int main( )
{
FPGroup G;
cout << "Enter nilpotentcy class first then group ";
int NilpotentcyClass;
cin >> NilpotentcyClass;
Chars errMsg = cin >> G;
if (errMsg.length()>0)
return 1;
NilpotentGroup ng(G.namesOfGenerators(),
NilpotentcyClass,makeVectorOf(G.getRelators()));
ng.initialize();
VectorOf<Word> vw;
Word w;
for (int i=1;true;i++){
cout << endl << "Enter the "<<i<<" generator of subgroup"<< endl;
cout << "Empty word to finish: ";
w = G.readWord(cin,errMsg);
if (w.length()==0)
break;
if (errMsg.length()>0)
return 1;
vw.append(w);
}
SGOfNilpotentGroup sg(ng,vw);
sg.initBasis();
sg.printBasis(cout);
cout << "The Hirsch number :" << sg.theHirschNumber() << endl;
cout << "Index in parent group :" << sg.index() << endl;
cout << "Is Trivial :" << sg.isTrivial() << endl;
cout << "Is Central :" << sg.isCentral() << endl;
cout << "Is normal :" << sg.isNormal() << endl;
cout << "Is abelian :" << sg.isAbelian() << endl;
cout << "Subgroup class :" << sg.subgroupClass() << endl;
cout << "Generators of normal closure :" << endl;
vw = sg.normalClosureGens();
for (int i=0;i<vw.length();i++){
G.printWord(cout,vw[i]);
cout << endl;
}
PresentationForSNG sgp = sg.makePresentation();
cout << "Presentation of subgroup :" << endl;
sgp.print(cout);
cout << endl << "Enter the word :";
errMsg = "";
w = G.readWord(cin,errMsg);
if (errMsg.length()>0){
cout << errMsg;
return 1;
}
cout << endl << "Does subgroup contain the word :" << sg.contains(w) << endl;
PolyWord result;
if (sg.decompose(ng.decompose(w),result))
cout << "Decomposition in sg basis :" << sg.asDecomposition(result);
else
cout << "Subgroup does not contain this word";
}
VectorOf<Chars> PresentationParser::parseGeneratorList( Chars& errMesg )
{
VectorOf<Chars> result;
if ( curToken == INIT ) getToken();
while ( curToken == GENERATOR ) {
Chars name(tokenName);
// Check for duplication and presence of inverses.
if ( result.indexOf(name) >= 0 ) {
parseError("Duplicate generator");
errMesg = parseErrorMessage;
return result;
} else {
invertName(tokenName);
if ( result.indexOf(Chars(tokenName)) >= 0 ) {
parseError("Duplicate generator: formal inverse");
errMesg = parseErrorMessage;
return result;
}
}
result.append(name); // Ok, it's inefficient, but time is $$
getToken();
if ( curToken == COMMA ) {
getToken();
if ( curToken == DOT ) {
if (!getGeneratorRange(name,result,errMesg))
return result;
} else {
if ( curToken != GENERATOR ) {
parseError("Expected a generator here");
errMesg = parseErrorMessage;
return result;
}
}
}
}
return result;
}
//@njz:default value removed. defined in .h file
//void AbelianEquationsSolver::findSolutions( File& file , bool out = true )
void AbelianEquationsSolver::findSolutions( File& file , bool out)
//
{
haveSol = 0;
if( !A.haveCyclicDecomposition() )
A.computeCyclicDecomposition();
if( !A.havePrimaryDecomposition() )
A.findPrimaryBasis();
if( !rawA.haveCyclicDecomposition() )
rawA.computeCyclicDecomposition();
if( !rawA.havePrimaryDecomposition() )
rawA.findPrimaryBasis();
makeSystem();
if( out )
{
if( system.length() > 1 )
file << "The system of equations: " << endl << endl;
else
file << "The equation: " << endl << endl;
printRawSystem( file );
file << endl << "can be transformed to the one: " << endl << endl;
