private void CheckPartitions(int n)
{
// Some sets to make sure partition and conjugate only appear once.
// Also tests equality, hash set.
HashSet <IntegerPartition> set = new HashSet <IntegerPartition>();
HashSet <IntegerPartition> conjugateSet = new HashSet <IntegerPartition>();
foreach (IntegerPartition partition in AdvancedIntegerMath.Partitions(n))
{
Assert.IsTrue(partition != null);
// Values should add to number.
int vCount = 0;
foreach (int v in partition.Values)
{
Assert.IsTrue(v > 0);
vCount += v;
}
Assert.IsTrue(vCount == n);
// Elements should add to number.
int eCount = 0;
foreach (Element e in partition.Elements)
{
Assert.IsTrue(e.Value > 0);
Assert.IsTrue(e.Multiplicity > 0);
eCount += e.Value * e.Multiplicity;
}
Assert.IsTrue(eCount == n);
// Partition should be generated only once
Assert.IsTrue(!set.Contains(partition));
set.Add(partition);
IntegerPartition conjugate = partition.Conjugate();
// Conjugate values should add to same number
int cCount = 0;
foreach (int c in conjugate.Values)
{
Assert.IsTrue(c > 0);
cCount += c;
}
Assert.IsTrue(cCount == n);
// Conujate should be generated only once
Assert.IsTrue(!conjugateSet.Contains(conjugate));
conjugateSet.Add(conjugate);
// Rank should fulfill inequality and be related to conjugate rank
Assert.IsTrue((-n < partition.Rank) && (partition.Rank < n));
Assert.IsTrue(conjugate.Rank == -partition.Rank);
// Double-conjugating should return us to the original
Assert.IsTrue(conjugate.Conjugate() == partition);
}
}
private long PartitionFunction(int n)
{
return(IntegerPartition.GetPartitions(n).LongCount());
}
