &p2);

Base.:*(p1::Permutation, p2::Permutation)::Permutation

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^ operator, pow

Raises a permutation to an integer power.

C++Julia

Permutation pow(Permutation const &p, int64_t power);

Base.:^(p::Permutation, power::Int64)::Permutation

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size

Returns the size of a Permutation.

C++Julia

int64_t size(Permutation const &p);

size(p::Permutation)::Int64

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to_string (operator<<)

Converts the Permutation to a readable string representation.

C++Julia

std::string to_string(Permutation const &perm);
std::ostream &operator<<(std::ostream &out, Permutation const &perm);

to_string(perm::Permutation)::String

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Usage Example

C++Julia

Permutation p1 = {0, 2, 1, 3};
Permutation p2 = {2, 0, 1, 3};

XDIAG_SHOW(inv(p1));
XDIAG_SHOW(p1*p2);

p1 = Permutation([1, 3, 2, 4])
p2 = Permutation([3, 1, 2, 4])

@show inv(p1)
@show p1 * p2
@show p1 ^ 2