coset.h

#pragma once
#include <iostream>
#include <ext.h>

class Coset;

#include "group.h"
#include "permutation.h"

// encodes a coset
class Coset {
	Group _G;
	Group _H;
	bool _right;
	Permutation _sigma;
public:
	// returns a shared reference to the group the coset is contained in, i.e. G in G/H
	Group supergroup() const;

	// returns a shared reference to the divisor group, i.e. H in G/H
	Group subgroup() const;

	// checks whether the coset is a right coset
	bool isRightCoset() const;

	// returns a reference to a representative of the coset
	const Permutation& representative() const;

	// checks whether cosets are equal
	bool operator==( const Coset& ) const;

	// constructs a coset
	Coset( Group G, Group H, Permutation sigma, bool right = true );
};

// prints the coset c to the output stream os
std::ostream& operator<<( std::ostream& os, const Coset& c );

// defines multiplication of permutations and cosets
Coset operator*( const Permutation& sigma, const Coset& tauH );

// encodes a set of isomorphisms, which is either a coset or empty
struct Iso : public Either<Coset,Empty> {
	// checks whether it is empty
	bool isEmpty() const;

	// returns the coset
	// WARNING: undefined behaviour if Iso is empty
	const Coset& coset() const;

	using Either::Either;
};

// defines multiplication of permutation and Iso sets
Iso operator*( const Permutation& sigma, const Iso& tauH );

// implements the union of cosets
class IsoJoiner {
	Group _supergroup;
	Group _subgroup;
	std::deque<Permutation> elements;
public:
	void join( Iso I );
	explicit operator Iso();
};