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// Copyright (C) 1994 The New York Group Theory Cooperative
// See magnus/doc/COPYRIGHT for the full notice.
// Contents: Definition of the FreeGroupRep class.
//
// Principal Authors: Stephane Collart, Roger Needham
//
// Status: in progress
//
// Revision History:
//
#ifndef _FREE_GROUP_REP_H_
#define _FREE_GROUP_REP_H_
#include "FGGroupRep.h"
#include "File.h"
struct FreeGroupRep : FGGroupRep {
public:
// Constructors:
// Copy constructor and operator= provided by compiler (do deep copy).
FreeGroupRep( int rank ) : FGGroupRep( rank ) { }
FreeGroupRep( const VectorOf<Chars>& gennames ) :
FGGroupRep( gennames ) { }
// Destructor provided by compiler.
// Operators:
private:
FreeGroupRep& operator = ( const FreeGroupRep& fgr ); // disable assignment
public:
// Representation methods:
PureRep* clone( ) const { return new FreeGroupRep(*this); }
// overrides PureRep* FGGroupRep::clone();
static const Type theFreeGroupType;
static Type type( ) { return theFreeGroupType; }
// dominates FGGroup::type()
Type actualType( ) const { return type(); }
// overrides FGGroup::actualType()
// Group structure methods:
int order( ) const;
// overrides int FGGroupRep::order() const;
Trichotomy isTrivial( ) const;
// overrides int FGGroupRep::isTrivial() const;
Trichotomy isFinite( ) const;
// overrides int FGGroupRep::isFinite() const;
Trichotomy isInfinite( ) const;
// overrides int FGGroupRep::isInfinite() const;
Trichotomy isAbelian( ) const;
// overrides int FGGroupRep::isAbelian() const;
bool compare( const GroupRep* G ) const;
// overrides int FGGroupRep::compare() const;
VectorOf<Word> nielsenBasis(const VectorOf<Word>& V) const;
// Returns a nielsen basis for the subgroup generated by `V'.
Bool isAutomorphism(const VectorOf<Word>& V) const;
// Returns TRUE iff generating vector `V' defines an
// automorphism of this group. The length of `V' should be
// equal to the rank of this group.
Bool isInnerAutomorphism(const VectorOf<Word>& V) const;
// Returns TRUE iff generating vector `V' defines an inner
// automorphism of this group. The length of `V' should be
// equal to the rank of this group and it should define an
// automorphism.
bool isIAAutomorphism(const VectorOf<Word>& V) const;
// Returns `true' iff generating vector `V' defines an
// IA-automorphism of this group. The length of `V' should be
// equal to the rank of this group and it should define an
// automorphism.
VectorOf<Word> inverseAutomorphism(const VectorOf<Word>& V) const;
// Returns a generating vector for the inverse automorphism.
// `V' should define an automorphism of this group.
// Methods dealing with group elements:
// Inhertited from FGGroupRep:
// virtual Elt makeIdentity( ) const;
// virtual Bool isSyntacticIdentity(const Elt&) const;
Trichotomy isTrivialElt( const Elt& e ) const
{ return Trichotomy( eval(e) == Word() ); }
// overrides FGGroupRep::isTrivialElt()
Elt eval( const Word& w ) const;
// overrides
Trichotomy areEqual(const Elt& e1, const Elt& e2) const;
// overrides
Trichotomy wordProblem( const Word& w ) const;
// overrides
Trichotomy conjugacyProblem( const Word& u, const Word& v ) const;
// overrides
Trichotomy conjugacyProblem( const Word& u, const Word& v ,Word& c) const;
Bool inCommutatorSG(const Word& w) const;
// Returns TRUE iff `w' is in the commutator subgroup.
Bool isCommutator(const Word& w, Word& u1, Word& u2) const;
// Returns TRUE iff `w' is a commutator. If TRUE, `u1' and `u2'
// are set to words such that w = [u1,u2].
Chars productOfCommutators( const Word& w , File& file );
// If the word is in derived subgroup this procedure rewrites the
// word as a product of commutators.
Chars productOfSquares( const Word& w , File& file );
// If the word is in the subgroup generated by all squares this procedure
// rewrites it as a product of squares.
Word getN_thElement( int n ) const;
int numberOfElement( const Word& w ) const;
// I/O:
void printOn(ostream&) const;
// overrides void FGGroupRep::printOn() const;
GroupRep* readFrom(istream&, Chars&) const;
// overrides FGGroupRep::
public:
class NielsenBasis {
public:
NielsenBasis( const VectorOf<Word>& vec,
const VectorOf<Chars>& namesOfGenerators,
bool writeToFile );
// Copy ctor, operator= and dtor supplied by compiler.
VectorOf<Word> oldGenerators( ) const { return theOldGenerators; }
VectorOf<Word> newGenerators( );
VectorOf<Word> expressNewGensInOldGens( );
Chars getFileName( ) const;
private:
void computeNielsenBasis( );
void printParentGroup( ostream& ostr ) const;
void printWord( ostream& ostr, const Word& w ) const;
void printBasis( ostream& ostr, const VectorOf<Word>& basis, bool lineByLine ) const;
void printTransformation( ostream& ostr, const VectorOf<Word>& basis,
int i, int g1, int g2 ) const;
// Data members:
VectorOf<Chars> theNamesOfGenerators;
VectorOf<Word> theOldGenerators;
VectorOf<Word> theNewGenerators;
VectorOf<Word> newGeneratorsExprssedInOldGerators;
Chars theFileName;
bool keepDetails;
bool basisComputed;
};
// No new data members.
private:
// getN_thElement()'s accessories:
Word getN_thWord( int n, int numberOfGenerators ) const;
Generator numToGen( int n ) const;
int genToNum( Generator g ) const;
};
#endif
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