printSystem( file );
if( system.length() > 1 )
file << endl << "Finding solutions of this system ..." << endl << endl;
else
file << endl << "Finding solutions of this equation ..." << endl << endl;
}
//@njz
// int **matrix = new (int*)[ system.length() ];
int **matrix = new int*[ system.length() ];
//
int i,j,k,i1,j1;
for( i = 0 ; i < system.length() ; i++ )
{
matrix[i] = new int[ numberOfVariables ];
for( j = 0 ; j < numberOfVariables ; j++ )
{
Integer u = (AbelianWord( numberOfVariables , system[i] ))[j];
matrix[i][j] = u.as_long();
}
}
VectorOf< VectorOf<int> > transform;
VectorOf<int> trans(3);
// diagonalization of the matrix
sysRank = 0;
for( i = 0 ; ( i < numberOfVariables && i < system.length() ) ; i++ )
{
bool flag = false;
for( j = i ; j < system.length() ; j++ )
{
for( k = i ; k < numberOfVariables ; k++ )
if( matrix[j][k] )
{
flag = true;
break;
}
if( flag ) break;
}
if( k == numberOfVariables && j == system.length() )
{
if( sysRank )
break;
int q;
for( q = 0 ; q < b.length() ; q++ )
if( !A.isTrivial( Word( b[q] ) ) )
{
haveSol = -1;
if( out )
if( system.length() > 1 )
file << "while computing the canonical form of the system it was found that this system has no solutions." << endl;
else
file << "while computing the canonical form of the equation it was found that this equation has no solutions." << endl;
return;
}
haveSol = 0;
if( out )
if( system.length() > 1 )
file << "while computing the canonical form of the system it was found that this system has all group as a set of solutions." << endl;
else
file << "while computing the canonical form of the equation it was found that this equation has all group as a set of solutions." << endl;
return;
}
int *tmp = matrix[i];
matrix[i] = matrix[j];
matrix[j] = tmp;
Word r = b[i];
b[i] = b[j];
b[j] = r;
for( j = 0 ; j < system.length() ; j++ )
{
int t = matrix[j][i];
matrix[j][i] = matrix[j][k];
matrix[j][k] = t;
}
if( i != k )
{
trans[0] = i;
trans[1] = k;
trans[2] = 0;
transform.append( trans );
}
while( true )
{
bool check;
bool flag;
int z;
bool done = false;
int count = i + 1;
while( !done )
{
for( j = count ; j < system.length() ; j++ )
if( matrix[j][i] && abs(matrix[i][i]) != abs(matrix[j][i]) )
break;
if( j == system.length() )
break;
count = j + 1;
flag = false;
while( !flag )
{
if( abs(matrix[i][i]) > abs(matrix[j][i]) )
{
z = matrix[i][i] / matrix[j][i];
for( k = i ; k < numberOfVariables ; k++ )
matrix[i][k] = matrix[i][k] - matrix[j][k] * z;
b[i] = b[i] * A.getFPGroup().raiseToPower(b[j],-z);
}
else
{
z = matrix[j][i] / matrix[i][i];
for( k = i ; k < numberOfVariables ; k++ )
matrix[j][k] = matrix[j][k] - matrix[i][k] * z;
b[j] = b[j] * A.getFPGroup().raiseToPower(b[i],-z);
}
if( !matrix[i][i] || !matrix[j][i] )
{
if( matrix[i][i] == 0 )
{
tmp = matrix[i];
matrix[i] = matrix[j];
matrix[j] = tmp;
r = b[i];
b[i] = b[j];
b[j] = r;
}
flag = true;
}
}
if( count == system.length() )
done = true;
}
check = true;
for( j = i + 1 ; j < numberOfVariables ; j++ )
if( matrix[i][j] % matrix[i][i] )
{
check = false;
break;
}
if( check )
break;
done = false;
count = i + 1;
while( !done )
{
for( j = count ; j < numberOfVariables ; j++ )
if( matrix[i][j] && abs(matrix[i][i]) != abs(matrix[i][j]) )
