/**
* Merges pairs of rows by making them identical and marking them as equivalent. For each merged
* pair, also merges each pair of not yet merged images by the same generator, and so on
* recursively, until no more pairs need to be merged.
*
* @param Q a list of row pairs to merge.
* @param P the row equivalence classes (modified by this method).
* @return the number of individual merges performed.
*/
private int performIdentifications(final LinkedList Q, final IntPartition P) {
int count = 0;
while (Q.size() > 0) {
final IntPair pair = (IntPair) Q.removeFirst();
final int a = P.find(pair.getFirst());
final int b = P.find(pair.getSecond());
if (a == b) {
continue;
}
P.unite(a, b);
++count;
final int row_a[] = (int[]) this.table.get(a);
final int row_b[] = (int[]) this.table.get(b);
for (int g = 0; g < this.ngens; ++g) {
final int ag = row_a[g];
final int bg = row_b[g];
if (ag == 0) {
row_a[g] = bg;
} else if (bg == 0) {
row_b[g] = ag;
} else if (!P.areEquivalent(ag, bg)) {
Q.addLast(new IntPair(ag, bg));
}
}
this.table.set(b, row_a);
}
return count;
}
/**
* Compresses the table by collapsing each set of rows tagged as equivalent, i.e., representing
* the same coset, into a single row. At this stage, equivalent rows are expected to have equal
* contents, as should have been established by {@link #performIdentifications(LinkedList,
* IntPartition)}.
*
* @param P a partition of the row set into equivalence classes.
* @return a mapping of old to new row numbers.
*/
private int[] compressTable(final IntPartition P) {
// --- initialize the mapping from old to new row numbers
final int old2new[] = new int[this.table.size()];
// --- initlalize the new coset table
final LinkedList newTable = new LinkedList();
// --- the row with number 0 is not used
newTable.add(this.table.get(0));
// --- collect the rows for the new table and establish the mapping
for (int i = 1; i < this.table.size(); ++i) {
// --- get the representative for i's equivalence class
final int ri = P.find(i);
// --- use only the first row in each equivalence class
if (old2new[ri] == 0) {
old2new[ri] = newTable.size();
newTable.add(this.table.get(ri));
}
// --- map i to the same row number as its representative
old2new[i] = old2new[ri];
}
// --- copy the new table into the old one
this.table.clear();
while (newTable.size() > 0) {
this.table.add(newTable.removeFirst());
}
// --- finally, translate all entries into the new numbering scheme
for (int i = 1; i < this.table.size(); ++i) {
final int row[] = (int[]) this.table.get(i);
for (int j = 0; j < this.ngens; ++j) {
row[j] = old2new[row[j]];
}
}
// --- return the mapping from old to new row numbers
return old2new;
}
/**
* Constructs a CosetTable instance with a limit on the number of table rows that may be present
* at any stage of the construction process. Note that this number may be much higher than the
* actual number of cosets, because multiple rows may be found correspond to a single coset long
* after their construction.
*
* @param group the group.
* @param subgroupGenerators generators of the subgroup.
* @param sizeLimit the limit on the number of coset rows.
*/
public CosetAction(final FpGroup group, final List subgroupGenerators, final int sizeLimit) {
// --- copy parameters to fields
this.group = group;
this.subgroupGenerators = Collections.unmodifiableList(subgroupGenerators);
this.sizeLimit = sizeLimit;
// --- extract generators and relators for group
final List groupGenerators = group.getGenerators();
final List groupRelators = group.getRelators();
// --- set up translation tables
this.ngens = 2 * groupGenerators.size();
this.idx2gen = new FreeWord[this.ngens];
this.gen2idx = new HashMap();
this.idx2invidx = new int[this.ngens];
int nu = 0;
for (Iterator iter = groupGenerators.iterator(); iter.hasNext(); ) {
final FreeWord g = (FreeWord) iter.next();
this.idx2gen[nu] = g;
this.gen2idx.put(g, new Integer(nu));
this.idx2gen[nu + 1] = g.inverse();
this.gen2idx.put(g.inverse(), new Integer(nu + 1));
this.idx2invidx[nu] = nu + 1;
this.idx2invidx[nu + 1] = nu;
nu += 2;
}
// --- translate relators
final List rels = new ArrayList();
for (Iterator iter = groupRelators.iterator(); iter.hasNext(); ) {
final FreeWord r = (FreeWord) iter.next();
final int n = r.length();
for (int i = 0; i < n; ++i) {
final FreeWord w = r.subword(i, n).times(r.subword(0, i));
rels.add(translateWord(w));
rels.add(translateWord(w.inverse()));
}
}
// --- translate subgroup generators
final List subgens = new ArrayList();
for (Iterator iter = subgroupGenerators.iterator(); iter.hasNext(); ) {
final FreeWord generator = (FreeWord) iter.next();
subgens.add(translateWord(generator));
subgens.add(translateWord(generator.inverse()));
}
// --- set up a coset table with one dummy row and one row for the trivial coset
this.table = new ArrayList();
this.table.add(new int[this.ngens]);
this.table.add(new int[this.ngens]);
// --- holds classes of rows known to correspond to the same coset
IntPartition equivalences = new IntPartition();
// --- number of rows made invalid but not yet deleted
int invalidRows = 0;
// --- scan the table row by row, creating and deleting rows on the fly
int i = 1;
while (i < this.table.size()) {
// --- proceed only if the current row is valid
if (equivalences.find(i) != i) {
++i;
continue;
}
// --- scan the current row
final int row[] = (int[]) this.table.get(i);
for (int j = 0; j < this.ngens; ++j) {
// --- proceed only if the current column is empty
if (row[j] != 0) {
continue;
}
// --- log the result of this construction step
if (LOGGING) {
System.out.println("\ni = " + i + ", j = " + j);
}
// --- make a new row for the product with g
final int newRow[] = new int[this.ngens];
this.table.add(newRow);
// --- set the correspondences
final int n = this.table.size();
row[j] = n - 1;
newRow[this.idx2invidx[j]] = i;
if (LOGGING) {
System.out.println("after setting item:");
dumpTable();
}
// --- scan relations to identify equivalent rows
final LinkedList identify = new LinkedList();
for (Iterator iter = rels.iterator(); iter.hasNext(); ) {
final int rel[] = (int[]) iter.next();
scanRelation(rel, n - 1, identify);
}
// --- scan subgroup generators
final int one = equivalences.find(1);
for (Iterator iter = subgens.iterator(); iter.hasNext(); ) {
final int gen[] = (int[]) iter.next();
scanRelation(gen, one, identify);
}
if (LOGGING) {
System.out.println("after scanning:");
dumpTable();
}
// --- perform pending identifications
invalidRows += performIdentifications(identify, equivalences);
if (LOGGING) {
System.out.println("after identifying:");
dumpTable();
}
// --- quit if the limit on the number of rows is reached
if (this.sizeLimit > 0 && n - invalidRows > this.sizeLimit) {
throw new RuntimeException("table limit reached");
}
// --- compress the table if necessary
if (invalidRows > n / 2) {
final int old2new[] = compressTable(equivalences);
equivalences = new IntPartition();
i = old2new[i];
invalidRows = 0;
if (LOGGING) {
System.out.println("after compressing:");
dumpTable();
}
}
}
// --- look at next row
++i;
}
// --- make a final cleanup
compressTable(equivalences);
if (LOGGING) {
System.out.println("\nAfter final compression:");
dumpTable();
}
// --- some finishing touches
this.numberOfCosets = this.table.size() - 1;
this.cosetRepresentatives = computeCosetRepresentatives();
}
