libsemigroups::bipartition Namespace Reference

This namespace contains helper functions for the Bipartition class.

Functions
Bipartition	one (Bipartition const &f)
	Return the identity bipartition with the same degree as the given bipartition.
void	throw_if_invalid (Bipartition const &x)
	Checks a bipartition.
std::vector< std::vector< int32_t > >	underlying_partition (Bipartition const &x)
	Return the underlying partition of a Bipartition object.

Function Documentation

one()

Bipartition one ( Bipartition const & f )

nodiscard

Parameters

f	the bipartition. Returns the identity bipartition of degree equal to f.degree().

The identity bipartition of degree \(n\) has blocks \(\{i, -i\}\) for all \(i\in \{0, \ldots, n - 1\}\). This member function returns a new identity bipartition of degree equal to the degree of this.

Returns

A newly constructed Bipartition.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

throw_if_invalid()

void throw_if_invalid

(

Bipartition const &

x

)

This function checks a Bipartition object, and throws an exception if the object is not valid.

Parameters

x	the bipartition.

Exceptions

LibsemigroupsException

if x is invalid.

underlying_partition()

std::vector< std::vector< int32_t > > underlying_partition ( Bipartition const & x )

nodiscard

The underlying partition of a bipartition x is the partition of a subset \(P\) of \(\{-n, \ldots, -1\}\cup \{1, \ldots, n\}\) such that:

• \(\{|x|\mid x\in P\} = \{1, \ldots, n\}\);
• a block of the partition consists of negative numbers if and only if the corresponding block of x is a transverse block.

Parameters

x	the bipartition.

Returns

A vector of vectors of integers.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Complexity

\(O(n)\) where \(n\) is the degree().