break;
if( j == numberOfVariables )
break;
count = j + 1;
flag = false;
while( !flag )
{
if( abs(matrix[i][i]) > abs(matrix[i][j]) )
{
z = matrix[i][i] / matrix[i][j];
for( k = i ; k < system.length() ; k++ )
matrix[k][i] = matrix[k][i] - matrix[k][j] * z;
trans[0] = j;
trans[1] = i;
trans[2] = -z;
transform.append( trans );
}
else
{
z = matrix[i][j] / matrix[i][i];
for( k = i ; k < system.length() ; k++ )
matrix[k][j] = matrix[k][j] - matrix[k][i] * z;
trans[0] = i;
trans[1] = j;
trans[2] = -z;
transform.append( trans );
}
if( !matrix[i][i] || !matrix[i][j] )
{
if( matrix[i][i] == 0 )
{
for( k = i ; k < system.length() ; k++ )
{
int a = matrix[k][i];
matrix[k][i] = matrix[k][j];
matrix[k][j] = a;
}
if( i != j )
{
trans[0] = i;
trans[1] = j;
trans[2] = 0;
transform.append( trans );
}
}
flag = true;
}
}
if( count == numberOfVariables )
done = true;
}
check = true;
for( j = i + 1 ; j < system.length() ; j++ )
if( matrix[j][i] % matrix[i][i] )
{
check = false;
break;
}
if( check )
break;
}
for( j = i + 1 ; j < system.length() ; j++ )
if( matrix[j][i] )
{
int z = matrix[j][i] / matrix[i][i];
for( k = i ; k < numberOfVariables ; k++ )
matrix[j][k] = matrix[j][k] - matrix[i][k] * z;
b[j] = b[j] * A.getFPGroup().raiseToPower(b[i],-z);
}
for( j = i + 1 ; j < numberOfVariables ; j++ )
if( matrix[i][j] )
{
int z = matrix[i][j] / matrix[i][i];
for( k = i ; k < system.length() ; k++ )
matrix[k][j] = matrix[k][j] - matrix[k][i] * z;
trans[0] = i;
trans[1] = j;
trans[2] = -z;
transform.append( trans );
}
sysRank++;
}
for( i = sysRank ; i < system.length() ; i++ )
{
if( !A.isTrivial( Word( b[i] ) ) )
{
haveSol = -1;
if( out )
if( system.length() > 1 )
file << "while computing the canonical form of the system it was found that this system has no solutions." << endl;
else
file << "while computing the canonical form of the equation it was found that this equation has no solutions." << endl;
return;
}
}
// finding solutions and output in file
if( out )
{
file << "The canonical form: ";
file << endl << endl;
}
for( int p = 0 ; p < sysRank ; p++ )
{
if( out )
{
file << "x" << p + 1;
if( matrix[p][p] != 1 )
file << "^" << matrix[p][p];
file << " = ";
}
AbelianWord w = A.oldInAbelianForm( b[p] );
w = A.oldToNewGens( w );
w = A.newToOldGens( w );
b[p] = w.getWord().freelyReduce();
if( out )
{
A.getFPGroup().printWord( file , b[p] );
file << endl;
}
}
VectorOf<int> xNums( numberOfVariables );
for( i = 0 ; i < sysRank ; i++ )
if( root( b[i] , matrix[i][i] ) )
{
x[i] = b[i];
xNums[i] = i;
if( !A.isFree() )
{
VectorOf<int> tmp(2);
tmp[0] = ( matrix[i][i] > 0 ) ? matrix[i][i] : -matrix[i][i];
tmp[1] = 1;
torsion[i].append( tmp );
}
}
else
{
haveSol = -1;
if( out )
{
if( system.length() > 1 )
file << endl << "The system is unsolvable because there are no solutions for: " << endl << endl;
else
file << endl << "The equation is unsolvable because there are no solutions for: " << endl << endl;
file << "x" << i + 1;
if( matrix[i][i] != 1 )
file << "^" << matrix[i][i];
file << " = ";
A.getFPGroup().printWord( file , b[i].freelyReduce() );
}
return;
}
for( j = sysRank ; j < numberOfVariables ; j++ )
{
x[j] = Word();
xNums[j] = j;
VectorOf<int> tmp(2);
tmp[0] = j - sysRank + 1;
