Word FPGroup::randomIdentity_Classic( int length , float conj_param ) const
{
if( theRelators.size( )==0 )
return Word();
int ngens = numberOfGenerators( );
int nrels = theRelators.size( );
Word result;
while( result.length()<length ) {
while( result.length()<length ) {
// generate conjugator
int conj_length = 0;
for( ; RandLib::ur.rand()<conj_param ; ++conj_length );
Word conjugator = Word::randomWord( numOfGenerators , conj_length );
Word rel( theRelators[RandLib::ur.irand( 0 , theRelators.size( )-1 )] );
rel = ( RandLib::ur.irand( 0 , 1 )==0 ? rel : rel.inverse( ) );
rel.cyclicallyPermute( RandLib::ur.irand( 0 , rel.length( )-1 ) );
result *= -conjugator * rel * conjugator;
}
}
return result;
}
void AbelianWordRep::printOn( ostream& ostr ) const
{
ostr << "[";
for( int i = 0; i < numberOfGenerators(); ++i )
ostr << " " << i+1 << "^" << thePowers[i];
ostr << " ]";
}
Word FPGroup::randomIdentity_Stack( int length ) const
{
if( theRelators.size( )==0 )
return Word();
// 1. Construct a set of rules
int ngens = numberOfGenerators( );
int nrels = theRelators.size( );
vector< pair< Word , Word > > rules;
for( int r=0 ; r<nrels ; ++r ) {
Word rel = theRelators[r];
for( int l=0 ; l<rel.length() ; ++l ) {
rel = rel.cyclicallyPermute( 1 );
for( int p=0 ; p<=rel.length() ; ++p ) {
Word left = rel.initialSegment( p );
Word right = rel.terminalSegment( p );
rules.push_back( pair< Word , Word >( left , right ) );
rules.push_back( pair< Word , Word >( -left , -right ) );
}
}
}
for( int i=0 ; i<ngens ; ++i ) {
rules.push_back( pair< Word , Word >( Generator( i+1 ) , Generator( -i-1 ) ) );
rules.push_back( pair< Word , Word >( Generator(-i-1 ) , Generator( i+1 ) ) );
}
int rule_num = rules.size( );
// 2. Construct a word using the rules
Word result;
while( result.length() < length ) {
while( result.length() < length ) {
int rn = RandLib::ur.irand( 0 , rule_num-1 );
result = rules[rn].first * result * rules[rn].second;
}
}
return result;
}
