pair< ThLeftNormalForm , ThLeftNormalForm > ThLeftNormalForm::cycle( ) const
{
if( theDecomposition.empty( ) )
return pair< ThLeftNormalForm , ThLeftNormalForm >( *this , ThLeftNormalForm( theRank ) );
ThLeftNormalForm result = *this;
Permutation first = *(theDecomposition.begin( ));
if( theOmegaPower%2!=0 )
first = first.flip( );
result.theDecomposition.push_back( first );
result.theDecomposition.pop_front( );
result.adjust( );
return pair< ThLeftNormalForm , ThLeftNormalForm >( result , ThLeftNormalForm(first) );
}
pair< ThLeftNormalForm , ThLeftNormalForm > ThLeftNormalForm::decycle( ) const
{
if( theDecomposition.empty( ) )
return pair< ThLeftNormalForm , ThLeftNormalForm >( *this , ThLeftNormalForm( theRank ) );
ThLeftNormalForm result = *this;
Permutation last = *(--theDecomposition.end( ));
if( theOmegaPower%2==0 )
result.theDecomposition.push_front( last );
else
result.theDecomposition.push_front( last.flip( ) );
result.theDecomposition.pop_back( );
result.adjust( );
return pair< ThLeftNormalForm , ThLeftNormalForm >( result , -ThLeftNormalForm(last) );
}
Permutation ThLeftNormalForm::getPullback( const Permutation& s ) const
{
Permutation result;
Permutation Delta = Permutation::getHalfTwistPermutation( theRank );
Permutation B1 = *theDecomposition.begin( );
Permutation b1 = s;
if( theOmegaPower%2!=0 ) {
B1 = B1.flip( );
b1 = b1.flip( );
}
B1 = Delta * -B1;
Permutation b0 = -B1 * B1.LeftLCM( s.flip( ) );
for( list< Permutation >::const_iterator d_it=++theDecomposition.begin( ) ; d_it!=theDecomposition.end( ) ; ++d_it ) {
const Permutation& B = *d_it;
b1 = -B * B.LeftLCM( b1 );
}
return getSimpleSummitConjugator( b0.LeftLCM( b1 ) );
}