tmp[1] = 1;
params[j].append( tmp );
}
for( i = transform.length() - 1 ; i >= 0 ; i-- )
{
trans = transform[i];
if( !trans[2] )
{
int ind1 = xNums.indexOf( trans[0] );
int ind2 = xNums.indexOf( trans[1] );
xNums[ind1] = trans[1];
xNums[ind2] = trans[0];
}
else
{
int ind1 = xNums.indexOf( trans[0] );
int ind2 = xNums.indexOf( trans[1] );
x[ind1] *= A.getFPGroup().raiseToPower( x[ind2] , trans[2] );
int len = torsion[ind1].length();
for( j = 0 ; j < torsion[ind2].length() ; j++ )
{
bool f = false;
for( k = 0 ; k < len ; k++ )
if( torsion[ind1][k][0] == torsion[ind2][j][0] )
{
f = true;
break;
}
if( f )
torsion[ind1][k][1] += torsion[ind2][j][1] * trans[2];
else
{
VectorOf<int> tmp = torsion[ind2][j];
tmp[1] *= trans[2];
torsion[ind1].append( tmp );
}
}
len = params[ind1].length();
for( j = 0 ; j < params[ind2].length() ; j++ )
{
bool f = false;
for( k = 0 ; k < len ; k++ )
if( params[ind1][k][0] == params[ind2][j][0] )
{
f = true;
break;
}
if( f )
params[ind1][k][1] += params[ind2][j][1] * trans[2];
else
{
VectorOf<int> tmp = params[ind2][j];
tmp[1] *= trans[2];
params[ind1].append( tmp );
}
}
}
}
for( i = 0 ; i < x.length() ; i++ )
{
AbelianWord w = A.oldInAbelianForm( x[i] );
w = A.oldToNewGens( w );
w = A.newToOldGens( w );
x[i] = w.getWord();
}
// output in file
if( out )
{
file << endl << "The set of solutions can be presented as follows: " << endl << endl;
FPGroup G = rawA.getFPGroup();
FPGroup G1 = A.getFPGroup();
for( i = 0 ; i < numberOfVariables ; i++ )
{
int n = xNums.indexOf( i );
bool flag = false;
G.printWord( file , Generator( i + 1 ) );
file << " -> ";
if( x[n].length() )
{
G1.printWord( file , x[n].freelyReduce() );
flag = true;
}
for( j = 0 ; j < torsion[n].length() ; j++ )
{
VectorOf<int> tmp = torsion[n][j];
int z = tmp[1] % tmp[0];
if( z )
if( tmp[1] > 0 )
{
if( flag )
file << " + ";
if( tmp[1] != 1 )
file << tmp[1] << " p( " << tmp[0] << " )";
else
file << "p( " << tmp[0] << " )";
flag = true;
}
else
{
file << " - ";
if( tmp[1] != -1 )
file << -tmp[1] << " p( " << tmp[0] << " )";
else
file << "p( " << tmp[0] << " )";
flag = true;
}
}
for( j = 0 ; j < params[n].length() ; j++ )
{
VectorOf<int> tmp = params[n][j];
if( tmp[1] )
if( tmp[1] > 0 )
{
if( flag )
file << " + ";
if( tmp[1] != 1 )
file << tmp[1] << " t" << tmp[0];
else
file << "t" << tmp[0];
flag = true;
}
else
{
file << " - ";
if( tmp[1] != -1 )
file << -tmp[1] << " t" << tmp[0];
else
file << "t" << tmp[0];
flag = true;
}
}
if( !flag )
file << "1 ";
if( i != numberOfVariables )
file << ",";
file << endl;
}
file << endl << "where p( n ) is any element of n-heigth and t_i - any element of the group." << endl;
}
VectorOf< VectorOf< VectorOf<int> > > t( numberOfVariables );
VectorOf< VectorOf< VectorOf<int> > > p( numberOfVariables );
VectorOf<Word> x1( numberOfVariables );
for( i = 0 ; i < numberOfVariables ; i++ )
{
int n = xNums.indexOf( i );
x1[i] = x[n];
t[i] = torsion[n];
p[i] = params[n];
}
torsion = t;
params = p;
x = x1;
for( i = 0 ; i < system.length() ; i++ )
delete [] matrix[i];
delete [] matrix;
}
main()
{
FPGroup G;
VectorOf<int> order;
cin >> G;
char ch;
cin >> ch;
if (ch != '[') { cerr << "Unexpected input, aborted"<<endl; exit(1);}
do {
int i;
cin >> i;
