// Write the Cayley table
private void writeOperationTables()
{
Factors = DiscreteMath.PrimeFactors(graph.Order);
divisors = DiscreteMath.Divisors(graph.Order);
Stack <int> element = new Stack <int>();
op = new int[graph.Order, graph.Order];
inv = new int[graph.Order];
for (int i = 0; i < graph.Order; i++)
{
element = new Stack <int>();
int j = i, k;
while (tree.Item1[j] != -1)
{
k = tree.Item1[j];
j = graph.InEdges[j, k];
element.Push(k);
}
for (j = 0; j < graph.Order; j++)
{
k = j;
foreach (int g in element)
{
k = graph.OutEdges[k, g];
}
op[j, i] = k;
if (k == 0)
{
inv[j] = i;
}
}
}
}
private Dictionary <int, int[]> AbelianStructure()
{
Dictionary <int, int[]> structure = new Dictionary <int, int[]>();
int[] primes = DiscreteMath.PrimeFactors(group.Order).Distinct().ToArray();
foreach (int p in primes)
{
int k = group.POrderStats[p].Length;
if (k == 2)
{
// Elementary abelian
structure[p] = new int[] {
MathUtils.Multiplicity(group.POrderStats[p][1] + 1, p)
};
}
else if (group.POrderStats[p][k - 1] > 0)
{
// Cyclic
structure[p] = new int[k - 1];
structure[p][k - 2] = 1;
}
else
{
structure[p] = new int[k - 1];
int[] sums = new int[k];
int[] mults = new int[k + 1];
sums[0] = 1;
mults[0] = 0;
for (int i = 1; i < k; i++)
{
sums[i] = sums[i - 1] + group.POrderStats[p][i];
mults[i] = MathUtils.Multiplicity(sums[i], p);
}
mults[k] = mults[k - 1];
for (int i = 1; i < k - 1; i++)
{
structure[p][i - 1] = 2 * mults[i] - mults[i - 1] - mults[i + 1];
}
}
}
return(structure);
}