order.append(i);
cin>> ch;
if (ch==']') break;
else if (ch!=','){ cerr << "Unexpected input, aborted"<<endl; exit(1);}
} while (ch==',');
WordOrder word_order("ShortLex",order);
KBmagPackage kbmag(G.namesOfGenerators(),G.getRelators(),word_order,20);
if ( !kbmag.sanityCheck() ) {
error("kbmag failed sanity check.\n");
}
if (kbmag.autgroup()==yes){
cout << "Group "<< G << " is proved shortlex automatic"<<endl;
GroupDFSA WA = kbmag.wordAcceptor();
WA.setName("Word_acceptor");
WA.printOn();
GenMult GM = kbmag.generalMultiplier();
GM.setName("General_multiplier");
GM.printOn();
DiffMachine D1 = kbmag.differenceMachine(1);
D1.setName("1stDiffMachine");
D1.printOn();
DiffMachine D2 = kbmag.differenceMachine(2);
D2.setName("2ndDiffMachine");
D2.printOn();
}
else
cout << "Group "<< G << " is not proved shortlex automatic"<<endl;
cout << endl;
FPGroup G2;
cin >> G2;
KBmagPackage kbmag2(G2.namesOfGenerators(),G2.getRelators());
if ( !kbmag2.sanityCheck() ) {
error("kbmag2 failed sanity check.\n");
}
if (kbmag2.kbprog()==yes && kbmag2.gpmakefsa()==yes && kbmag2.gpaxioms()==yes){
cout << "Group "<< G2 << " is proved shortlex automatic"<<endl;
GroupDFSA WA = kbmag2.wordAcceptor();
WA.setName("Word_acceptor");
WA.printOn();
GenMult GM = kbmag2.generalMultiplier();
GM.setName("General_multiplier");
GM.printOn();
DiffMachine D1 = kbmag2.differenceMachine(1);
D1.setName("1stDiffMachine");
D1.printOn();
DiffMachine D2 = kbmag2.differenceMachine(2);
D2.setName("2ndDiffMachine");
D2.printOn();
}
else
cout << "Group "<< G2 << " is not proved shortlex automatic"<<endl;
cout << endl;
FPGroup G3;
cin >> G3;
KBmagPackage kbmag3(G3.namesOfGenerators(),G3.getRelators());
if ( !kbmag3.sanityCheck() ) {
error("kbmag3 failed sanity check.\n");
}
if (kbmag3.kbprog()>0){
Bool abort=NO;
int loop=0;
do {
loop++;
cout << "Trying to built automata."<< endl;
if (loop>1) cout << "Pass no. " << loop <<" though loop."<< endl;
if (kbmag3.gpwa()!=yes || kbmag3.gpgenmult()!=yes) abort=YES;
if (abort){ cout << "Failed, giving up!"<< endl; break;}
GroupDFSA WA = kbmag3.wordAcceptor();
WA.setName("Word_acceptor");
WA.printOn();
GenMult GM = kbmag3.generalMultiplier();
GM.setName("GeneralMultiplier");
GM.printOn();
DiffMachine D1 = kbmag3.differenceMachine(1);
D1.setName("1stDiffMachine");
D1.printOn();
DiffMachineRep D2 = kbmag3.differenceMachineRep(2);
D2.setName("2ndDiffMachine");
D2.printOn();
} while (kbmag3.gpcheckmult()==no);
if (abort==NO && kbmag3.gpaxioms()==yes)
cout << "Group "<< G3 << " is proved shortlex automatic"<<endl;
else
cout << "Group "<< G3 << " is not proved shortlex automatic"<<endl;
}
GroupDFSARep WA2 = kbmag3.wordAcceptorRep();
DiffMachineRep D3 = kbmag3.differenceMachineRep(2);
KBmagPackage kbmag4(G3.namesOfGenerators(),G3.getRelators());
kbmag4.setWordAcceptor(WA2);
kbmag4.setDifferenceMachine(D3,2);
kbmag4.gpgenmult();
DFSA F;
F.readFrom();
kbmag4.minimize(F);
F.printOn();
GroupDFSARep F2;
F2.readFrom();
kbmag4.minimize(F2);
F2.printOn();
GroupDFSA M1;
M1.readFrom();
GroupDFSA M2;
M2.readFrom();
GroupDFSA M3;
kbmag4.gpcomp(M1,M2,M3);
M3.printOn();
GroupDFSARep N1;
N1.readFrom();
GroupDFSARep N2;
N2.readFrom();
GroupDFSARep N3;
kbmag4.gpcomp(N1,N2,N3);
N3.printOn();
}
